Germán Sierra

Germán Sierra is a Spanish theoretical physicist, author, and academic. He is Professor of Research at the Institute of Theoretical Physics Autonomous University of Madrid-Spanish National Research Council.[1]

Germán Sierra
Born (1955-05-13) May 13, 1955
Caracas (Venezuela)
NationalitySpanish
Occupation(s)theoretical physicist, author, and academic
Academic background
EducationBS in Physics
PhD in Physics
Alma materComplutense de Madrid, Spain
Thesis (1981)
Academic work
InstitutionsSpanish National Research Council (CSIC)

Sierra's research interests span the field of physics and mathematical physics, focusing particularly on condensed matter physics, conformal field theory, exactly solved models, quantum information and computation and number theory. He has authored two books entitled, Quantum Groups in Two-dimensional Physics and Quantum electron liquids and hight-Tc Superconductivity[2] and also has published over 200 articles.[3]

Sierra serves as an Editor of the Journal of Statistical Mechanics: Theory and Experiment,[4] Journal of High Energy Physics[5] and Nuclear Physics B.[6]

Education

Sierra earned his Baccalaureate degree in physics from the University of Complutense de Madrid in 1978, followed by a Ph.D. in physics from the same university in 1981. He then completed his Postdoc from the l’École Normale Supérieure in Paris in 1983.[1]

Career

Following his Postdoc, Sierra began his academic career as a Titular Professor at the University of Complutense de Madrid in 1984, a position he held for three years. In 1987 he was appointed as a research fellow at the European Council for Nuclear Research (CERN) in Geneva and as a Scientific Researcher at Spanish National Research Council in 1989. Since 2005, he has been serving as a Full Professor of Physics at the Spanish National Research Council in Spain.[7] He has held visiting appointments at Erwin Schrödinger Institute,[8] Kavli Institute for Theoretical Physics,[9] Max Planck Institute for Quantum Optics,[10] University of Sao Paulo,[11] Princeton University,[12] Isaac Newton Institute for Mathematical Sciences,[13] Stony Brook University,[14] and University of Innsbruck[15]

From 2014 to 2017, he was a Member of the International Union of Pure and Applied Physics (IUPAP), Panel C18 on Mathematical Physics.[16]

Research

Sierra's research focuses on quantum physics with a particular emphasis on supergravity, quantum groups, quantum many body systems, integrable models. His research has contributed to the understanding of supergravity theories, conformal field theory,[17] superconductivity[18] spin chains and ladders,[19] Richardson-Gaudin model,[20] physical models of the Riemann Zeros,[21] quantum Hall states,[22] inhomogeneous spin chains,[23] infinite matrix product states,[24] The Prime State,[25] quantum computation, and quantum games.[26]

Supergravity

During his early research career, Sierra worked in the area of supergravity to construct and classify the N = 2 Maxwell-Einstein Supergravity theories (MESGT).[27] His work involved an investigation of the algebraic and geometric structures underlying these theories, as well as their compact and non-compact gaugings.[28] In collaboration with M. Gunaydin and P.K. Townsend, he derived the magic square of Freudenthal, Rozenfeld, and Tits by utilizing the geometric principles found in a specific group of N=2 Maxwell-Einstein supergravity theories.[29]

Quantum groups

In 1990, Sierra's research diverted toward the construction, interpretation, and application of quantum groups[30] in the context of conformal field theories,[31] two-dimensional physics,[32] and renormalization groups.[33] He demonstrated that the representation theory of the q-deformation of SU(2) offers solutions to the polynomial equations formulated by Moore and Seiberg for rational conformal field theories, as long as q is a root of unity.[34] Together with Cesar Gomez, he defined the representation spaces of the quantum group in terms of screened vertex operators and interpreted the number of screening operators as the genuine quantum group number.[35] He introduced a spin chain Hamiltonian that possesses integrability and invariance under 14 (sI(2)) transformations within nilpotent irreducible representations when r3 = 1.[36] Additionally, he proved that the elliptic R-matrix of the eight vertex free fermion model is the intertwiner R-matrix of a quantum deformed Clifford-Hopf algebra that the elliptic R-matrix of the eight-vertex free fermion model corresponds to the intertwiner R-matrix of a quantum deformed Clifford-Hopf algebra.[37] In his work, he also presented a new mathematical structure entitled, graph quantum group which merges the tower of algebras associated with a graph G with the structure of a Hopf algebra {\cal A}.[38] Furthermore, he explored spin-anisotropy commensurable chains, a class of 2D integrable models, and described their mathematics using quantum groups with the deformation parameter as an Nth root of unity.[39] Moreover, alongside Miguel A. Martín-Delgado, he employed real space renormalization group (RG) methods[40] to examine the interplay between two different variants of quantum groups, exploring their relationship.[41]

