Chaos detection; Correlation holes; Form factors; Level correlation; Level statistics; Many body; Quantum chaos; Random matrices theory; Spectral correlation; Survival probabilities; Physics and Astronomy (all); Physics - Statistical Mechanics; Quantum Physics
Abstract :
[en] In this work, the term "quantum chaos"refers to spectral correlations similar to those found in the random matrix theory. Quantum chaos can be diagnosed through the analysis of level statistics using, e.g., the spectral form factor, which detects both short- and long-range level correlations. The spectral form factor corresponds to the Fourier transform of the two-point spectral correlation function and exhibits a typical slope-dip-ramp-plateau structure (aka correlation hole) when the system is chaotic. We discuss how this structure could be detected through the quench dynamics of two physical quantities accessible to experimental many-body quantum systems: the survival probability and the spin autocorrelation function. The survival probability is equivalent to the spectral form factor with an additional filter. When the system is small, the dip of the correlation hole reaches sufficiently large values at times which are short enough to be detected with current experimental platforms. As the system is pushed away from chaos, the correlation hole disappears, signaling integrability or localization. We also provide a relatively shallow circuit with which the correlation hole could be detected with commercially available quantum computers.
Disciplines :
Physics
Author, co-author :
Das, Adway Kumar ; Department of Physics, University of Connecticut, Storrs, United States ; Department of Physical Sciences, Indian Institute of Science Education and Research Kolkata, Mohanpur, India
Cianci, Cameron ; Department of Physics, University of Connecticut, Storrs, United States ; Mirion Technologies (Canberra) Inc., Meriden, United States
Cabral, Delmar G. A.; Department of Chemistry, Yale University, New Haven, United States
Zarate-Herrada, David A. ; Institut of Physics, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
Pinney, Patrick ; Department of Physics, University of Connecticut, Storrs, United States
Pilatowsky-Cameo, Saúl ; Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, United States
MATSOUKAS, Stylianos Apollonas ; University of Luxembourg > Faculty of Science, Technology and Medicine > Department of Physics and Materials Science > Team Adolfo DEL CAMPO ECHEVARRIA
Batista, Victor S.; Department of Chemistry, Yale University, New Haven, United States
DEL CAMPO ECHEVARRIA, Adolfo ; University of Luxembourg > Faculty of Science, Technology and Medicine (FSTM) > Department of Physics and Materials Science (DPHYMS)
Torres-Herrera, E. Jonathan ; Institut of Physics, Benemérita Universidad Autónoma de Puebla, Puebla, Mexico
Santos, Lea F. ; Department of Physics, University of Connecticut, Storrs, United States
Fulbright Association Consejo Nacional de Humanidades, Ciencias y Tecnologías National Science Foundation Center for Cultural Innovation Department of Forestry and Natural Resources, Purdue University Vicerrectoría de Investigación y Estudios de Posgrado, Benemérita Universidad Autónoma de Puebla Kavli Institute for Theoretical Physics, University of California, Santa Barbara Nehru Luxembourg National Research Fund Fulbright Association Consejo Nacional de Humanidades, Ciencias y Tecnologías National Science Foundation Center for Cultural Innovation Department of Forestry and Natural Resources, Purdue University Vicerrectoría de Investigación y Estudios de Posgrado, Benemérita Universidad Autónoma de Puebla Kavli Institute for Theoretical Physics, University of California, Santa Barbara Nehru Luxembourg National Research Fund
Funding text :
A.K.D. is supported by the Fulbright-Nehru Grant No. 2879/FNDR/2023-2024. D.A.Z.-H. and E.J.T.-H. are supported by CONAHCYT through Project No. CF-2023-I-1748. D.C. and V.S.B. are funded by the NSF CCI grant (Award No. 2124511). A.d.C. is supported by the Luxembourg National Research Fund (FNR), Grant Reference [17132054]. E.J.T.-H. is grateful for financial support from VIEP-BUAP, Project No. 00165-2023. D.A.Z.-H. and E.J.T.-H. are grateful to LNS-BUAP for their supercomputing facility. L.F.S. is supported by the NSF Grant No. DMR-1936006. This research was supported in part by grant NSF PHY-2309135 to the Kavli Institute for Theoretical Physics (KITP).
