Entanglement spectroscopy of SU(2)-broken phases in two dimensions

TL;DR

This paper demonstrates that the entanglement spectrum in 2D antiferromagnetic models reveals signatures of SU(2) symmetry breaking, providing a new way to identify magnetic order through DMRG calculations.

Contribution

It establishes a correspondence between the tower of states in energy spectra and the low-lying entanglement spectrum levels in 2D magnetic systems, introducing entanglement spectroscopy as a diagnostic tool.

Findings

Entanglement spectrum shows low-lying levels analogous to tower of states.

Finite size scaling confirms the correspondence in the thermodynamic limit.

An entanglement gap separates TOS levels from higher entanglement spectrum levels.

Abstract

In magnetically ordered systems the breaking of SU(2) symmetry in the thermodynamic limit is associated with the appearance of a special type of low-lying excitations in finite size energy spectra, the so called tower of states (TOS). In the present work we numerically demonstrate that there is a correspondence between the SU(2) tower of states and the lower part of the ground state entanglement spectrum (ES). Using state-of-the-art DMRG calculations, we examine the ES of the 2D antiferromagnetic J1-J2 Heisenberg model on both the triangular and kagom\'e lattice. At large ferromagnetic J2 the model exhibits a magnetically ordered ground state. Correspondingly, its ES contains a family of low-lying levels that are reminiscent of the energy tower of states. Their behavior (level counting, finite size scaling in the thermodynamic limit) sharply reflects tower of states features, and is characterized in terms of an effective entanglement Hamiltonian that we provide. At large system sizes TOS levels are divided from the rest by an entanglement gap. Our analysis suggests that (TOS) entanglement spectroscopy provides an alternative tool for detecting and characterizing SU(2)-broken phases using DMRG.