Spin chains and ladders

In 1996, Sierra started working in condensed matter physics, more concretely on spin chains, spin ladders and high-Tc superconductors. He generalized Haldane's conjecture from spin chains to spin ladders using the O(3) non-linear sigma model.[19] He also investigated phase transitions in staggered spin ladders[42][43] and three-legged antiferromagnetic ladders.[44] In addition, he applied the variational matrix product ansatz to determine the ground state of several ladder systems.[45][46] In a joint study with J. Dukelsky, M.A. Martín-Delgado and T. Nishino, he showed that the latter method is equivalent to the DMRG method introduced by S. R. White in 1992.[47] Working together with Martín-Delgado in 1998, he proposed an extension of the variational matrix product ansatzs to two dimensions.[33] In 2004, F. Verstraete and J.I. Cirac rediscovered the latter ansatz using quantum information techniques, designating it as PEPS.[48]

Richardson-Gaudin models

In 1999, Sierra in collaboration with J. Dukelsky applied the DMRG method to the pairing model that describes ultrasmall superconducting grains,[49] confirming the exact solution of the pairing model obtained by Richardson and Sherman in 1963–64.[50][51] Shortly after its application, a close relationship was revealed between Richardson's solution and another set of exactly solvable models called the Gaudin magnets,[52] collectively known as Richardson-Gaudin models.[53] Several subsequent applications involved studying the effect of level statistics in nanograins,[54] the connection with conformal field theory[55] and Chern-Simons theory,[56] as well as exploring the implications with mean-field solutions[57] and p-wave symmetry.[58]

Russian doll renormalization group

In 2003–04, Sierra, in conjunction with A. LeClair and J.M. Román, introduced multiple models exhibiting a Russian doll renormalization group flow, featuring a cyclic nature instead of converging to a fixed point. Among them was a BCS model with pairing scattering phases that break time-reversal symmetry,[18] which was later demonstrated to be solvable using the algebraic Bethe ansatz.[59] Moreover, they put forward two scattering S-matrices exhibiting a cyclic renormalization group (RG) structure, which is related to both the cycle regime of the Kosterlitz-Thouless flow and an analytic extension of the massive sine-Gordon S matrix.[60]

Physical models of the Riemann zeros

In 2005, Sierra presented a Russian doll model of superconductivity whose spectrum contains the average Riemann zeros as missing spectral lines,[21] and this model is connected to the xp Hamiltonian of Berry, Keating, and Connes. In addition to proposing several variations of the xp model,[61][62][63] he collaborated with C. E. Creffield to propose a different physical realization of the Riemann zeros using periodically driven cold atoms;[64] this idea was eventually experimentally achieved in 2021 using trapped ions.[65]

Entanglement in quantum hall states

In 2009, Sierra and I. D. Rodríguez evaluated the entanglement entropy for integer quantum Hall states, involving the computation of the entanglement spectrum, proposed by Li and Haldane[22] to identify topological order in non-abelian quantum Hall states.[66][67]

Entanglement in conformal field theory

Sierra computed with F. C. Alcaraz and M. Ibáñez the entanglement properties of the low-lying excitations in conformal field theory in 2011 and found several applications to condensed matter systems, holography,[17][68] and systems with boundaries.[69] Furthermore, he independently discovered with J. C. Xavier and F. C Alcaraz the property of "entanglement equipartition" in conformal systems with U(1) symmetry, where the entanglement entropy is equally distributed in different charge sectors[70] and this finding holds for more general systems up to corrections, separate from the works.[71][72]

Entanglement in inhomogeneous spin chains

In 2014, Sierra, along with J. Rodríguez-Laguna and G. Ramírez, introduced an inhomogeneous spin chain model called rainbow chain that exhibits a maximal violation of the area law of entanglement entropy, in stark contrast to the behavior observed in homogeneous chains.[73] The rainbow chain model, earlier proposed by J. I. Latorre in a separate joint work,[74] was examined using conformal field theory techniques[75][76] and was found to support symmetry-protected phases.[77]

Infinite matrix product states and conformal field theory

In 2010, Sierra proposed a variational ansatz for the ground state of the XXZ spin chain using the chiral vertex operators of a CFT[24] to describe the critical region of this model, resulting in a matrix product state with an infinite bond dimension to capture logarithmic entanglement entropy. The ansatz also replicated the Haldane-Shastry wave function for the XXX spin chain, notably matching a conformal block of the WZW model SU(2) at level k=1, and was later extended to any level k jointly with A. E. B. Nielsen and J. Ignacio Cirac.[78] In two spatial dimensions, the CFT wave function demonstrated a bosonic Laughlin spin liquid state on a lattice,[79] that was experimentally realized using optical lattices.[80] This method was extended to other bosonic and fermionic Laughlin states,[81] WZW model SU(N)_1, etc.[82] The CFT wave functions described earlier were derived as tensor network states where the individual tensors are functionals of fields[83] which allowed the analysis of the symmetries of the field tensor network states.[84]

The prime state

Along with J. I. Latorre, Sierra proposed a quantum circuit that creates a pure state corresponding to the quantum superposition of all prime numbers less than 2^n, where n is the number of qubits of the register.[25] They showed the construction of the Prime state using the Gover algorithm that combined with the quantum counting algorithm allows for a verification of the Riemann hypothesis for numbers far beyond the reach of any classical computer. Moreover, the Prime state turned out to be highly entangled with an entanglement spectrum intimately related to the Hardy-Littlewood constants for the pairwise distribution of primes.[85][86]

