Eigenstate thermalization in ( 2 + 1 )-dimensional SU(2) lattice gauge theory

Ebner, Lukas; Schäfer, Andreas; Seidl, Clemens; Müller, Berndt; Yao, Xiaojun

doi:10.1103/PhysRevD.109.014504

Eigenstate thermalization in ( $2 + 1$ )-dimensional SU(2) lattice gauge theory

Journal Article · Mon Jan 08 23:00:00 EST 2024 · Physical Review. D.

DOI:https://doi.org/10.1103/PhysRevD.109.014504· OSTI ID:2280441

Ebner, Lukas; Schäfer, Andreas; ; ;

We present preliminary numerical evidence for the hypothesis that the Hamiltonian SU(2) gauge theory discretized on a lattice obeys the eigenstate thermalization hypothesis (ETH). To do so we study three approximations: (a) a linear plaquette chain in a reduced Hilbert space limiting the electric field basis to $j = 0, \frac{1}{2}$ , (b) a two-dimensional honeycomb lattice with periodic or closed boundary condition and the same Hilbert space constraint, and (c) a chain of only three plaquettes but such a sufficiently large electric field Hilbert space ( $j \leq \frac{7}{2}$ ) that convergence of all energy eigenvalues in the analyzed energy window is observed. While an unconstrained Hilbert space is required to reach the continuum limit of SU(2) gauge theory, numerical resource constraints do not permit us to realize this requirement for all values of the coupling constant and large lattices. In each of the three studied cases we check first for random matrix theory (RMT) behavior in the eigenenergy spectrum and then analyze the diagonal as well as the off-diagonal matrix elements between energy eigenstates for a few operators. Within current uncertainties all results for (a), (b) and (c) agree with ETH predictions. Furthermore, we find the off-diagonal matrix elements of the electric energy operator exhibit RMT behavior in frequency windows that are small enough in (b) and (c). To unambiguously establish ETH behavior and determine for which class of operators it applies, an extension of our investigations is necessary.

Published by the American Physical Society 2024

View Journal Article

Sponsoring Organization:: USDOE Office of Science (SC), Nuclear Physics (NP)

Grant/Contract Number:: FG02-05ER41367; SC0020970

OSTI ID:: 2280441

Alternate ID(s):: OSTI ID: 2352118

Journal Information:: Physical Review. D., Journal Name: Physical Review. D. Journal Issue: 1 Vol. 109; ISSN PRVDAQ; ISSN 2470-0010

Publisher:: American Physical SocietyCopyright Statement

Country of Publication:: United States

Language:: English

References (50)

