Probing RG flows, symmetry resolution and quench dynamics through the capacity of entanglement

TL;DR

This paper investigates the capacity of entanglement in free bosonic and fermionic models, comparing it with entanglement entropy, and explores its behavior under RG flow, symmetry resolution, and quench dynamics.

Contribution

It introduces the capacity of entanglement as a new tool, analyzing its differences from entanglement entropy and its monotonic behavior under RG flow in various models.

Findings

Capacity of entanglement shows distinct subleading terms for disjoint intervals.

Defined $c$-functions based on capacity exhibit monotonic RG flow behavior.

Capacity of entanglement effectively probes symmetry resolution and quench dynamics.

Abstract

We compare the capacity of entanglement with the entanglement entropy by considering various aspects of these quantities for free bosonic and fermionic models in one spatial dimension, both in the continuum and on the lattice. Substantial differences are observed in the subleading terms of these entanglement quantifiers when the subsystem is made by two disjoint intervals, in the massive scalar field and in the fermionic chain. We define $c$-functions based on the capacity of entanglement similar to the one based on the entanglement entropy, showing through a numerical analysis that they display a monotonic behaviour under the renormalisation group flow generated by the mass. The capacity of entanglement and its related quantities are employed to explore the symmetry resolution. The temporal evolutions of the capacity of entanglement and of the corresponding contour function after a global quench are also discussed.