New exact results on density matrix for XXX spin chain

TL;DR

This paper derives exact density matrix expectation values for the XXX spin chain's generalized Gibbs ensemble, enabling precise entanglement entropy calculations and comparisons with conformal field theory predictions.

Contribution

It provides new exact results for the density matrix of the XXX spin chain using fermionic basis methods, covering up to 10 sites with general Matsubara data.

Findings

Exact expectation values for local operators on 10 sites

Computed entanglement entropy at various temperatures

Validated results against conformal field theory predictions

Abstract

Using the fermionic basis we obtain the expectation values of all $\slt$-invariant and $C$-invariant local operators on 10 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. This is equivalent to the generalised Gibbs ensemble for the XXX spin chain. In the case when the $\slt$ and $C$ symmetries are not broken this computation is equivalent to finding the entire density matrix up to 10 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.