Colliding localized, lumpy holographic shocks with a granular nuclear structure Waeber, Sebastian; Yaffe, Laurence G. Journal of High Energy Physics, Vol. 2023, Issue 3 https://doi.org/10.1007/JHEP03(2023)208	journal	March 2023
Scaling and adiabaticity in a rapidly expanding gluon plasma Brewer, Jasmine; Scheihing-Hitschfeld, Bruno; Yin, Yi Journal of High Energy Physics, Vol. 2022, Issue 5 https://doi.org/10.1007/JHEP05(2022)145	journal	May 2022
String-net formulation of Hamiltonian lattice Yang-Mills theories and quantum many-body scars in a nonabelian gauge theory Hayata, Tomoya; Hidaka, Yoshimasa Journal of High Energy Physics, Vol. 2023, Issue 9 https://doi.org/10.1007/JHEP09(2023)126	journal	September 2023
Thermalization in weakly coupled nonabelian plasmas Kurkela, Aleksi; Moore, Guy D. Journal of High Energy Physics, Vol. 2011, Issue 12 https://doi.org/10.1007/JHEP12(2011)044	journal	December 2011
Lyapunov exponent of classical SU(3) gauge theory Gong, C. Physics Letters B, Vol. 298, Issue 3-4 https://doi.org/10.1016/0370-2693(93)91816-6	journal	January 1993
Variational approach to real-time evolution of Yang-Mills gauge fields on the lattice Gong, C.; Müller, B.; Biró, T. S. Nuclear Physics A, Vol. 568, Issue 4 https://doi.org/10.1016/0375-9474(94)90357-3	journal	February 1994
Thermalization and its mechanism for generic isolated quantum systems Rigol, Marcos; Dunjko, Vanja; Olshanii, Maxim Nature, Vol. 452, Issue 7189 https://doi.org/10.1038/nature06838	journal	April 2008
Quantum simulation of fundamental particles and forces Bauer, Christian W.; Davoudi, Zohreh; Klco, Natalie Nature Reviews Physics, Vol. 5, Issue 7 https://doi.org/10.1038/s42254-023-00599-8	journal	June 2023
From quantum chaos and eigenstate thermalization to statistical mechanics and thermodynamics D'Alessio, Luca; Kafri, Yariv; Polkovnikov, Anatoli Advances in Physics, Vol. 65, Issue 3 https://doi.org/10.1080/00018732.2016.1198134	journal	May 2016
Can transport peak explain the low-mass enhancement of dileptons at RHIC? Akamatsu, Y.; Hamagaki, H.; Hatsuda, T. Journal of Physics G: Nuclear and Particle Physics, Vol. 38, Issue 12 https://doi.org/10.1088/0954-3899/38/12/124184	journal	November 2011
Thermalization and prethermalization in isolated quantum systems: a theoretical overview Mori, Takashi; Ikeda, Tatsuhiko N.; Kaminishi, Eriko Journal of Physics B: Atomic, Molecular and Optical Physics, Vol. 51, Issue 11 https://doi.org/10.1088/1361-6455/aabcdf	journal	May 2018
Quantum statistical mechanics in a closed system Deutsch, J. M. Physical Review A, Vol. 43, Issue 4 https://doi.org/10.1103/PhysRevA.43.2046	journal	February 1991
Simulating lattice gauge theories on a quantum computer Byrnes, Tim; Yamamoto, Yoshihisa Physical Review A, Vol. 73, Issue 2 https://doi.org/10.1103/PhysRevA.73.022328	journal	February 2006
Localization of interacting fermions at high temperature Oganesyan, Vadim; Huse, David A. Physical Review B, Vol. 75, Issue 15 https://doi.org/10.1103/PhysRevB.75.155111	journal	April 2007
Eigenstate thermalization and quantum chaos in the Holstein polaron model Jansen, David; Stolpp, Jan; Vidmar, Lev Physical Review B, Vol. 99, Issue 15 https://doi.org/10.1103/PhysRevB.99.155130	journal	April 2019
Mechanism of macroscopic equilibration of isolated quantum systems Dymarsky, Anatoly Physical Review B, Vol. 99, Issue 22 https://doi.org/10.1103/PhysRevB.99.224302	journal	June 2019
SU(2) non-Abelian gauge field theory in one dimension on digital quantum computers Klco, Natalie; Savage, Martin J.; Stryker, Jesse R. Physical Review D, Vol. 101, Issue 7 https://doi.org/10.1103/PhysRevD.101.074512	journal	April 2020
Trailhead for quantum simulation of SU(3) Yang-Mills lattice gauge theory in the local multiplet basis Ciavarella, Anthony; Klco, Natalie; Savage, Martin J. Physical Review D, Vol. 103, Issue 9 https://doi.org/10.1103/PhysRevD.103.094501	journal	May 2021
