Entanglement, combinatorics and finite-size effects in spin-chains

TL;DR

This paper provides exact analytical expressions for the reduced density matrices and entanglement properties of finite segments in an XXZ spin chain at a specific anisotropy, revealing detailed entanglement structure and scaling behavior.

Contribution

It introduces the first explicit analytic formulas for reduced density matrices of small segments in an interacting spin chain, enabling detailed entanglement analysis.

Findings

Exact formulas for reduced density matrices for segments of up to 6 spins.

Derived entanglement entropy and spectrum for the model.

Identified scaling behavior of entanglement in the ground state.

Abstract

We carry out a systematic study of the exact block entanglement in XXZ spin-chain at Delta=-1/2. We present, the first analytic expressions for reduced density matrices of n spins in a chain of length L (for n<=6 and arbitrary but odd L) of a truly interacting model. The entanglement entropy, the moments of the reduced density matrix, and its spectrum are then easily derived. We explicitely construct the "entanglement Hamiltonian" as the logarithm of this matrix. Exploiting the degeneracy of the ground-state, we find the scaling behavior of entanglement of the zero-temperature mixed state.