Equilibrium Dynamics of Infinite-Range Quantum Spin Glasses in a Field

Tikhanovskaya, Maria; Sachdev, Subir; Samajdar, Rhine

doi:10.1103/PRXQuantum.5.020313

Title: Equilibrium Dynamics of Infinite-Range Quantum Spin Glasses in a Field

Journal Article · 16 April 2024 · PRX Quantum

DOI: https://doi.org/10.1103/PRXQuantum.5.020313 · OSTI ID:2337984

Tikhanovskaya, Maria;

;

We determine the low-energy spectrum and Parisi replica-symmetry-breaking function for the spin-glass phase of the quantum Ising model with infinite-range random exchange interactions and transverse and longitudinal ( $h$ ) fields. We show that, for all $h$ , the spin-glass state has full replica symmetry breaking and the local spin spectrum is gapless, with a spectral density that vanishes linearly with frequency. These results are obtained using an action functional—argued to yield exact results at low frequencies—that expands in powers of a spin-glass order parameter, which is bilocal in time, and a matrix in replica space. We also present the exact solution of the infinite-range spherical quantum $p$ -rotor model at nonzero $h$ : here, the spin-glass state has one-step replica symmetry breaking and gaplessness only appears after imposition of an additional marginal stability condition. Possible connections to experiments on random arrays of trapped Rydberg atoms are noted. Published by the American Physical Society 2024

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Sponsoring Organization:: USDOE

Grant/Contract Number:: SC0019030

OSTI ID:: 2337984

Journal Information:: PRX Quantum, Journal Name: PRX Quantum Journal Issue: 2 Vol. 5; ISSN 2691-3399; ISSN PQRUAG

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (69)