T. A. Brody, J. Flores, J. B. French, P. A. Mello, A. Pandey, and S. S. M. Wong, Random-matrix physics: Spectrum and strength fluctuations, Rev. Mod. Phys. 53, 385 (1981) 0034-6861 10.1103/RevModPhys.53.385.
V. Zelevinsky, B. A. Brown, N. Frazier, and M. Horoi, The nuclear shell model as a testing ground for many-body quantum chaos, Phys. Rep. 276, 85 (1996) 0370-1573 10.1016/S0370-1573(96)00007-5.
F. Borgonovi, F. M. Izrailev, L. F. Santos, and V. G. Zelevinsky, Quantum chaos and thermalization in isolated systems of interacting particles, Phys. Rep. 626, 1 (2016) 0370-1573 10.1016/j.physrep.2016.02.005.
L. D'Alessio, Y. Kafri, A. Polkovnikov, and M. Rigol, From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics, Adv. Phys. 65, 239 (2016) 0001-8732 10.1080/00018732.2016.1198134.
D. Luitz and Y. B. Lev, The ergodic side of the many-body localization transition, Ann. Phys. (Berlin, Germany) 529, 1600350 (2017) 0003-3804 10.1002/andp.201600350.
J. Šuntajs, J. Bonča, T. Prosen, and L. Vidmar, Quantum chaos challenges many-body localization, Phys. Rev. E 102, 062144 (2020) 2470-0045 10.1103/PhysRevE.102.062144.
D. Abanin, J. Bardarson, G. De Tomasi, S. Gopalakrishnan, V. Khemani, S. Parameswaran, F. Pollmann, A. Potter, M. Serbyn, and R. Vasseur, Distinguishing localization from chaos: Challenges in finite-size systems, Ann. Phys. (NY) 427, 168415 (2021) 0003-4916 10.1016/j.aop.2021.168415.
M. L. Mehta, Random Matrices (Academic Press, Boston, 1991).
A. Tameshtit and J. E. Sipe, Survival probability and chaos in an open quantum system, Phys. Rev. A 45, 8280 (1992) 1050-2947 10.1103/PhysRevA.45.8280.
Z. Xu, A. Chenu, T. Prosen, and A. del Campo, Thermofield dynamics: Quantum chaos versus decoherence, Phys. Rev. B 103, 064309 (2021) 2469-9950 10.1103/PhysRevB.103.064309.
J. Cornelius, Z. Xu, A. Saxena, A. Chenu, and A. del Campo, Spectral filtering induced by non-hermitian evolution with balanced gain and loss: Enhancing quantum chaos, Phys. Rev. Lett. 128, 190402 (2022) 0031-9007 10.1103/PhysRevLett.128.190402.
Z. Cao, Z. Xu, and A. del Campo, Probing quantum chaos in multipartite systems, Phys. Rev. Res. 4, 033093 (2022) 2643-1564 10.1103/PhysRevResearch.4.033093.
A. S. Matsoukas-Roubeas, F. Roccati, J. Cornelius, Z. Xu, A. Chenu, and A. del Campo, Non-Hermitian hamiltonian deformations in quantum mechanics, J. High Energ. Phys. 01 (2023) 060 1029-8479 10.1007/JHEP01(2023)060.
A. S. Matsoukas-Roubeas, M. Beau, L. F. Santos, and A. del Campo, Unitarity breaking in self-averaging spectral form factors, Phys. Rev. A 108, 062201 (2023) 2469-9926 10.1103/PhysRevA.108.062201.
A. S. Matsoukas-Roubeas, T. Prosen, and A. del Campo, Quantum chaos and coherence: Random parametric quantum channels, Quantum 8, 1446 (2024) 10.22331/q-2024-08-27-1446.
I. Vallejo-Fabila, A. K. Das, D. A. Zarate-Herrada, A. S. Matsoukas-Roubeas, E. J. Torres-Herrera, and L. F. Santos, Reducing dynamical fluctuations and enforcing self-averaging by opening many-body quantum systems, Phys. Rev. B 110, 075138 (2024) 10.1103/PhysRevB.110.075138.
