Brookhaven National Lab
Rare States and Anomalous Thermalization in the 1D and 2D Quantum Ising Model
We show that confinement in the Ising model leads to rare atypical (nonthermal) eigenstates, in both continuum and lattice theories, in both one (1D) and two dimensions (2D) (arXiv:1808.10782 and 1804.09990). In the ordered phase, the presence of a confining longitudinal field leads to a profound restructuring of the excitation spectrum, with the low-energy two-particle continuum being replaced by discrete ‘meson’ modes (linearly confined pairs of domain walls). These modes are atypical, in the sense that expectation values in the state with energy E do not agree with the microcanonical (thermal) ensemble constructed at the same energy. Single meson states persist above the two meson threshold, due to a surprising lack of hybridization with the continuum that can be understood from analytical calculations. The presence of such states in the spectrum is revealed in anomalous post-quench dynamics, such as the lack of a light cone and the suppression of the growth of entanglement entropy.