Anomalous Thermalization in the 1D and 2D Quantum Ising Models: Presence of Rare States

Anomalous Thermalization in the 1D and 2D Quantum Ising Models: Presence of Rare States
Robert M. Konik, Brookhaven National Lab
Robert M. Konik
Date and time: Thu, Mar 21, 2019 - 11:30am
Refreshments at 11:15am
Location: LGRT 1033
Category: Condensed Matter Seminar
Abstract:

We consider the physics of the eigenstate thermalization hypothesis in the 1D and 2D quantum Ising models.  This hypothesis provides a way to understand the notion of thermalization in closed quantum systems.  It argues that if the expectation value of a physical observable with respect to an eigenstate of the system's Hamiltonian depends smoothly on the eigenstate's energy, thermalization will occur in the sense that the long time average of the observable will equal its microcanonical value.   We argue here that the eigenstate thermalization hypothesis appears to be violated in the 1D and 2D quantum Ising model because of the presence of so-called rare states, states whose expectation values deviate from the mean value at their eigenenergy.  These rare states appear in the ordered phases of these models in the presence of a longitudinal magnetic field.  Such a field leads to a profound restructuring of the excitation spectrum, with the low-energy two-excitation continuum being replaced by discrete ‘meson’ modes (linearly confined pairs of domain walls).  Such confined meson states are robust: they appear above the two meson threshold, due to a surprising lack of hybridization with the continuum.  The presence of such states in the spectrum is revealed in anomalous behavior after a quantum quench including the lack of a light cone and the suppression of the growth of entanglement entropy.  The work presented here is based on two papers,arXiv:1808.10782 and 1804.09990.