T. Kinoshita, T. Wenger, and D. S. Weiss, A quantum Newton's cradle, Nature (London) 440, 900 (2006) 0028-0836 10.1038/nature04693.
A. M. Kaufman, A. L. M. Eric Tai, M. Rispoli, R. Schittko, P. M. Preiss, and M. Greiner, Quantum thermalization through entanglement in an isolated many-body system, Science 353, 794 (2016) 0036-8075 10.1126/science.aaf6725.
P. Bordia, H. P. Lüschen, S. S. Hodgman, M. Schreiber, I. Bloch, and U. Schneider, Coupling identical one-dimensional many-body localized systems, Phys. Rev. Lett. 116, 140401 (2016) 0031-9007 10.1103/PhysRevLett.116.140401.
S. Hild, T. Fukuhara, P. Schauß, J. Zeiher, M. Knap, E. Demler, I. Bloch, and C. Gross, Far-from-equilibrium spin transport in Heisenberg quantum magnets, Phys. Rev. Lett. 113, 147205 (2014) 0031-9007 10.1103/PhysRevLett.113.147205.
M. Schreiber, S. S. Hodgman, P. Bordia, H. P. Lüschen, M. H. Fischer, R. Vosk, E. Altman, U. Schneider, and I. Bloch, Observation of many-body localization of interacting fermions in a quasirandom optical lattice, Science 349, 842 (2015) 0036-8075 10.1126/science.aaa7432.
M. Rispoli, A. Lukin, R. Schittko, S. Kim, M. E. Tai, J. Léonard, and M. Greiner, Quantum critical behaviour at the many-body localization transition, Nature (London) 573, 385 (2019) 0028-0836 10.1038/s41586-019-1527-2.
P. Jurcevic, B. P. Lanyon, P. Hauke, C. Hempel, P. Zoller, R. Blatt, and C. F. Roos, Quasiparticle engineering and entanglement propagation in a quantum many-body system, Nature (London) 511, 202 (2014) 0028-0836 10.1038/nature13461.
P. Richerme, Z.-X. Gong, A. Lee, C. Senko, J. Smith, M. Foss-Feig, S. Michalakis, A. V. Gorshkov, and C. Monroe, Non-local propagation of correlations in quantum systems with long-range interactions, Nature (London) 511, 198 (2014) 0028-0836 10.1038/nature13450.
J. Smith, A. Lee, P. Richerme, B. Neyenhuis, P. W. Hess, P. Hauke, M. Heyl, D. A. Huse, and C. Monroe, Many-body localization in a quantum simulator with programmable random disorder, Nat. Phys. 12, 907 (2016) 1745-2473 10.1038/nphys3783.
F. Kranzl, S. Birnkammer, M. K. Joshi, A. Bastianello, R. Blatt, M. Knap, and C. F. Roos, Observation of magnon bound states in the long-range, anisotropic Heisenberg model, Phys. Rev. X 13, 031017 (2023) 2160-3308 10.1103/PhysRevX.13.031017.
IBM Q: https://www.research.ibm.com/ibm-q/.
A. Smith, M. S. Kim, F. Pollmann, and J. Knolle, Simulating quantum many-body dynamics on a current digital quantum computer, npj Quantum Inf. 5, 106 (2019) 2056-6387 10.1038/s41534-019-0217-0.
L. K. Joshi, A. Elben, A. Vikram, B. Vermersch, V. Galitski, and P. Zoller, Probing many-body quantum chaos with quantum simulators, Phys. Rev. X 12, 011018 (2022) 2160-3308 10.1103/PhysRevX.12.011018.
D. V. Vasilyev, A. Grankin, M. A. Baranov, L. M. Sieberer, and P. Zoller, Monitoring quantum simulators via quantum nondemolition couplings to atomic clock qubits, PRX Quantum 1, 020302 (2020) 2691-3399 10.1103/PRXQuantum.1.020302.
A. Browaeys and T. Lahaye, Many-body physics with individually controlled Rydberg atoms, Nat. Phys. 16, 132 (2020) 1745-2473 10.1038/s41567-019-0733-z.