Quantum computation

Through collaborative research efforts, Sierra implemented multiple quantum algorithms on the newly launched IBM quantum computers and introduced a quantum circuit capable of generating the Bethe eigenstates for the XXZ Hamiltonian.[87] Additionally, he proposed a simple mitigation strategy for a systematic gate error in IBMQ quantum computers[88] and demonstrated the implementation of data-driven error mitigation techniques to simulate quench dynamics on a digital quantum computer.[89]

Quantum games

In 2022, Sierra, together with A. Bera and S. Singha Roy, demonstrated a connection between the ground state of a topological Hamiltonian and the optimal strategy in a causal order game, where the maximum violation of the classical bound is associated with a second-order quantum phase transition.[26] Furthermore, working in conjunction with D. Centeno led to the development of several quantum versions of the Morra game, known as Chinos in Spain.[90]

Bibliography

Books
  • Quantum Electron Liquids and High-Tc Superconductivity (1995) ISBN 978-3662140123
  • Quantum Groups in Two-dimensional Physics (2011) ISBN 978-0521460651

Selected articles
  • Günaydin, M, Sierra, G & Townsend, PK (1984). The geometry of N=2 Maxwell-Einstein supergravity and Jordan algebras. Nuclear Physics B 242 (1), 244–268.
  • Alvarez-Gaume, L, Gomez, C. & Sierra, G (1989). Quantum group interpretation of some conformal field theories. Physics Letters B 220 (1–2), 142–152.
  • Dukelsky, J., Martín-Delgado, M. A., Nishino, T., & Sierra, G. (1998). Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains. Europhysics letters, 43(4), 457.
  • Dukelsky, J., Pittel, S., & Sierra, G. (2004). Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems. Reviews of modern physics, 76(3), 643.
  • Cirac, JI & Sierra, G (2010). Infinite matrix product states, conformal field theory and the Haldane-Shastry model. Physical Review B 81 (10), 104431.
  • Alcaraz, F. C., Berganza, M. I., & Sierra, G. (2011). Entanglement of low-energy excitations in Conformal Field Theory. Physical Review Letters, 106(20), 201601.
  • Latorre, J. I. & Sierra, G (2014), Quantum Computation of Prime Number Functions, Quantum Information and Computation, Vol. 14, 0577.
  • Ramírez, G, Rodríguez-Laguna, J & Sierra, G. (2015). Entanglement over the rainbow. Journal of Statistical Mechanics: Theory and Experiment 2015 (6), P06002.
  • Xavier, J. C., Alcaraz, F. C., & Sierra, G. (2018). Equipartition of the entanglement entropy. Physical Review B, 98(4), 041106.
  • Sierra, G (2019). The Riemann zeros as spectrum and the Riemann hypothesis. Symmetry 11 (4), 494.