Stability analysis of an Ising spin glass with transverse field Büttner, G.; Usadel, K. D. Physical Review B, Vol. 41, Issue 1 https://doi.org/10.1103/PhysRevB.41.428	journal	January 1990
Quantum optimization of maximum independent set using Rydberg atom arrays Ebadi, S.; Keesling, A.; Cain, M. Science, Vol. 376, Issue 6598 https://doi.org/10.1126/science.abo6587	journal	June 2022
Imaginary-time replica formalism study of a quantum spherical p -spin-glass model Cugliandolo, Leticia F.; Grempel, D. R.; da Silva Santos, Constantino A. Physical Review B, Vol. 64, Issue 1 https://doi.org/10.1103/PhysRevB.64.014403	journal	June 2001
Landau theory of quantum spin glasses of rotors and Ising spins Read, N.; Sachdev, Subir; Ye, J. Physical Review B, Vol. 52, Issue 1 https://doi.org/10.1103/PhysRevB.52.384	journal	July 1995
Classical-to-quantum crossover in the critical behavior of the transverse-field Sherrington-Kirkpatrick spin glass model Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K. Physical Review E, Vol. 92, Issue 4 https://doi.org/10.1103/PhysRevE.92.042107	journal	October 2015
Analytical solution of the off-equilibrium dynamics of a long-range spin-glass model Cugliandolo, L. F.; Kurchan, J. Physical Review Letters, Vol. 71, Issue 1 https://doi.org/10.1103/PhysRevLett.71.173	journal	July 1993
Gapless spin-fluid ground state in a random quantum Heisenberg magnet Sachdev, Subir; Ye, Jinwu Physical Review Letters, Vol. 70, Issue 21 https://doi.org/10.1103/PhysRevLett.70.3339	journal	May 1993
Rydberg quantum wires for maximum independent set problems Kim, Minhyuk; Kim, Kangheun; Hwang, Jaeyong Nature Physics, Vol. 18, Issue 7 https://doi.org/10.1038/s41567-022-01629-5	journal	June 2022
Stability and susceptibility in Parisi's solution of a spin glass model Thouless, D. J.; Almeida, J. R. L. de; Kosterlitz, J. M. Journal of Physics C: Solid State Physics, Vol. 13, Issue 17 https://doi.org/10.1088/0022-3719/13/17/017	journal	June 1980
Real-time nonequilibrium dynamics of quantum glassy systems Cugliandolo, Leticia F.; Lozano, Gustavo Physical Review B, Vol. 59, Issue 2 https://doi.org/10.1103/PhysRevB.59.915	journal	January 1999
Quantum Thouless-Anderson-Palmer equations for glassy systems Biroli, Giulio; Cugliandolo, Leticia F. Physical Review B, Vol. 64, Issue 1 https://doi.org/10.1103/PhysRevB.64.014206	journal	June 2001
The sphericalp-spin interaction spin glass model: the statics Crisanti, A.; Sommers, H. -J. Zeitschrift f�r Physik B Condensed Matter, Vol. 87, Issue 3 https://doi.org/10.1007/BF01309287	journal	October 1992
A Quantum Adiabatic Evolution Algorithm Applied to Random Instances of an NP-Complete Problem Farhi, E.; Goldstone, J.; Gutmann, S. Science, Vol. 292, Issue 5516 https://doi.org/10.1126/science.1057726	journal	April 2001
Solvable spin glass of quantum rotors Ye, J.; Sachdev, S.; Read, N. Physical Review Letters, Vol. 70, Issue 25 https://doi.org/10.1103/PhysRevLett.70.4011	journal	June 1993
Non-Fermi-liquid regime of a doped Mott insulator Parcollet, Olivier; Georges, Antoine Physical Review B, Vol. 59, Issue 8 https://doi.org/10.1103/PhysRevB.59.5341	journal	February 1999
Adiabatic quantum computation Albash, Tameem; Lidar, Daniel A. Reviews of Modern Physics, Vol. 90, Issue 1 https://doi.org/10.1103/RevModPhys.90.015002	journal	January 2018
Time-Dependent Order Parameters in Spin-Glasses Sompolinsky, H. Physical Review Letters, Vol. 47, Issue 13 https://doi.org/10.1103/PhysRevLett.47.935	journal	September 1981
