Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids

TL;DR

This paper investigates the structure and properties of the entanglement spectrum in critical spin chains, revealing conformal and thermal features, and introduces spin-resolved entanglement entropies with notable scaling behaviors.

Contribution

It provides a detailed analysis of the reduced density matrix in critical XXZ spin chains, exploring conformal structure, entanglement Hamiltonian, and introduces spin-resolved entanglement entropies.

Findings

Conformal structure of entanglement spectra confirmed

Thermal-quantum correspondence established for reduced density matrices

Spin-resolved entanglement entropies exhibit unique scaling behaviors

Abstract

Quantum critical chains are well described and understood by virtue of conformal field theory. Still the meaning of the real space entanglement spectrum -- the eigenvalues of the reduced density matrix -- of such systems remains in general elusive, even when there is an additional quantum number available such as spin or particle number. In this paper we explore in details the properties and the structure of the reduced density matrix of critical XXZ spin-$\frac{1}{2}$ chains. We investigate the quantum/thermal correspondence between the reduced density matrix of a $T=0$ pure quantum state and the thermal density matrix of an effective entanglement Hamiltonian. Using large scale DMRG and QMC simulations, we investigate the conformal structure of the spectra, the entanglement Hamiltonian and temperature. We then introduce the notion of spin-resolved entanglement entropies which display interesting scaling features.