SU(2) lattice gauge theory on a quantum annealer A. Rahman, Sarmed; Lewis, Randy; Mendicelli, Emanuele Physical Review D, Vol. 104, Issue 3 https://doi.org/10.1103/PhysRevD.104.034501	journal	August 2021
Thermalization of non-Abelian gauge theories at next-to-leading order Fu, Yu; Ghiglieri, Jacopo; Iqbal, Shahin Physical Review D, Vol. 105, Issue 5 https://doi.org/10.1103/PhysRevD.105.054031	journal	March 2022
Self-mitigating Trotter circuits for SU(2) lattice gauge theory on a quantum computer A. Rahman, Sarmed; Lewis, Randy; Mendicelli, Emanuele Physical Review D, Vol. 106, Issue 7 https://doi.org/10.1103/PhysRevD.106.074502	journal	October 2022
Simple Hamiltonian for quantum simulation of strongly coupled (2+1)D SU(2) lattice gauge theory on a honeycomb lattice Müller, Berndt; Yao, Xiaojun Physical Review D, Vol. 108, Issue 9 https://doi.org/10.1103/PhysRevD.108.094505	journal	November 2023
SU(2) gauge theory in 2+1 dimensions on a plaquette chain obeys the eigenstate thermalization hypothesis Yao, Xiaojun Physical Review D, Vol. 108, Issue 3 https://doi.org/10.1103/PhysRevD.108.L031504	journal	August 2023
Hamiltonian formulation of Wilson's lattice gauge theories Kogut, John; Susskind, Leonard Physical Review D, Vol. 11, Issue 2 https://doi.org/10.1103/PhysRevD.11.395	journal	January 1975
Phase diagram of QCD Halasz, M. A.; Jackson, A. D.; Shrock, R. E. Physical Review D, Vol. 58, Issue 9 https://doi.org/10.1103/PhysRevD.58.096007	journal	September 1998
Ergodic properties of classical SU(2) lattice gauge theory Bolte, J.; Müller, B.; Schäfer, A. Physical Review D, Vol. 61, Issue 5 https://doi.org/10.1103/PhysRevD.61.054506	journal	February 2000
Holographic thermalization Balasubramanian, V.; Bernamonti, A.; de Boer, J. Physical Review D, Vol. 84, Issue 2 https://doi.org/10.1103/PhysRevD.84.026010	journal	July 2011
Formulation of lattice gauge theories for quantum simulations Zohar, Erez; Burrello, Michele Physical Review D, Vol. 91, Issue 5 https://doi.org/10.1103/PhysRevD.91.054506	journal	March 2015
Charge transport and vector meson dissociation across the thermal phase transition in lattice QCD with two light quark flavors Brandt, Bastian B.; Francis, Anthony; Jäger, Benjamin Physical Review D, Vol. 93, Issue 5 https://doi.org/10.1103/PhysRevD.93.054510	journal	March 2016
Quantum chaos, thermalization, and entanglement generation in real-time simulations of the Banks-Fischler-Shenker-Susskind matrix model Buividovich, P. V.; Hanada, M.; Schäfer, A. Physical Review D, Vol. 99, Issue 4 https://doi.org/10.1103/PhysRevD.99.046011	journal	February 2019
Eigenstate thermalization hypothesis beyond standard indicators: Emergence of random-matrix behavior at small frequencies Richter, Jonas; Dymarsky, Anatoly; Steinigeweg, Robin Physical Review E, Vol. 102, Issue 4 https://doi.org/10.1103/PhysRevE.102.042127	journal	October 2020
Chaos and quantum thermalization Srednicki, Mark Physical Review E, Vol. 50, Issue 2 https://doi.org/10.1103/PhysRevE.50.888	journal	August 1994
Quantum systems equilibrate rapidly for most observables Malabarba, Artur S. L.; García-Pintos, Luis Pedro; Linden, Noah Physical Review E, Vol. 90, Issue 1 https://doi.org/10.1103/PhysRevE.90.012121	journal	July 2014
Testing whether all eigenstates obey the eigenstate thermalization hypothesis Kim, Hyungwon; Ikeda, Tatsuhiko N.; Huse, David A. Physical Review E, Vol. 90, Issue 5 https://doi.org/10.1103/PhysRevE.90.052105	journal	November 2014
Eigenstate thermalization in the two-dimensional transverse field Ising model Mondaini, Rubem; Fratus, Keith R.; Srednicki, Mark Physical Review E, Vol. 93, Issue 3 https://doi.org/10.1103/PhysRevE.93.032104	journal	March 2016
Thermalization of Strongly Coupled Field Theories Balasubramanian, V.; Bernamonti, A.; de Boer, J. Physical Review Letters, Vol. 106, Issue 19 https://doi.org/10.1103/PhysRevLett.106.191601	journal	May 2011