Dynamical mean-field theory and aging dynamics Altieri, Ada; Biroli, Giulio; Cammarota, Chiara Journal of Physics A: Mathematical and Theoretical, Vol. 53, Issue 37 https://doi.org/10.1088/1751-8121/aba3dd	journal	August 2020
Relaxational dynamics of the Edwards-Anderson model and the mean-field theory of spin-glasses Sompolinsky, H.; Zippelius, Annette Physical Review B, Vol. 25, Issue 11 https://doi.org/10.1103/PhysRevB.25.6860	journal	June 1982
Out-of-equilibrium dynamics of a quantum Heisenberg spin glass Biroli, Giulio; Parcollet, Olivier Physical Review B, Vol. 65, Issue 9 https://doi.org/10.1103/PhysRevB.65.094414	journal	February 2002
Instabilities in the quantum Sherrington-Kirkpatrick Ising spin glass in transverse and longitudinal fields Kopeć, T. K.; Usadel, K. D.; Büttner, G. Physical Review B, Vol. 39, Issue 16 https://doi.org/10.1103/PhysRevB.39.12418	journal	June 1989
Spectral form factor of a quantum spin glass Winer, Michael; Barney, Richard; Baldwin, Christopher L. Journal of High Energy Physics, Vol. 2022, Issue 9 https://doi.org/10.1007/JHEP09(2022)032	journal	September 2022
Spin liquid to spin glass crossover in the random quantum Heisenberg magnet Christos, Maine; Haehl, Felix M.; Sachdev, Subir Physical Review B, Vol. 105, Issue 8 https://doi.org/10.1103/PhysRevB.105.085120	journal	February 2022
Random-energy model: An exactly solvable model of disordered systems Derrida, Bernard Physical Review B, Vol. 24, Issue 5 https://doi.org/10.1103/PhysRevB.24.2613	journal	September 1981
Quantum Quenches in Isolated Quantum Glasses out of Equilibrium Thomson, S. J.; Urbani, P.; Schiró, M. Physical Review Letters, Vol. 125, Issue 12 https://doi.org/10.1103/PhysRevLett.125.120602	journal	September 2020
Critical metallic phase in the overdoped randomt-Jmodel Christos, Maine; Joshi, Darshan G.; Sachdev, Subir Proceedings of the National Academy of Sciences, Vol. 119, Issue 29 https://doi.org/10.1073/pnas.2206921119	journal	July 2022
Spin-glass theory for pedestrians Castellani, Tommaso; Cavagna, Andrea Journal of Statistical Mechanics: Theory and Experiment, Vol. 2005, Issue 05 https://doi.org/10.1088/1742-5468/2005/05/P05012	journal	May 2005
Information, Physics, and Computation Mézard, Marc; Montanari, Andrea https://doi.org/10.1093/acprof:oso/9780198570837.001.0001	book	January 2009
Quantum and Thermal Fluctuations in the SU( N ) Heisenberg Spin-Glass Model near the Quantum Critical Point Camjayi, Alberto; Rozenberg, Marcelo J. Physical Review Letters, Vol. 90, Issue 21 https://doi.org/10.1103/PhysRevLett.90.217202	journal	May 2003
Spin glasses with p-spin interactions Gardner, E. Nuclear Physics B, Vol. 257 https://doi.org/10.1016/0550-3213(85)90374-8	journal	January 1985
Quantum Optimization with Arbitrary Connectivity Using Rydberg Atom Arrays Nguyen, Minh-Thi; Liu, Jin-Guo; Wurtz, Jonathan PRX Quantum, Vol. 4, Issue 1 https://doi.org/10.1103/PRXQuantum.4.010316	journal	February 2023
Infinite Number of Order Parameters for Spin-Glasses Parisi, G. Physical Review Letters, Vol. 43, Issue 23 https://doi.org/10.1103/PhysRevLett.43.1754	journal	December 1979
Sachdev-Ye-Kitaev models and beyond: Window into non-Fermi liquids Chowdhury, Debanjan; Georges, Antoine; Parcollet, Olivier Reviews of Modern Physics, Vol. 94, Issue 3 https://doi.org/10.1103/RevModPhys.94.035004	journal	September 2022
Stability of the quantum Sherrington-Kirkpatrick spin glass model Young, A. P. Physical Review E, Vol. 96, Issue 3 https://doi.org/10.1103/PhysRevE.96.032112	journal	September 2017