M. Kjaergaard, M. E. Schwartz, J. Braumüller, P. Krantz, J. I.-J. Wang, S. Gustavsson, and W. D. Oliver, Superconducting qubits: Current state of play, Annu. Rev. Condens. Matter Phys. 11, 369 (2020) 1947-5454 10.1146/annurev-conmatphys-031119-050605.
C. B. Daǧ, S. I. Mistakidis, A. Chan, and H. R. Sadeghpour, Many-body quantum chaos in stroboscopically-driven cold atoms, Commun. Phys. 6, 136 (2023) 2399-3650 10.1038/s42005-023-01258-1.
L. Leviandier, M. Lombardi, R. Jost, and J. P. Pique, Fourier transform: A tool to measure statistical level properties in very complex spectra, Phys. Rev. Lett. 56, 2449 (1986) 0031-9007 10.1103/PhysRevLett.56.2449.
J. P. Pique, Y. Chen, R. W. Field, and J. L. Kinsey, Chaos and dynamics on 0.5-300 ps time scales in vibrationally excited acetylene: Fourier transform of stimulated-emission pumping spectrum, Phys. Rev. Lett. 58, 475 (1987) 0031-9007 10.1103/PhysRevLett.58.475.
T. Guhr and H. Weidenmüller, Correlations in anticrossing spectra and scattering theory. Analytical aspects, Chem. Phys. 146, 21 (1990) 0301-0104 10.1016/0301-0104(90)90003-R.
U. Hartmann, H. Weidenmüller, and T. Guhr, Correlations in anticrossing spectra and scattering theory: Numerical simulations, Chem. Phys. 150, 311 (1991) 0301-0104 10.1016/0301-0104(91)87105-5.
Y. Alhassid and R. D. Levine, Spectral autocorrelation function in the statistical theory of energy levels, Phys. Rev. A 46, 4650 (1992) 1050-2947 10.1103/PhysRevA.46.4650.
M. Lombardi and T. H. Seligman, Universal and nonuniversal statistical properties of levels and intensities for chaotic Rydberg molecules, Phys. Rev. A 47, 3571 (1993) 1050-2947 10.1103/PhysRevA.47.3571.
L. Michaille and J.-P. Pique, Influence of experimental resolution on the spectral statistics used to show quantum chaos: The case of molecular vibrational chaos, Phys. Rev. Lett. 82, 2083 (1999) 0031-9007 10.1103/PhysRevLett.82.2083.
F. Leyvraz, A. García, H. Kohler, and T. H. Seligman, Fidelity under isospectral perturbations: a random matrix study, J. Phys. A: Math. Theor. 46, 275303 (2013) 1751-8113 10.1088/1751-8113/46/27/275303.
E. J. Torres-Herrera and L. F. Santos, Dynamical manifestations of quantum chaos: correlation hole and bulge, Philos. Trans. R. Soc., A 375, 20160434 (2017) 1364-503X 10.1098/rsta.2016.0434.
E. J. Torres-Herrera and L. F. Santos, Extended nonergodic states in disordered many-body quantum systems, Ann. Phys. (Berlin, Germany) 529, 1600284 (2017) 0003-3804 10.1002/andp.201600284.
E. J. Torres-Herrera, A. M. García-García, and L. F. Santos, Generic dynamical features of quenched interacting quantum systems: Survival probability, density imbalance, and out-of-time-ordered correlator, Phys. Rev. B 97, 060303 (R) (2018) 2469-9950 10.1103/PhysRevB.97.060303.
A. K. Das, A. Ghosh-Herrera, and L. F. Santos, Spectral form factor and energy correlations in banded random matrices, arXiv:2502.02648.
M. Schiulaz, E. J. Torres-Herrera, and L. F. Santos, Thouless and relaxation time scales in many-body quantum systems, Phys. Rev. B 99, 174313 (2019) 2469-9950 10.1103/PhysRevB.99.174313.
S. Lerma-Hernández, D. Villaseñor, M. A. Bastarrachea-Magnani, E. J. Torres-Herrera, L. F. Santos, and J. G. Hirsch, Dynamical signatures of quantum chaos and relaxation time scales in a spin-boson system, Phys. Rev. E 100, 012218 (2019) 2470-0045 10.1103/PhysRevE.100.012218.