References
  1. "Francisco German Sierra Rodero | Fulbright Scholar Program". fulbrightscholars.org.
  2. "Quantum electron liquids and high-Tc superconductivity | WorldCat.org". www.worldcat.org.
  3. "German Sierra Rodero". scholar.google.com.
  4. "ShieldSquare Captcha". hcvalidate.perfdrive.com.
  5. "Editor".
  6. "Editorial board – Nuclear Physics B | ScienceDirect.com by Elsevier". www.sciencedirect.com.
  7. "Instituto de Física Teórica | Centro de excelencia Severo Ochoa". www.ift.uam-csic.es.
  8. "Annual Report 2018" (PDF).
  9. "Kavli Institute for Theoretical Physics - Visitors Photos".
  10. "Prof. German Sierra".
  11. "Relatório de Atividades 2017" (PDF).
  12. "Francisco German Sierra Rodero".
  13. "Mathematical aspects of quantum integrable models in and out of equilibrium". 25 February 2021.
  14. "Number Theory And Physics: October 24 – November 18 2022".
  15. "Welcome to German Sierra". 30 June 2022.
  16. "C18: MEMBERS (2014-2017)".
  17. Alcaraz, Francisco Castilho; Berganza, Miguel Ibáñez; Sierra, Germán (May 17, 2011). "Entanglement of Low-Energy Excitations in Conformal Field Theory". Physical Review Letters. 106 (20): 201601. arXiv:1101.2881. Bibcode:2011PhRvL.106t1601A. doi:10.1103/PhysRevLett.106.201601. PMID 21668218. S2CID 5946721 – via APS.
  18. LeClair, André; María Román, José; Sierra, Germán (January 27, 2004). "Russian doll renormalization group and superconductivity". Physical Review B. 69 (2): 020505. arXiv:cond-mat/0211338. Bibcode:2004PhRvB..69b0505L. doi:10.1103/PhysRevB.69.020505. S2CID 119077666 – via APS.
  19. Sierra, Germán (1996). "The nonlinear sigma model and spin ladders". Journal of Physics A: Mathematical and General. 29 (12): 3299–3310. arXiv:cond-mat/9512007. Bibcode:1996JPhA...29.3299S. doi:10.1088/0305-4470/29/12/032. S2CID 18962367.
  20. Dukelsky, J.; Sierra, G. (July 5, 1999). "Density Matrix Renormalization Group Study of Ultrasmall Superconducting Grains". Physical Review Letters. 83 (1): 172–175. arXiv:cond-mat/9903332. Bibcode:1999PhRvL..83..172D. doi:10.1103/PhysRevLett.83.172. hdl:10261/99509. S2CID 44923045 – via APS.
  21. Sierra, Germán (2005). "The Riemann zeros and the cyclic renormalization group". Journal of Statistical Mechanics: Theory and Experiment. 2005 (12): P12006. arXiv:math/0510572. Bibcode:2005JSMTE..12..006S. doi:10.1088/1742-5468/2005/12/p12006. S2CID 119757268.
  22. Li, Hui; Haldane, F. D. M. (July 3, 2008). "Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States". Physical Review Letters. 101 (1): 010504. arXiv:0805.0332. Bibcode:2008PhRvL.101a0504L. doi:10.1103/PhysRevLett.101.010504. PMID 18764098. S2CID 23453061 – via APS.
  23. Ramírez, Giovanni; Rodríguez-Laguna, Javier; Sierra, Germán (2014). "From conformal to volume law for the entanglement entropy in exponentially deformed critical spin 1/2 chains". Journal of Statistical Mechanics: Theory and Experiment. 2014 (10): P10004. arXiv:1407.3456. Bibcode:2014JSMTE..10..004R. doi:10.1088/1742-5468/2014/10/p10004. hdl:10016/30536. S2CID 119223250.
  24. Cirac, J. Ignacio; Sierra, Germán (March 31, 2010). "Infinite matrix product states, conformal field theory, and the Haldane-Shastry model". Physical Review B. 81 (10): 104431. arXiv:0911.3029. Bibcode:2010PhRvB..81j4431C. doi:10.1103/PhysRevB.81.104431. S2CID 119213632 – via APS.
  25. Latorre, Jose I.; Sierra, German (September 5, 2013). "Quantum Computation of Prime Number Functions". arXiv:1302.6245 [quant-ph].
  26. Singha Roy, Sudipto; Bera, Anindita; Sierra, Germán (March 18, 2022). "Simulating violation of causality using a topological phase transition". Physical Review A. 105 (3): 032432. arXiv:2105.09795. Bibcode:2022PhRvA.105c2432S. doi:10.1103/PhysRevA.105.032432. S2CID 247560898 – via APS.
  27. Günaydin, M.; Sierra, G.; Townsend, P. K. (January 1, 1985). "Gauging the d = 5 Maxwell/Einstein supergravity theories: More on Jordan algebras". Nuclear Physics B. 253: 573–608. Bibcode:1985NuPhB.253..573G. doi:10.1016/0550-3213(85)90547-4 – via ScienceDirect.
  28. M., Guenaydin; G., Sierra; P.K., Townsend (August 7, 1985). "N = 2 Maxwell-Einstein Supergravity theories: their compact and non-compact gaugings and Jordan algebras". {{cite journal}}: Cite journal requires |journal= (help)