Planckian metal at a doping-induced quantum critical point Dumitrescu, Philipp T.; Wentzell, Nils; Georges, Antoine Physical Review B, Vol. 105, Issue 18 https://doi.org/10.1103/PhysRevB.105.L180404	journal	May 2022
Conformal Invariance and the Yang-Lee Edge Singularity in Two Dimensions Cardy, John L. Physical Review Letters, Vol. 54, Issue 13 https://doi.org/10.1103/PhysRevLett.54.1354	journal	April 1985
Dynamical Response of Quantum Spin-Glass Models atT=0 Arrachea, L.; Rozenberg, M. J. Physical Review Letters, Vol. 86, Issue 22 https://doi.org/10.1103/PhysRevLett.86.5172	journal	May 2001
Quantum Annealing of a Disordered Magnet Brooke, J. Science, Vol. 284, Issue 5415 https://doi.org/10.1126/science.284.5415.779	journal	April 1999
Measuring Equilibrium Properties in Aging Systems Franz, Silvio; Mézard, Marc; Parisi, Giorgio Physical Review Letters, Vol. 81, Issue 9 https://doi.org/10.1103/PhysRevLett.81.1758	journal	August 1998
Mean Field Theory of a Quantum Heisenberg Spin Glass Georges, Antoine; Parcollet, Olivier; Sachdev, Subir Physical Review Letters, Vol. 85, Issue 4 https://doi.org/10.1103/PhysRevLett.85.840	journal	July 2000
A perturbation expansion for the Sherrington-Kirkpatrick model with a transverse field Yamamoto, T.; Ishii, H. Journal of Physics C: Solid State Physics, Vol. 20, Issue 35 https://doi.org/10.1088/0022-3719/20/35/020	journal	December 1987
The de Almeida–Thouless Line in Hierarchical Quantum Spin Glasses Manai, Chokri; Warzel, Simone Journal of Statistical Physics, Vol. 186, Issue 1 https://doi.org/10.1007/s10955-021-02860-9	journal	December 2021
The quantum p-spin glass model: a user manual for holographers Anous, Tarek; Haehl, Felix M. Journal of Statistical Mechanics: Theory and Experiment, Vol. 2021, Issue 11 https://doi.org/10.1088/1742-5468/ac2cb9	journal	November 2021
Infinite-range quantum random Heisenberg magnet Arrachea, Liliana; Rozenberg, Marcelo J. Physical Review B, Vol. 65, Issue 22 https://doi.org/10.1103/PhysRevB.65.224430	journal	June 2002
Dynamics of the Infinite-Range Ising Spin-Glass Model in a Transverse Field Rozenberg, M. J.; Grempel, D. R. Physical Review Letters, Vol. 81, Issue 12 https://doi.org/10.1103/PhysRevLett.81.2550	journal	September 1998
Free energy of the spherical mean field model Talagrand, Michel Probability Theory and Related Fields, Vol. 134, Issue 3 https://doi.org/10.1007/s00440-005-0433-8	journal	May 2005
The simplest spin glass Gross, D. J.; Mezard, M. Nuclear Physics B, Vol. 240, Issue 4 https://doi.org/10.1016/0550-3213(84)90237-2	journal	November 1984
Random-Energy Model: Limit of a Family of Disordered Models Derrida, B. Physical Review Letters, Vol. 45, Issue 2 https://doi.org/10.1103/PhysRevLett.45.79	journal	July 1980
Aging dynamics of quantum spin glasses of rotors Kennett, Malcolm P.; Chamon, Claudio; Ye, Jinwu Physical Review B, Vol. 64, Issue 22 https://doi.org/10.1103/PhysRevB.64.224408	journal	November 2001
Replica field theory for random manifolds Mézard, Marc; Parisi, Giorgio Journal de Physique I, Vol. 1, Issue 6 https://doi.org/10.1051/jp1:1991171	journal	June 1991
Yang-Lee Edge Singularity and ϕ 3 Field Theory Fisher, Michael E. Physical Review Letters, Vol. 40, Issue 25 https://doi.org/10.1103/PhysRevLett.40.1610	journal	June 1978
Finding the Maximum Independent Sets of Platonic Graphs Using Rydberg Atoms Byun, Andrew; Kim, Minhyuk; Ahn, Jaewook PRX Quantum, Vol. 3, Issue 3 https://doi.org/10.1103/PRXQuantum.3.030305	journal	July 2022
VariationalAnsatzfor the Ground State of the Quantum Sherrington-Kirkpatrick Model Schindler, Paul M.; Guaita, Tommaso; Shi, Tao Physical Review Letters, Vol. 129, Issue 22 https://doi.org/10.1103/PhysRevLett.129.220401	journal	November 2022
