Thermal Correction to Entanglement Spectrum for Conformal Field Theories

TL;DR

This paper analytically computes the thermal correction to the entanglement spectrum in 2D conformal field theories, revealing how temperature influences eigenvalue distribution and enabling extraction of universal conformal data, supported by numerical simulations.

Contribution

It provides the first analytical derivation of thermal corrections to the entanglement spectrum in CFTs, including symmetry resolution, at low temperatures.

Findings

Thermal corrections decrease large eigenvalues and increase small eigenvalues in the spectrum.

The corrections depend on the first excited state's scaling dimension and degeneracy.

Numerical simulations confirm the analytical results for free fermions.

Abstract

We calculate the thermal correction to the entanglement spectrum for separating a single interval of two dimensional conformal field theories. Our derivation is a direct extension of the thermal correction to the R\'enyi entropy. Within a low-temperature expansion by including only the first excited state in the thermal density matrix, we approach analytical results of the thermal correction to the entanglement spectrum at both of the small and large interval limit. We find the temperature correction reduces the large eigenvalues in the entanglement spectrum while increases the small eigenvalues in the entanglement spectrum, leading to an overall crossover changing pattern of the entanglement spectrum. Crucially, at low-temperature limit, the thermal corrections are dominated by the first excited state and depend on its scaling dimension $\Delta$ and degeneracy $g$. This opens an avenue to extract universal information of underlying conformal data via the thermal entanglement spectrum. All of these analytical computation is supported from numerical simulations using 1+1 dimensional free fermion. Finally, we extend our calculation to resolve the thermal correction to the symmetry-resolved entanglement spectrum.