Microcanonical windows on quantum operators

Silvia Pappalardi1,2, Laura Foini3, and Jorge Kurchan1

1Laboratoire de Physique de l’École Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université de Paris, F-75005 Paris, France
2Institut für Theoretische Physik, Universität zu Köln, Zülpicher Straße 77, 50937 Köln, Germany
3IPhT, CNRS, CEA, Université Paris Saclay, 91191 Gif-sur-Yvette, France

Find this paper interesting or want to discuss? Scite or leave a comment on SciRate.


We discuss the construction of a microcanonical projection WOW of a quantum operator O induced by an energy window filter W, its spectrum, and the retrieval of canonical many-time correlations from it.

► BibTeX data

► References

[1] J. M. Deutsch. Quantum statistical mechanics in a closed system. Physical Review A, 43 (4): 2046–2049, February 1991. URL https:/​/​doi.org/​10.1103/​physreva.43.2046.

[2] Mark Srednicki. The approach to thermal equilibrium in quantized chaotic systems. Journal of Physics A: Mathematical and General, 32 (7): 1163–1175, January 1999. URL https:/​/​doi.org/​10.1088/​0305-4470/​32/​7/​007.

[3] Luca D'Alessio, Yariv Kafri, Anatoli Polkovnikov, and Marcos Rigol. From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics. Advances in Physics, 65 (3): 239–362, May 2016. URL https:/​/​doi.org/​10.1080/​00018732.2016.1198134.

[4] Laura Foini and Jorge Kurchan. Eigenstate thermalization hypothesis and out of time order correlators. Physical Review E, 99 (4), April 2019. URL https:/​/​doi.org/​10.1103/​physreve.99.042139.

[5] Yan V Fyodorov and Alexander D Mirlin. Scaling properties of localization in random band matrices: a $\sigma$-model approach. Physical review letters, 67 (18): 2405, 1991. URL https:/​/​doi.org/​10.1103/​PhysRevLett.124.120602.

[6] M Kuś, M Lewenstein, and Fritz Haake. Density of eigenvalues of random band matrices. Physical Review A, 44 (5): 2800, 1991. URL https:/​/​doi.org/​10.1103/​PhysRevA.44.2800.

[7] Ya V Fyodorov, OA Chubykalo, FM Izrailev, and G Casati. Wigner random banded matrices with sparse structure: local spectral density of states. Physical review letters, 76 (10): 1603, 1996. URL https:/​/​doi.org/​10.1103/​PhysRevLett.76.1603.

[8] Tomaz Prosen. Statistical properties of matrix elements in a hamilton system between integrability and chaos. Annals of Physics, 235 (1): 115–164, 1994. URL https:/​/​doi.org/​10.1006/​aphy.1994.1093.

[9] Jordan Cotler, Nicholas Hunter-Jones, Junyu Liu, and Beni Yoshida. Chaos, complexity, and random matrices. Journal of High Energy Physics, 2017 (11): 1–60, 2017. URL https:/​/​doi.org/​10.1007/​JHEP11(2017)048.

[10] Anatoly Dymarsky and Hong Liu. New characteristic of quantum many-body chaotic systems. Phys. Rev. E, 99: 010102, Jan 2019. URL https:/​/​doi.org/​10.1103/​PhysRevE.99.010102.

[11] Anatoly Dymarsky. Mechanism of macroscopic equilibration of isolated quantum systems. Physical Review B, 99 (22): 224302, 2019. URL https:/​/​doi.org/​10.1103/​PhysRevB.99.224302.

[12] Anatoly Dymarsky. Bound on eigenstate thermalization from transport. Phys. Rev. Lett., 128: 190601, May 2022. URL https:/​/​doi.org/​10.1103/​PhysRevLett.128.190601.

[13] Jonas Richter, Anatoly Dymarsky, Robin Steinigeweg, and Jochen Gemmer. Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies. Physical Review E, 102 (4), October 2020. URL https:/​/​doi.org/​10.1103/​physreve.102.042127.

[14] Jiaozi Wang, Mats H Lamann, Jonas Richter, Robin Steinigeweg, Anatoly Dymarsky, and Jochen Gemmer. Eigenstate thermalization hypothesis and its deviations from random-matrix theory beyond the thermalization time. Physical Review Letters, 128 (18): 180601, 2022. URL https:/​/​doi.org/​10.1103/​PhysRevLett.128.180601.

