Exact density matrix for quantum group invariant sector of XXZ model

TL;DR

This paper derives the exact density matrix for the U_q(sl2)-invariant sector of the XXZ model on 8 sites, enabling precise entanglement entropy calculations and comparison with conformal field theory predictions.

Contribution

It provides the first explicit construction of the density matrix for the U_q(sl2)-invariant sector of the XXZ model on 8 sites using a fermionic basis.

Findings

Computed entanglement entropy at various temperatures.

Confirmed agreement with conformal field theory predictions.

Provided explicit density matrix for the invariant sector.

Abstract

Using the fermionic basis we obtain the expectation values of all $U_q(\slt)$-invariant local operators on 8 sites for the anisotropic six-vertex model on a cylinder with generic Matsubara data. In the case when the $U_q(\slt)$ symmetry is not broken this computation is equivalent to finding the entire density matrix up to 8 sites. As application, we compute the entanglement entropy without and with temperature, and compare the results with CFT predictions.