  29. Günaydin, M.; Sierra, G.; Townsend, P. K. (December 8, 1983). "Exceptional supergravity theories and the magic square". Physics Letters B. 133 (1): 72–76. Bibcode:1983PhLB..133...72G. doi:10.1016/0370-2693(83)90108-9 – via ScienceDirect.
  30. Doebner, H.-D.; Dobrev, V. K.; Ushveridze, A. G. (July 7, 1994). "Generalized Symmetries in Physics". World Scientific. pp. 1–444. doi:10.1142/9789814534314. ISBN 978-981-02-1771-6 – via worldscientific.com (Atypon). {{cite book}}: Missing or empty |title= (help)
  31. G., Sierra (August 7, 1989). "Duality and quantum groups". {{cite journal}}: Cite journal requires |journal= (help)
  32. Sierra, German (1996). Quantum Groups in Two-Dimensional Physics. ISBN 9780511628825 – via Academia.edu.
  33. Krasnitz, A.; Kubyshin, Y. A.; Potting, R.; Sá, P. (August 7, 1999). "The Exact Renormalization Group". WORLD SCIENTIFIC. pp. 1–238. doi:10.1142/9789814527293. ISBN 978-981-02-3939-8 – via worldscientific.com (Atypon). {{cite book}}: Missing or empty |title= (help)
  34. Alvarez-Gaumé, L.; Gomez, C.; Sierra, G. (March 30, 1989). "Quantum group interpretation of some conformal field theories". Physics Letters B. 220 (1): 142–152. Bibcode:1989PhLB..220..142A. doi:10.1016/0370-2693(89)90027-0 – via ScienceDirect.
  35. Gómez, César; Sierra, Germán (April 19, 1990). "Quantum group meaning of the Coulomb gas". Physics Letters B. 240 (1): 149–157. Bibcode:1990PhLB..240..149G. doi:10.1016/0370-2693(90)90424-5 – via ScienceDirect.
  36. Cuerno, R.; Sierra, G.; Gómez, C. (June 1, 1993). "On integrable quantum group invariant antiferromagnets". Journal of Geometry and Physics. 11 (1): 453–462. arXiv:hep-th/9205109. Bibcode:1993JGP....11..453C. doi:10.1016/0393-0440(93)90071-L. hdl:10016/7155. S2CID 119448576 – via ScienceDirect.
  37. Cuerno, R.; Gómez, C.; López, E.; Sierra, G. (June 10, 1993). "The hidden quantum group of the eight-vertex free fermion model: q-Clifford algebras". Physics Letters B. 307 (1): 56–60. arXiv:hep-th/9302089. Bibcode:1993PhLB..307...56C. doi:10.1016/0370-2693(93)90192-K. hdl:10016/7151. S2CID 119488308 – via ScienceDirect.
  38. Gomez, C.; Sierra, G. (December 22, 1993). "Graph Quantum Groups". arXiv:hep-th/9312177.
  39. Bérkovich, Alexander; Gómez, César; Sierra, Germán (March 14, 1994). "Spin-anisotropy commensurable chains. Quantum group symmetries and N = 2 SUSY". Nuclear Physics B. 415 (3): 681–733. arXiv:hep-th/9302001. Bibcode:1994NuPhB.415..681B. doi:10.1016/0550-3213(94)90307-7. S2CID 119328363 – via ScienceDirect.
  40. Martín-Delgado, Miguel A.; Sierra, Germán (February 12, 1996). "Real Space Renormalization Group Methods and Quantum Groups". Physical Review Letters. 76 (7): 1146–1149. arXiv:cond-mat/9507115. Bibcode:1996PhRvL..76.1146M. doi:10.1103/PhysRevLett.76.1146. hdl:10261/102722. PMID 10061645. S2CID 7812291 – via APS.
  41. Mart?n-Delgado, Miguel A.; Sierra, Germ?n (June 7, 1996). "The renormalization group method and quantum groups: The postman always rings twice". From Field Theory to Quantum Groups. WORLD SCIENTIFIC. pp. 113–139. arXiv:hep-th/9511190. doi:10.1142/9789812830425_0007. ISBN 9789810225445. S2CID 15210167 – via worldscientific.com (Atypon).
  42. Martín-Delgado, M. A.; Shankar, R.; Sierra, G. (October 14, 1996). "Phase Transitions in Staggered Spin Ladders". Physical Review Letters. 77 (16): 3443–3446. Bibcode:1996PhRvL..77.3443M. doi:10.1103/PhysRevLett.77.3443. hdl:10261/102696. PMID 10062221 – via APS.
  43. Martín-Delgado, M. A.; Dukelsky, J.; Sierra, G. (December 28, 1998). "Phase diagram of the 2-leg Heisenberg ladder with alternating dimerization". Physics Letters A. 250 (4): 430–434. arXiv:cond-mat/9810379. Bibcode:1998PhLA..250..430M. doi:10.1016/S0375-9601(98)00849-4. S2CID 39479040 – via ScienceDirect.
  44. Frischmuth, Beat; Haas, Stephan; Sierra, German; Rice, T. M. (February 1, 1997). "Low-energy properties of antiferromagnetic spin-1/2 Heisenberg ladders with an odd number of legs". Physical Review B. 55 (6): R3340–R3343. arXiv:cond-mat/9606183. Bibcode:1997PhRvB..55.3340F. doi:10.1103/PhysRevB.55.R3340. S2CID 119074714 – via APS.