L. F. Santos, F. Pérez-Bernal, and E. J. Torres-Herrera, Speck of chaos, Phys. Rev. Res. 2, 043034 (2020) 2643-1564 10.1103/PhysRevResearch.2.043034.
T. L. M. Lezama, E. J. Torres-Herrera, F. Pérez-Bernal, Y. Bar Lev, and L. F. Santos, Equilibration time in many-body quantum systems, Phys. Rev. B 104, 085117 (2021) 2469-9950 10.1103/PhysRevB.104.085117.
A. K. Das and A. Ghosh, Nonergodic extended states in the (Equation presented) ensemble, Phys. Rev. E 105, 054121 (2022) 2470-0045 10.1103/PhysRevE.105.054121.
A. K. Das and A. Ghosh, Chaos due to symmetry-breaking in deformed poisson ensemble, J. Stat. Mech. (2022) 063101 1742-5468 10.1088/1742-5468/ac70dd.
A. K. Das and A. Ghosh, Dynamical signatures of chaos to integrability crossover in (Equation presented) generalized random matrix ensembles, J. Phys. A: Math. Theor. 56, 495003 (2023) 1751-8113 10.1088/1751-8121/ad0b5a.
R. Shir, P. Martinez-Azcona, and A. Chenu, Full range spectral correlations and their spectral form factors in chaotic and integrable models, arXiv:2311.09292.
K. X. Wei, C. Ramanathan, and P. Cappellaro, Exploring localization in nuclear spin chains, Phys. Rev. Lett. 120, 070501 (2018) 0031-9007 10.1103/PhysRevLett.120.070501.
P. Peng, B. Ye, N. Y. Yao, and P. Cappellaro, Exploiting disorder to probe spin and energy hydrodynamics, Nat. Phys. 19, 1027 (2023) 1745-2473 10.1038/s41567-023-02024-4.
H. Dong, P. Zhang, C. B. Dag, Y. Gao, N. Wang, J. Deng, X. Zhang, J. Chen, S. Xu, K. Wang, Y. Wu, C. Zhang, F. Jin, X. Zhu, A. Zhang, Y. Zou, Z. Tan, Z. Cui, Z. Zhu, F. Shen, Measuring spectral form factor in many-body chaotic and localized phases of quantum processors, Phys. Rev. Lett. 134, 010402 (2025) 10.1103/PhysRevLett.134.010402.
M. Hopjan and L. Vidmar, Scale-invariant critical dynamics at eigenstate transitions, Phys. Rev. Res. 5, 043301 (2023) 10.1103/PhysRevResearch.5.043301.
R. E. Prange, The spectral form factor is not self-averaging, Phys. Rev. Lett. 78, 2280 (1997) 0031-9007 10.1103/PhysRevLett.78.2280.
M. Schiulaz, E. J. Torres-Herrera, F. Pérez-Bernal, and L. F. Santos, Self-averaging in many-body quantum systems out of equilibrium: Chaotic systems, Phys. Rev. B 101, 174312 (2020) 2469-9950 10.1103/PhysRevB.101.174312.
E. J. Torres-Herrera, G. De Tomasi, M. Schiulaz, F. Pérez-Bernal, and L. F. Santos, Self-averaging in many-body quantum systems out of equilibrium: Approach to the localized phase, Phys. Rev. B 102, 094310 (2020) 2469-9950 10.1103/PhysRevB.102.094310.
E. J. Torres-Herrera, I. Vallejo-Fabila, A. J. Martínez-Mendoza, and L. F. Santos, Self-averaging in many-body quantum systems out of equilibrium: Time dependence of distributions, Phys. Rev. E 102, 062126 (2020) 2470-0045 10.1103/PhysRevE.102.062126.
A. del Campo, J. Molina-Vilaplana, L. Santos, and J. Sonner, Decay of a thermofield-double state in chaotic quantum systems, Eur. Phys. J. Spec. Top. 227, 247 (2018) 1951-6355 10.1140/epjst/e2018-00083-5.
V. V. Flambaum and F. M. Izrailev, Excited eigenstates and strength functions for isolated systems of interacting particles, Phys. Rev. E 61, 2539 (2000) 1063-651X 10.1103/PhysRevE.61.2539.