Spherical Model of a Spin-Glass Kosterlitz, J. M.; Thouless, D. J.; Jones, Raymund C. Physical Review Letters, Vol. 36, Issue 20 https://doi.org/10.1103/PhysRevLett.36.1217	journal	May 1976
Quantum Phases of Matter Sachdev, Subir https://doi.org/10.1017/9781009212717	book	March 2023
Possible ergodic-nonergodic regions in the quantum Sherrington-Kirkpatrick spin glass model and quantum annealing Mukherjee, Sudip; Rajak, Atanu; Chakrabarti, Bikas K. Physical Review E, Vol. 97, Issue 2 https://doi.org/10.1103/PhysRevE.97.022146	journal	February 2018
Quantum critical dynamics in a 5,000-qubit programmable spin glass King, Andrew D.; Raymond, Jack; Lanting, Trevor Nature, Vol. 617, Issue 7959 https://doi.org/10.1038/s41586-023-05867-2	journal	April 2023
Sherrington-Kirkpatrick model in a transverse field: Absence of replica symmetry breaking due to quantum fluctuations Ray, P.; Chakrabarti, B. K.; Chakrabarti, Arunava Physical Review B, Vol. 39, Issue 16 https://doi.org/10.1103/PhysRevB.39.11828	journal	June 1989
Long-Range Quantum Ising Spin Glasses atT=0: Gapless Collective Excitations and Universality Andreanov, A.; Müller, M. Physical Review Letters, Vol. 109, Issue 17 https://doi.org/10.1103/PhysRevLett.109.177201	journal	October 2012
Existence of Replica-Symmetry Breaking in Quantum Glasses Leschke, Hajo; Manai, Chokri; Ruder, Rainer Physical Review Letters, Vol. 127, Issue 20 https://doi.org/10.1103/PhysRevLett.127.207204	journal	November 2021
Solvable model of the quantum spin glass in a transverse field Goldschmidt, Yadin Y. Physical Review B, Vol. 41, Issue 7 https://doi.org/10.1103/PhysRevB.41.4858	journal	March 1990
On the out-of-equilibrium relaxation of the Sherrington-Kirkpatrick model Cugliandolo, L. F.; Kurchan, J. Journal of Physics A: Mathematical and General, Vol. 27, Issue 17 https://doi.org/10.1088/0305-4470/27/17/011	journal	September 1994
Dynamic Theory of the Spin-Glass Phase Sompolinsky, H.; Zippelius, Annette Physical Review Letters, Vol. 47, Issue 5 https://doi.org/10.1103/PhysRevLett.47.359	journal	August 1981
Quantum fluctuations in the transverse Ising spin glass model: A field theory of random quantum spin systems Takahashi, Kazutaka Physical Review B, Vol. 76, Issue 18 https://doi.org/10.1103/PhysRevB.76.184422	journal	November 2007
The Quantum Approximate Optimization Algorithm at High Depth for MaxCut on Large-Girth Regular Graphs and the Sherrington-Kirkpatrick Model Basso, Joao; Farhi, Edward; Marwaha, Kunal Schloss Dagstuhl - Leibniz-Zentrum für Informatik https://doi.org/10.4230/LIPIcs.TQC.2022.7	text	January 2022
Quantum Phase Transition at Nonzero Doping in a Random t − J Model Shackleton, Henry; Wietek, Alexander; Georges, Antoine Physical Review Letters, Vol. 126, Issue 13 https://doi.org/10.1103/PhysRevLett.126.136602	journal	March 2021
Quenched complexity of the mean-fieldp-spin spherical model with external magnetic field Cavagna, Andrea; Garrahan, Juan P.; Giardina, Irene Journal of Physics A: Mathematical and General, Vol. 32, Issue 5 https://doi.org/10.1088/0305-4470/32/5/004	journal	January 1999
Quantum fluctuations of a nearly critical Heisenberg spin glass Georges, A.; Parcollet, O.; Sachdev, S. Physical Review B, Vol. 63, Issue 13 https://doi.org/10.1103/PhysRevB.63.134406	journal	March 2001
Zero-temperature critical behavior of the infinite-range quantum Ising spin glass Miller, Jonathan; Huse, David A. Physical Review Letters, Vol. 70, Issue 20 https://doi.org/10.1103/PhysRevLett.70.3147	journal	May 1993