  45. Sierra, Germán; Martín-Delgado, Miguel A. (October 1, 1997). "Short-range resonating-valence-bond state of even-spin ladders: A recurrent variational approach". Physical Review B. 56 (14): 8774–8785. arXiv:cond-mat/9704212. Bibcode:1997PhRvB..56.8774S. doi:10.1103/PhysRevB.56.8774. S2CID 15281550 – via APS.
  46. Martín-Delgado, M. A.; Roncaglia, M.; Sierra, G. (July 31, 2001). "Stripe ans\"atze from exactly solved models". Physical Review B. 64 (7): 075117. arXiv:cond-mat/0101458. Bibcode:2001PhRvB..64g5117M. doi:10.1103/PhysRevB.64.075117. S2CID 14541090 – via APS.
  47. Dukelsky, J.; Martín-Delgado, M. A.; Nishino, T.; Sierra, G. (1998). "Equivalence of the variational matrix product method and the density matrix renormalization group applied to spin chains". Europhysics Letters. 43 (4): 457–462. arXiv:cond-mat/9710310. Bibcode:1998EL.....43..457D. doi:10.1209/epl/i1998-00381-x. S2CID 250914148.
  48. Verstraete, F.; Cirac, J. I. (July 2, 2004). "Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions". arXiv:cond-mat/0407066.
  49. Dukelsky, J.; Sierra, G. (May 1, 2000). "Crossover from bulk to few-electron limit in ultrasmall metallic grains". Physical Review B. 61 (18): 12302–12314. arXiv:cond-mat/9906166. Bibcode:2000PhRvB..6112302D. doi:10.1103/PhysRevB.61.12302. hdl:10261/96600. S2CID 10931592 – via APS.
  50. "A Restricted Class of Exact Eigenstates of the Pairing-Force Hamiltonian".
  51. Richardson, R. W.; Sherman, N. (March 1, 1964). "Exact eigenstates of the pairing-force Hamiltonian". Nuclear Physics. 52: 221–238. Bibcode:1964NucPh..52..221R. doi:10.1016/0029-5582(64)90687-X. hdl:2027.42/32140 – via ScienceDirect.
  52. "Diagonalisation of a class of spin hamiltoniansDiagonalisation d'une classe d'hamiltoniens de spin – Journal de Physique".
  53. Dukelsky, J.; Pittel, S.; Sierra, G. (August 6, 2004). "Colloquium: Exactly solvable Richardson-Gaudin models for many-body quantum systems". Reviews of Modern Physics. 76 (3): 643–662. arXiv:nucl-th/0405011. Bibcode:2004RvMP...76..643D. doi:10.1103/RevModPhys.76.643. S2CID 611020 – via APS.
  54. Sierra, G.; Dukelsky, J.; Dussel, G. G.; von Delft, Jan; Braun, Fabian (May 1, 2000). "Exact study of the effect of level statistics in ultrasmall superconducting grains". Physical Review B. 61 (18): R11890–R11893. arXiv:cond-mat/9909015. Bibcode:2000PhRvB..6111890S. doi:10.1103/PhysRevB.61.R11890. hdl:10261/96855. S2CID 6473797 – via APS.
  55. Sierra, Germán (April 24, 2000). "Conformal field theory and the exact solution of the BCS Hamiltonian". Nuclear Physics B. 572 (3): 517–534. arXiv:hep-th/9911078. Bibcode:2000NuPhB.572..517S. doi:10.1016/S0550-3213(00)00036-5. S2CID 119495901 – via ScienceDirect.
  56. Asorey, Manuel; Falceto, Fernando; Sierra, Germán (February 11, 2002). "Chern–Simons theory and BCS superconductivity". Nuclear Physics B. 622 (3): 593–614. arXiv:hep-th/0110266. Bibcode:2002NuPhB.622..593A. doi:10.1016/S0550-3213(01)00614-9. S2CID 17782590 – via ScienceDirect.
  57. Román, J. M.; Sierra, G.; Dukelsky, J. (July 15, 2002). "Large-N limit of the exactly solvable BCS model: analytics versus numerics". Nuclear Physics B. 634 (3): 483–510. arXiv:cond-mat/0202070. Bibcode:2002NuPhB.634..483R. doi:10.1016/S0550-3213(02)00317-6. S2CID 118913100 – via ScienceDirect.
  58. Ibañez, Miguel; Links, Jon; Sierra, Germán; Zhao, Shao-You (May 1, 2009). "Exactly solvable pairing model for superconductors with ${p}_{x}+i{p}_{y}$-wave symmetry". Physical Review B. 79 (18): 180501. doi:10.1103/PhysRevB.79.180501. hdl:10261/20555. S2CID 119268490 – via APS.
  59. Dunning, Clare; Links, Jon (December 13, 2004). "Integrability of the Russian doll BCS model". Nuclear Physics B. 702 (3): 481–494. arXiv:cond-mat/0406234. Bibcode:2004NuPhB.702..481D. doi:10.1016/j.nuclphysb.2004.09.021. S2CID 16641548 – via ScienceDirect.
  60. LeClair, André; Román, José Marı́a; Sierra, Germán (December 29, 2003). "Russian doll renormalization group and Kosterlitz–Thouless flows". Nuclear Physics B. 675 (3): 584–606. arXiv:hep-th/0301042. Bibcode:2003NuPhB.675..584L. doi:10.1016/j.nuclphysb.2003.09.032 – via ScienceDirect.
