Capacity of Entanglement in Lifshitz Theories

TL;DR

This paper investigates the capacity of entanglement in Lifshitz theories, revealing its universal properties, dependence on the dynamical exponent, and behavior after quantum quenches, thus enriching understanding of quantum information in nonrelativistic critical systems.

Contribution

It introduces the capacity of entanglement as a measure in Lifshitz theories, analyzing its universal terms, RG flow behavior, and dynamics post-quench, which were not previously explored.

Findings

Capacity of entanglement exhibits universal terms at ground state.

The c-function based on capacity of entanglement is non-monotonic in Lifshitz theories.

Post-quench dynamics follow quasiparticle interpretation similar to entanglement entropy.

Abstract

We study the capacity of entanglement in certain integrable scale-invariant theories which exhibit Lifshitz scaling symmetry with a generic dynamical exponent z at the critical point. This measure characterizes the width of the eigenvalue spectrum of the reduced density matrix and is a quantum informational counterpart of heat capacity. We explore various aspects of capacity of entanglement, such as the corresponding universal terms for the ground state, its z-dependence and also its temporal evolution after a global quantum quench in two dimensions. We carefully examine the existence of a convenient entropic c-function based on this quantity both in bosonic and fermionic theories. While in the relativistic case the corresponding c-function displays a monotonic behavior under the RG flow, this is not the case for the nonrelativistic theories. We also investigate the dynamics of capacity of entanglement after a mass quench and show that it follows the quasiparticle interpretation for the spreading of entanglement. Finally, we discuss how these results are consistent with the behavior of other entanglement measures including the entanglement entropy.