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Eigenstate thermalization in (1+1)-dimensional SU(2) lattice gauge theory coupled with dynamical fermions

Diptarka Das1,*, Lukas Ebner2,3,4,†, Saurabh V. Kadam5,‡, Indrakshi Raychowdhury6,7,§, Andreas Schäfer2,∥, and Xiaojun Yao5,¶

  • *Contact author: didas@iitk.ac.in
  • †Contact author: lukas.ebner@mpq.mpg.de
  • ‡Contact author: ksaurabh@uw.edu
  • §Contact author: indrakshir@goa.bits-pilani.ac.in
  • ∥Contact author: andreas.schaefer@physik.uni-r.de
  • Contact author: xjyao@uw.edu
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Phys. Rev. D 113, 074514 – Published 20 April, 2026

DOI: https://doi.org/10.1103/19c2-k9x9

Abstract

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.

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Phys. Rev. D 113, 074514– Published 20 April, 2026
  • Received 20 October 2025
  • Accepted 26 March 2026
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