Distribution of the Ratio of Consecutive Level Spacings in Random Matrix Ensembles Atas, Y. Y.; Bogomolny, E.; Giraud, O. Physical Review Letters, Vol. 110, Issue 8 https://doi.org/10.1103/PhysRevLett.110.084101	journal	February 2013
Parton Physics on a Euclidean Lattice Ji, Xiangdong Physical Review Letters, Vol. 110, Issue 26 https://doi.org/10.1103/PhysRevLett.110.262002	journal	June 2013
Time Scales in the Approach to Equilibrium of Macroscopic Quantum Systems Goldstein, Sheldon; Hara, Takashi; Tasaki, Hal Physical Review Letters, Vol. 111, Issue 14 https://doi.org/10.1103/PhysRevLett.111.140401	journal	October 2013
Transport Peak in the Thermal Spectral Function of N = 4 Supersymmetric Yang-Mills Plasma at Intermediate Coupling Casalderrey-Solana, Jorge; Grozdanov, Sašo; Starinets, Andrei O. Physical Review Letters, Vol. 121, Issue 19 https://doi.org/10.1103/PhysRevLett.121.191603	journal	November 2018
Time Evolution of Correlation Functions in Quantum Many-Body Systems Alhambra, Álvaro M.; Riddell, Jonathon; García-Pintos, Luis Pedro Physical Review Letters, Vol. 124, Issue 11 https://doi.org/10.1103/PhysRevLett.124.110605	journal	March 2020
Eigenstate Thermalization Hypothesis and Its Deviations from Random-Matrix Theory beyond the Thermalization Time Wang, Jiaozi; Lamann, Mats H.; Richter, Jonas Physical Review Letters, Vol. 128, Issue 18 https://doi.org/10.1103/PhysRevLett.128.180601	journal	May 2022
Thermalization of Gauge Theories from their Entanglement Spectrum Mueller, Niklas; Zache, Torsten V.; Ott, Robert Physical Review Letters, Vol. 129, Issue 1 https://doi.org/10.1103/PhysRevLett.129.011601	journal	June 2022
Quantum and Classical Spin-Network Algorithms for q -Deformed Kogut-Susskind Gauge Theories Zache, Torsten V.; González-Cuadra, Daniel; Zoller, Peter Physical Review Letters, Vol. 131, Issue 17 https://doi.org/10.1103/PhysRevLett.131.171902	journal	October 2023
Deterministic chaos in non-Abelian lattice gauge theory Müller, Berndt; Trayanov, Atanas Physical Review Letters, Vol. 68, Issue 23 https://doi.org/10.1103/PhysRevLett.68.3387	journal	June 1992
Microscopic Universality in the Spectrum of the Lattice Dirac Operator Berbenni-Bitsch, M. E.; Meyer, S.; Schäfer, A. Physical Review Letters, Vol. 80, Issue 6 https://doi.org/10.1103/PhysRevLett.80.1146	journal	February 1998
The kernel polynomial method Weiße, Alexander; Wellein, Gerhard; Alvermann, Andreas Reviews of Modern Physics, Vol. 78, Issue 1 https://doi.org/10.1103/RevModPhys.78.275	journal	March 2006
Simulating lattice gauge theories within quantum technologies Bañuls, Mari Carmen; Blatt, Rainer; Catani, Jacopo The European Physical Journal D, Vol. 74, Issue 8 https://doi.org/10.1140/epjd/e2020-100571-8	journal	August 2020
High Energy Nuclear Events Fermi, E. Progress of Theoretical Physics, Vol. 5, Issue 4 https://doi.org/10.1143/ptp/5.4.570	journal	July 1950
Random Matrix Theory and Chiral Symmetry in QCD Verbaarschot, J. J. M.; Wettig, T. Annual Review of Nuclear and Particle Science, Vol. 50, Issue 1 https://doi.org/10.1146/annurev.nucl.50.1.343	journal	December 2000

Similar Records

Classical and quantum computing of shear viscosity for

(2 + 1) D

SU(2) gauge theory

Journal Article · Thu Jun 13 00:00:00 EDT 2024 · Physical Review. D. · OSTI ID:2474447

Entanglement entropy of (

2 + 1

)-dimensional SU(2) lattice gauge theory on plaquette chains

Journal Article · Tue Jul 09 00:00:00 EDT 2024 · Physical Review. D. · OSTI ID:2396396

Emergent hydrodynamic mode on SU(2) plaquette chains and quantum simulation

Journal Article · Mon May 05 00:00:00 EDT 2025 · Physical Review. D. · OSTI ID:2564511

Eigenstate thermalization in ( 2 + 1 )-dimensional SU(2) lattice gauge theory

Citation Formats

References (50)

Similar Records

Related Subjects

Eigenstate thermalization in ( $2 + 1$ )-dimensional SU(2) lattice gauge theory