[15] Marlon Brenes, Silvia Pappalardi, Mark T. Mitchison, John Goold, and Alessandro Silva. Out-of-time-order correlations and the fine structure of eigenstate thermalization. Physical Review E, 104 (3), September 2021. URL https:/​/​doi.org/​10.1103/​physreve.104.034120.

[16] Silvia Pappalardi and Jorge Kurchan. Quantum bounds on the generalized lyapunov exponents. Entropy, 25 (2): 246, 2023. URL https:/​/​doi.org/​10.3390/​e25020246.

[17] Juan Maldacena, Stephen H. Shenker, and Douglas Stanford. A bound on chaos. Journal of High Energy Physics, 2016 (8), August 2016. URL https:/​/​doi.org/​10.1007/​jhep08(2016)106.

[18] Felix M Haehl, R Loganayagam, Prithvi Narayan, Amin A Nizami, and Mukund Rangamani. Thermal out-of-time-order correlators, kms relations, and spectral functions. Journal of High Energy Physics, 2017 (12): 1–55, 2017. URL https:/​/​doi.org/​10.1007/​jhep12(2017)154.

[19] Naoto Tsuji, Tomohiro Shitara, and Masahito Ueda. Bound on the exponential growth rate of out-of-time-ordered correlators. Physical Review E, 98 (1), July 2018. URL https:/​/​doi.org/​10.1103/​physreve.98.012216.

[20] Silvia Pappalardi, Laura Foini, and Jorge Kurchan. Quantum bounds and fluctuation-dissipation relations. SciPost Physics, 12 (4), April 2022a. URL https:/​/​doi.org/​10.21468/​scipostphys.12.4.130.

[21] Silvia Pappalardi, Laura Foini, and Jorge Kurchan. Eigenstate thermalization hypothesis and free probability. Phys. Rev. Lett., 129: 170603, Oct 2022b. URL https:/​/​doi.org/​10.1103/​PhysRevLett.129.170603.

[22] James A Mingo and Roland Speicher. Free probability and random matrices, volume 35. Springer, 2017. URL https:/​/​doi.org/​10.1007/​978-1-4939-6942-5.

[23] Tarek A. Elsayed, Benjamin Hess, and Boris V. Fine. Signatures of chaos in time series generated by many-spin systems at high temperatures. Phys. Rev. E, 90: 022910, Aug 2014. URL https:/​/​doi.org/​10.1103/​PhysRevE.90.022910.

[24] Daniel E Parker, Xiangyu Cao, Alexander Avdoshkin, Thomas Scaffidi, and Ehud Altman. A universal operator growth hypothesis. Physical Review X, 9 (4): 041017, 2019. URL.

[25] Alexander Avdoshkin and Anatoly Dymarsky. Euclidean operator growth and quantum chaos. Physical Review Research, 2 (4): 043234, 2020. URL https:/​/​doi.org/​10.1103/​PhysRevResearch.2.043234.

[26] Chaitanya Murthy and Mark Srednicki. Bounds on chaos from the eigenstate thermalization hypothesis. Physical Review Letters, 123 (23), December 2019. URL https:/​/​doi.org/​10.1103/​physrevlett.123.230606.

[27] Sirui Lu, Mari Carmen Bañuls, and J. Ignacio Cirac. Algorithms for quantum simulation at finite energies. PRX Quantum, 2: 020321, May 2021. URL https:/​/​doi.org/​10.1103/​PRXQuantum.2.020321.

[28] Yilun Yang, J. Ignacio Cirac, and Mari Carmen Bañuls. Classical algorithms for many-body quantum systems at finite energies. Phys. Rev. B, 106: 024307, Jul 2022. URL https:/​/​doi.org/​10.1103/​PhysRevB.106.024307.

[29] Ehsan Khatami, Guido Pupillo, Mark Srednicki, and Marcos Rigol. Fluctuation-dissipation theorem in an isolated system of quantum dipolar bosons after a quench. Physical Review Letters, 111 (5), July 2013. URL https:/​/​doi.org/​10.1103/​physrevlett.111.050403.

[30] MW Long, P Prelovšek, S El Shawish, J Karadamoglou, and X Zotos. Finite-temperature dynamical correlations using the microcanonical ensemble and the lanczos algorithm. Physical Review B, 68 (23): 235106, 2003. URL https:/​/​doi.org/​10.1103/​PhysRevB.68.235106.

