Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry

Osamu Fukushima; Ryusuke Hamazaki

doi:10.1103/PhysRevLett.131.131602

paper

Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry

arXiv:2305.04984 · doi:10.1103/PhysRevLett.131.131602

Abstract

We elucidate how the presence of higher-form symmetries affects the dynamics of thermalization in isolated quantum systems. Under reasonable assumptions, we analytically show that a $p$ -form symmetry in a $(d + 1)$ -dimensional quantum field theory leads to the breakdown of the eigenstate thermalization hypothesis for many nontrivial $(d - p)$ -dimensional observables. For higher-form (i.e., $p \geq 1$ ) symmetry, this indicates the absence of thermalization for observables that are non-local but much smaller than the whole system size. We numerically demonstrate this argument for the (2+1)-dimensional $Z_{2}$ lattice gauge theory. While local observables such as the plaquette operator thermalize, the non-local observable exciting a magnetic dipole instead relaxes to the generalized Gibbs ensemble that takes account of the $Z_{2}$ 1-form symmetry.

arXiv comment7 pages, 4 figures, supplemental material with 6 pages and 1 figure; v2: minor modifications, references added, published version in PRL

Violation of Eigenstate Thermalization Hypothesis in Quantum Field Theories with Higher-Form Symmetry

Abstract

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