Entanglement spectrum degeneracy and Cardy formula in 1+1 dimensional conformal field theories

TL;DR

This paper explores how boundary-induced degeneracies in the entanglement spectrum of 1+1D conformal field theories relate to the Cardy formula, revealing how non-integer degeneracies influence entanglement measures.

Contribution

It establishes a direct connection between entanglement spectrum degeneracies and the Cardy formula, clarifying the impact of boundary conditions on entanglement properties in conformal field theories.

Findings

Degeneracy in entanglement spectrum linked to boundary conditions.

Non-integer degeneracy affects the spectrum of partial transpose.

Analytical evidence from integrable spin-chains supports the results.

Abstract

We investigate the effect of a global degeneracy in the distribution of entanglement spectrum in conformal field theories in one spatial dimension. We relate the recently found universal expression for the entanglement hamiltonian to the distribution of the entanglement spectrum. The main tool to establish this connection is the Cardy formula. It turns out that the Affleck-Ludwig non-integer degeneracy, appearing because of the boundary conditions induced at the entangling surface, can be directly read from the entanglement spectrum distribution. We also clarify the effect of the non-integer degeneracy on the spectrum of the partial transpose, which is the central object for quantifying the entanglement in mixed states. We show that the exact knowledge of the entanglement spectrum in some integrable spin-chains provides strong analytical evidences corroborating our results.