[31] Xenophon Zotos. Microcanonical lanczos method. Philosophical Magazine, 86 (17-18): 2591–2601, 2006. URL https:/​/​doi.org/​10.1080/​14786430500227830.

[32] Satoshi Okamoto, Gonzalo Alvarez, Elbio Dagotto, and Takami Tohyama. Accuracy of the microcanonical lanczos method to compute real-frequency dynamical spectral functions of quantum models at finite temperatures. Physical Review E, 97 (4): 043308, 2018. URL https:/​/​doi.org/​10.1103/​PhysRevE.97.043308.

[33] Marcos Rigol, Vanja Dunjko, and Maxim Olshanii. Thermalization and its mechanism for generic isolated quantum systems. Nature, 452 (7189): 854–858, April 2008. URL https:/​/​doi.org/​10.1038/​nature06838.

[34] Peter Reimann. Typical fast thermalization processes in closed many-body systems. Nature communications, 7 (1): 1–10, 2016. URL https:/​/​doi.org/​10.1038/​ncomms10821.

[35] Dieter Forster. Hydrodynamic fluctuations, broken symmetry, and correlation functions. CRC Press, 2018. URL https:/​/​doi.org/​10.1201/​9780429493683.

[36] Roland Speicher. Free probability theory and non-crossing partitions. Séminaire Lotharingien de Combinatoire [electronic only], 39: B39c–38, 1997. URL http:/​/​eudml.org/​doc/​119380.

[37] Kurusch Ebrahimi-Fard and Frédéric Patras. The combinatorics of green’s functions in planar field theories. Frontiers of Physics, 11: 1–23, 2016. URL https:/​/​doi.org/​10.1007/​s11467-016-0585-2.

[38] Ludwig Hruza and Denis Bernard. Coherent fluctuations in noisy mesoscopic systems, the open quantum ssep, and free probability. Phys. Rev. X, 13: 011045, Mar 2023. URL https:/​/​doi.org/​10.1103/​PhysRevX.13.011045.

[39] Joël Bun, Jean-Philippe Bouchaud, and Marc Potters. Cleaning large correlation matrices: tools from random matrix theory. Physics Reports, 666: 1–109, 2017. URL https:/​/​doi.org/​10.1016/​j.physrep.2016.10.005.

[40] Felix Fritzsch and Tomaž Prosen. Eigenstate thermalization in dual-unitary quantum circuits: Asymptotics of spectral functions. Phys. Rev. E, 103: 062133, Jun 2021. URL https:/​/​doi.org/​10.1103/​PhysRevE.103.062133.

[41] Silvia Pappalardi, Felix Fritzsch, and Tomaž Prosen. General eigenstate thermalization via free cumulants in quantum lattice systems. arXiv preprint arXiv:2303.00713, 2023. URL https:/​/​doi.org/​10.48550/​arXiv.2303.00713.

Cited by

[1] Tomasz Szołdra, Piotr Sierant, Maciej Lewenstein, and Jakub Zakrzewski, "Catching thermal avalanches in the disordered XXZ model", Physical Review B 109 13, 134202 (2024).

[2] Maxine Luo, Rahul Trivedi, Mari Carmen Bañuls, and J. Ignacio Cirac, "Probing off-diagonal eigenstate thermalization with tensor networks", Physical Review B 109 13, 134304 (2024).

[3] Ding-Zu Wang, Hao Zhu, Jian Cui, Javier Argüello-Luengo, Maciej Lewenstein, Guo-Feng Zhang, Piotr Sierant, and Shi-Ju Ran, "Eigenstate thermalization and its breakdown in quantum spin chains with inhomogeneous interactions", Physical Review B 109 4, 045139 (2024).

[4] Xhek Turkeshi, Anatoly Dymarsky, and Piotr Sierant, "Pauli Spectrum and Magic of Typical Quantum Many-Body States", arXiv:2312.11631, (2023).

[5] Siddharth Jindal and Pavan Hosur, "Generalized Free Cumulants for Quantum Chaotic Systems", arXiv:2401.13829, (2024).

The above citations are from Crossref's cited-by service (last updated successfully 2024-07-15 18:16:17) and SAO/NASA ADS (last updated successfully 2024-07-15 18:16:18). The list may be incomplete as not all publishers provide suitable and complete citation data.