  61. Sierra, Germán (August 6, 2007). "H=xp with interaction and the Riemann zeros". Nuclear Physics B. 776 (3): 327–364. arXiv:math-ph/0702034. Bibcode:2007NuPhB.776..327S. doi:10.1016/j.nuclphysb.2007.03.049. S2CID 118176000 – via ScienceDirect.
  62. Sierra, Germán; Townsend, Paul K. (September 12, 2008). "Landau Levels and Riemann Zeros". Physical Review Letters. 101 (11): 110201. arXiv:0805.4079. Bibcode:2008PhRvL.101k0201S. doi:10.1103/PhysRevLett.101.110201. PMID 18851266. S2CID 2871070 – via APS.
  63. Sierra, Germán (2014). "The Riemann zeros as energy levels of a Dirac fermion in a potential built from the prime numbers in Rindler spacetime". Journal of Physics A: Mathematical and Theoretical. 47 (32): 325204. arXiv:1404.4252. Bibcode:2014JPhA...47F5204S. doi:10.1088/1751-8113/47/32/325204. S2CID 119709107.
  64. Creffield, C. E.; Sierra, G. (June 8, 2015). "Finding zeros of the Riemann zeta function by periodic driving of cold atoms". Physical Review A. 91 (6): 063608. arXiv:1411.0459. Bibcode:2015PhRvA..91f3608C. doi:10.1103/PhysRevA.91.063608. hdl:10486/676030. S2CID 53331963 – via APS.
  65. He, Ran; Ai, Ming-Zhong; Cui, Jin-Ming; Huang, Yun-Feng; Han, Yong-Jian; Li, Chuan-Feng; Guo, Guang-Can; Sierra, G.; Creffield, C. E. (July 14, 2021). "Riemann zeros from a periodically-driven trapped ion". npj Quantum Information. 7 (1): 109. arXiv:2102.06936. doi:10.1038/s41534-021-00446-7. S2CID 256707919.
  66. Rodríguez, Iván D.; Sierra, Germán (October 7, 2009). "Entanglement entropy of integer quantum Hall states". Physical Review B. 80 (15): 153303. arXiv:0811.2188. Bibcode:2009PhRvB..80o3303R. doi:10.1103/PhysRevB.80.153303. S2CID 118686155 – via APS.
  67. Rodríguez, Iván D.; Sierra, Germán (2010). "Entanglement entropy of integer quantum Hall states in polygonal domains". Journal of Statistical Mechanics: Theory and Experiment. 2010 (12): P12033. arXiv:1007.5356. Bibcode:2010JSMTE..12..033R. doi:10.1088/1742-5468/2010/12/p12033. S2CID 118477323.
  68. Ibáñez Berganza, Miguel; Alcaraz, Francisco Castilho; Sierra, Germán (2012). "Entanglement of excited states in critical spin chains". Journal of Statistical Mechanics: Theory and Experiment. 2012 (1): P01016. arXiv:1109.5673. Bibcode:2012JSMTE..01..016I. doi:10.1088/1742-5468/2012/01/p01016. S2CID 119214108.
  69. Taddia, L.; Xavier, J. C.; Alcaraz, F. C.; Sierra, G. (August 5, 2013). "Entanglement entropies in conformal systems with boundaries". Physical Review B. 88 (7): 075112. arXiv:1302.6222. Bibcode:2013PhRvB..88g5112T. doi:10.1103/PhysRevB.88.075112. S2CID 53462122 – via APS.
  70. Xavier, J. C.; Alcaraz, F. C.; Sierra, G. (July 17, 2018). "Equipartition of the entanglement entropy". Physical Review B. 98 (4): 041106. arXiv:1804.06357. Bibcode:2018PhRvB..98d1106X. doi:10.1103/PhysRevB.98.041106. S2CID 53490532 – via APS.
  71. Laflorencie, Nicolas; Rachel, Stephan (2014). "Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids". Journal of Statistical Mechanics: Theory and Experiment. 2014 (11): P11013. arXiv:1407.3779. Bibcode:2014JSMTE..11..013L. doi:10.1088/1742-5468/2014/11/p11013. S2CID 119237142.
  72. Goldstein, Moshe; Sela, Eran (May 16, 2018). "Symmetry-Resolved Entanglement in Many-Body Systems". Physical Review Letters. 120 (20): 200602. arXiv:1711.09418. Bibcode:2018PhRvL.120t0602G. doi:10.1103/PhysRevLett.120.200602. PMID 29864300. S2CID 46975599 – via APS.
  73. Ramírez, Giovanni; Rodríguez-Laguna, Javier; Sierra, Germán (2015). "Entanglement over the rainbow". Journal of Statistical Mechanics: Theory and Experiment. 2015 (6): P06002. arXiv:1503.02695. Bibcode:2015JSMTE..06..002R. doi:10.1088/1742-5468/2015/06/p06002. S2CID 118523429.
  74. Vitagliano, G.; Riera, A.; Latorre, J. I. (2010). "Volume-law scaling for the entanglement entropy in spin-1/2 chains". New Journal of Physics. 12 (11): 113049. arXiv:1003.1292. Bibcode:2010NJPh...12k3049V. doi:10.1088/1367-2630/12/11/113049. S2CID 119119917.
  75. Rodríguez-Laguna, Javier; Dubail, Jérôme; Ramírez, Giovanni; Calabrese, Pasquale; Sierra, Germán (2017). "More on the rainbow chain: Entanglement, space-time geometry and thermal states". Journal of Physics A: Mathematical and Theoretical. 50 (16): 164001. arXiv:1611.08559. Bibcode:2017JPhA...50p4001R. doi:10.1088/1751-8121/aa6268. S2CID 119225985.