E. J. Torres-Herrera, M. Vyas, and L. F. Santos, General features of the relaxation dynamics of interacting quantum systems, New J. Phys. 16, 063010 (2014) 1367-2630 10.1088/1367-2630/16/6/063010.
E. J. Torres-Herrera, J. Karp, M. Távora, and L. F. Santos, Realistic many-body quantum systems vs. full random matrices: Static and dynamical properties, Entropy 18, 359 (2016) 1099-4300 10.3390/e18100359.
M. Távora, E. J. Torres-Herrera, and L. F. Santos, Inevitable power-law behavior of isolated many-body quantum systems and how it anticipates thermalization, Phys. Rev. A 94, 041603 (R) (2016) 2469-9926 10.1103/PhysRevA.94.041603.
M. Távora, E. J. Torres-Herrera, and L. F. Santos, Power-law decay exponents: A dynamical criterion for predicting thermalization, Phys. Rev. A 95, 013604 (2017) 2469-9926 10.1103/PhysRevA.95.013604.
A. del Campo, J. Molina-Vilaplana, and J. Sonner, Scrambling the spectral form factor: Unitarity constraints and exact results, Phys. Rev. D 95, 126008 (2017) 2470-0010 10.1103/PhysRevD.95.126008.
A. Scheie, P. Laurell, B. Lake, S. E. Nagler, M. B. Stone, J.-S. Caux, and D. A. Tennant, Quantum wake dynamics in Heisenberg antiferromagnetic chains, Nat. Commun. 13, 5796 (2022) 2041-1723 10.1038/s41467-022-33571-8.
A. Signoles, T. Franz, R. Ferracini Alves, M. Gärttner, S. Whitlock, G. Zürn, and M. Weidemüller, Glassy dynamics in a disordered Heisenberg quantum spin system, Phys. Rev. X 11, 011011 (2021) 2160-3308 10.1103/PhysRevX.11.011011.
C. J. van Diepen, T.-K. Hsiao, U. Mukhopadhyay, C. Reichl, W. Wegscheider, and L. M. K. Vandersypen, Quantum simulation of antiferromagnetic Heisenberg chain with gate-defined quantum dots, Phys. Rev. X 11, 041025 (2021) 2160-3308 10.1103/PhysRevX.11.041025.
L. F. Santos, G. Rigolin, and C. O. Escobar, Entanglement versus chaos in disordered spin chains, Phys. Rev. A 69, 042304 (2004) 1050-2947 10.1103/PhysRevA.69.042304.
L. F. Santos, M. I. Dykman, M. Shapiro, and F. M. Izrailev, Strong many-particle localization and quantum computing with perpetually coupled qubits, Phys. Rev. A 71, 012317 (2005) 1050-2947 10.1103/PhysRevA.71.012317.
R. Nandkishore and D. A. Huse, Many-body localization and thermalization in quantum statistical mechanics, Annu. Rev. Condens. Matter Phys. 6, 15 (2015) 1947-5454 10.1146/annurev-conmatphys-031214-014726.
H. Bethe, On the theory of metal I. Eigenvalues and eigenfunctions of a linear chain of atoms, Eur. Phys. J. A 71, 205 (1931) 1434-6001 10.1007/BF01341708.
P. Jacquod and D. L. Shepelyansky, Emergence of quantum chaos in finite interacting fermi systems, Phys. Rev. Lett. 79, 1837 (1997) 0031-9007 10.1103/PhysRevLett.79.1837.
Y. Avishai, J. Richert, and R. Berkovits, Level statistics in a Heisenberg chain with random magnetic field, Phys. Rev. B 66, 052416 (2002) 0163-1829 10.1103/PhysRevB.66.052416.
L. F. Santos, Integrability of a disordered Heisenberg spin-1/2 chain, J. Phys. A: Math. Gen. 37, 4723 (2004) 0305-4470 10.1088/0305-4470/37/17/004.
K. Binder and A. P. Young, Spin glasses: Experimental facts, theoretical concepts, and open questions, Rev. Mod. Phys. 58, 801 (1986) 0034-6861 10.1103/RevModPhys.58.801.
