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EPJ Web of Conferences

Testing eigenstate thermalization hypothesis for non-Abelian gauge theories

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

Published Jan 1, 2024• 3 citations
Publisher

Abstract

We report on progress in full quantum understanding of thermalization in non-Abelian gauge theories. Specifically, we test the eigenstate thermalization hypothesis for (2+1)-dimensional SU(2) lattice gauge theory.
DOI
10.1051/epjconf/202429613008

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Abstract The existence of p-form symmetry in a (d + 1)-dimensional quantum field is known to always lead to the breakdown of the eigenstate thermalization hypothesis for certain (d − p)-dimensional operators other than symmetry operators under some assumptions. The assumptions include the mixing of symmetry sectors within a given energy shell, which is rather challenging to verify because it requires information on the eigenstates in the middle of the spectrum. We reconsider this assumption from the viewpoint of projective representations to avoid this difficulty. In the case of ZN\mathbb {Z}_NZN​ symmetries, we can circumvent the difficulty by considering ZN×ZN\mathbb {Z}_N\times \mathbb {Z}_NZN​×ZN​-symmetric theories with nontrivial projective phases, and perturbing the Hamiltonian while preserving one of the ZN\mathbb {Z}_NZN​ symmetries of our interest. We also perform numerical analyses for (1 + 1)-dimensional spin chains and the (2 + 1)-dimensional Z2\mathbb {Z}_2Z2​ lattice gauge theory.
We test the eigenstate thermalization hypothesis (ETH) in 1 + 1 -dimensional SU(2) lattice gauge theory (LGT) with one flavor of dynamical fermions. Using the loop-string-hadron framework of the LGT with a bosonic cutoff, we exactly diagonalize the Hamiltonian for finite size systems and calculate matrix elements (MEs) in the eigenbasis for both local and nonlocal operators. We analyze different indicators to identify the parameter space for quantum chaos at finite lattice sizes and investigate how the ETH behavior emerges in both the diagonal and off-diagonal MEs. Our investigations allow us to study various timescales of thermalization and the emergence of random matrix behavior, and highlight the interplays of the several diagnostics with each other. Furthermore, from the off-diagonal MEs, we extract a smooth function that is closely related to the spectral function for both local and nonlocal operators. We find numerical evidence of the spectral gap and the memory peak in the nonlocal operator case. Finally, we investigate aspects of subsystem ETH in the lattice gauge theory and identify certain features in the subsystem reduced density matrix that are unique to gauge theories.
We test the eigenstate thermalization hypothesis (ETH) for 2+12+12+1 dimensional SU(2) lattice gauge theory. By considering the theory on a chain of plaquettes and truncating basis states for link variables at j=1/2j=1/2j=1/2, we can map it onto a quantum spin chain with local interactions and numerically exactly diagonalize the Hamiltonian for reasonably large lattice sizes. We find energy level repulsion in momentum sectors with no remaining discrete symmetry. We study two local observables made up of Wilson loops and calculate their matrix elements in the energy eigenbasis, which are shown consistent with the ETH.