  76. Tonni, Erik; Rodríguez-Laguna, Javier; Sierra, Germán (2018). "Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems". Journal of Statistical Mechanics: Theory and Experiment. 2018 (4): 043105. arXiv:1712.03557. Bibcode:2018JSMTE..04.3105T. doi:10.1088/1742-5468/aab67d. S2CID 119448770.
  77. De Buruaga, Nadir Samos Sáenz; Santalla, Silvia N.; Rodríguez-Laguna, Javier; Sierra, Germán (2019). "Symmetry protected phases in inhomogeneous spin chains". Journal of Statistical Mechanics: Theory and Experiment. 2019 (9): 093102. arXiv:1812.04869. Bibcode:2019JSMTE..09.3102S. doi:10.1088/1742-5468/ab3192. S2CID 119406881.
  78. Nielsen, Anne E B.; Ignacio Cirac, J.; Sierra, Germán (2011). "Quantum spin Hamiltonians for the SU (2) k WZW model". Journal of Statistical Mechanics: Theory and Experiment. 2011 (11): P11014. arXiv:1109.5470. Bibcode:2011JSMTE..11..014N. doi:10.1088/1742-5468/2011/11/p11014. S2CID 119223177.
  79. Nielsen, Anne E. B.; Cirac, J. Ignacio; Sierra, Germán (June 20, 2012). "Laughlin Spin-Liquid States on Lattices Obtained from Conformal Field Theory". Physical Review Letters. 108 (25): 257206. arXiv:1201.3096. Bibcode:2012PhRvL.108y7206N. doi:10.1103/PhysRevLett.108.257206. PMID 23004652. S2CID 11713272 – via APS.
  80. Nielsen, Anne E. B.; Sierra, Germán; Cirac, J. Ignacio (November 28, 2013). "Local models of fractional quantum Hall states in lattices and physical implementation". Nature Communications. 4 (1): 2864. arXiv:1304.0717. doi:10.1038/ncomms3864. PMID 24284969. S2CID 118677640 – via www.nature.com.
  81. Tu, Hong-Hao; Nielsen, Anne E B.; Cirac, J Ignacio; Sierra, Germán (2014). "Lattice Laughlin states of bosons and fermions at filling fractions 1/ q". New Journal of Physics. 16 (3): 033025. arXiv:1311.3958. Bibcode:2014NJPh...16c3025T. doi:10.1088/1367-2630/16/3/033025. S2CID 119202413.
  82. Tu, Hong-Hao; Nielsen, Anne E. B.; Sierra, Germán (September 1, 2014). "Quantum spin models for the SU(n)1 Wess–Zumino–Witten model". Nuclear Physics B. 886: 328–363. arXiv:1405.2950. Bibcode:2014NuPhB.886..328T. doi:10.1016/j.nuclphysb.2014.06.027. S2CID 119125729 – via ScienceDirect.
  83. Nielsen, Anne E. B.; Herwerth, Benedikt; Cirac, J. Ignacio; Sierra, Germán (April 16, 2021). "Field tensor network states". Physical Review B. 103 (15): 155130. arXiv:2001.07723. Bibcode:2021PhRvB.103o5130N. doi:10.1103/PhysRevB.103.155130. S2CID 210861136 – via APS.
  84. Gasull, Albert; Tilloy, Antoine; Cirac, J. Ignacio; Sierra, Germán (April 3, 2023). "Symmetries and field tensor network states". Physical Review B. 107 (15): 155102. arXiv:2209.11253. Bibcode:2023PhRvB.107o5102G. doi:10.1103/PhysRevB.107.155102. S2CID 252519432 – via APS.
  85. Latorre, José Ignacio; Sierra, Germán (April 7, 2014). "There is entanglement in the primes". arXiv:1403.4765 [quant-ph].
  86. García-Martín, D.; Ribas, E.; Carrazza, S.; Latorre, J. I.; Sierra, G. (December 11, 2020). "The Prime state and its quantum relatives". Quantum. 4: 371. arXiv:2005.02422. Bibcode:2020Quant...4..371G. doi:10.22331/q-2020-12-11-371. S2CID 218516768 – via quantum-journal.org.
  87. Sopena, Alejandro; Gordon, Max Hunter; García-Martín, Diego; Sierra, Germán; López, Esperanza (September 8, 2022). "Algebraic Bethe Circuits". Quantum. 6: 796. arXiv:2202.04673. Bibcode:2022Quant...6..796S. doi:10.22331/q-2022-09-08-796. S2CID 246706299 – via quantum-journal.org.
  88. Bultrini, Daniel; Gordon, Max Hunter; López, Esperanza; Sierra, Germȧn (December 10, 2020). "Simple Mitigation Strategy for a Systematic Gate Error in IBMQ". arXiv:2012.00831 [quant-ph].
  89. Sopena, Alejandro; Gordon, Max Hunter; Sierra, Germán; López, Esperanza (2021). "Simulating quench dynamics on a digital quantum computer with data-driven error mitigation". Quantum Science and Technology. 6 (4): 045003. arXiv:2103.12680. Bibcode:2021QS&T....6d5003S. doi:10.1088/2058-9565/ac0e7a. S2CID 232320788.
  90. Centeno, Daniel; Sierra, Germán (2022). "General quantum Chinos games". Journal of Physics Communications. 6 (7): 075009. arXiv:2112.05175. Bibcode:2022JPhCo...6g5009C. doi:10.1088/2399-6528/ac7434. S2CID 250739663.
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