L. F. Santos, M. Távora, and F. Pérez-Bernal, Excited-state quantum phase transitions in many-body systems with infinite-range interaction: Localization, dynamics, and bifurcation, Phys. Rev. A 94, 012113 (2016) 2469-9926 10.1103/PhysRevA.94.012113.
P. Cejnar, P. Stránský, M. Macek, and M. Kloc, Excited-state quantum phase transitions, J. Phys. A: Math. Theor. 54, 133001 (2021) 1751-8113 10.1088/1751-8121/abdfe8.
N. Defenu, A. Lerose, and S. Pappalardi, Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions, Phys. Rep. 1074, 1 (2024) 10.1016/j.physrep.2024.04.005.
A. Lerose, T. Parolini, R. Fazio, D. A. Abanin, and S. Pappalardi, Theory of robust quantum many-body scars in long-range interacting systems, Phys. Rev. X 15, 011020 (2025) 10.1103/PhysRevX.15.011020.
X. Yuan, S. Endo, Q. Zhao, Y. Li, and S. C. Benjamin, Theory of variational quantum simulation, Quantum 3, 191 (2019) 2521-327X 10.22331/q-2019-10-07-191.
P. W. Anderson, Absence of diffusion in certain random lattices, Phys. Rev. 109, 1492 (1958) 0031-899X 10.1103/PhysRev.109.1492.
F. Izrailev, S. Ruffo, and L. Tessieri, Classical representation of the one-dimensional Anderson model, J. Phys. A: Math. Gen. 31, 5263 (1998) 0305-4470 10.1088/0305-4470/31/23/008.
A. K. Das, A. Ghosh, and I. M. Khaymovich, Absence of Mobility Edge in Short-Range Uncorrelated Disordered Model Coexistence of Localized and Extended States, Phys. Rev. Lett. 131, 166401 (2023) 10.1103/PhysRevLett.131.166401.
A. K. Das, A. Ghosh, and I. M. Khaymovich, Robust nonergodicity of the ground states in the (Equation presented) ensemble, Phys. Rev. B 109, 064206 (2024) 10.1103/PhysRevB.109.064206.
A. K. Das, A. Ghosh, and I. M. Khaymovich, Emergent multifractality in power-law decaying eigenstates, arXiv:2501.17242.
S. Sorathia, F. M. Izrailev, V. G. Zelevinsky, and G. L. Celardo, From closed to open one-dimensional Anderson model: Transport versus spectral statistics, Phys. Rev. E 86, 011142 (2012) 1539-3755 10.1103/PhysRevE.86.011142.
E. J. Torres-Herrera, J. A. Méndez-Bermúdez, and L. F. Santos, Level repulsion and dynamics in the finite one-dimensional Anderson model, Phys. Rev. E 100, 022142 (2019) 2470-0045 10.1103/PhysRevE.100.022142.
A. A. Elkamshishy and C. H. Greene, Observation of Wigner-Dyson level statistics in a classically integrable system, Phys. Rev. E 103, 062211 (2021) 2470-0045 10.1103/PhysRevE.103.062211.
V. Oganesyan and D. A. Huse, Localization of interacting fermions at high temperature, Phys. Rev. B 75, 155111 (2007) 1098-0121 10.1103/PhysRevB.75.155111.
Y. Y. Atas and E. Bogomolny, Multifractality of eigenfunctions in spin chains, Phys. Rev. E 86, 021104 (2012) 1539-3755 10.1103/PhysRevE.86.021104.
The spectrum of this model for (Equation presented) presents a combination of GSE-like statistics, in the case of short-range correlations, and GOE-like statistics for long-range correlations. It has been shown analytically with full random matrices that the minimum value of (Equation presented) and the saturation value (Equation presented), where (Equation presented) for GOE, GUE, and GSE, respectively [38].
D. Villaseñor, S. Pilatowsky-Cameo, M. A. Bastarrachea-Magnani, S. Lerma-Hernández, L. F. Santos, and J. G. Hirsch, Quantum vs classical dynamics in a spin-boson system: manifestations of spectral correlations and scarring, New J. Phys. 22, 063036 (2020) 1367-2630 10.1088/1367-2630/ab8ef8.
