Entanglement Hamiltonian of the quantum N\'eel state

TL;DR

This paper investigates the entanglement Hamiltonian and spectrum of a quantum Ne9el state using PEPS, revealing unique features due to spontaneous SU(2) symmetry breaking in a two-dimensional antiferromagnet.

Contribution

It introduces a PEPS-based method to compute the entanglement Hamiltonian for a Ne9el state with broken symmetry, highlighting differences from symmetric ground states.

Findings

The entanglement Hamiltonian resembles a chain of dilute heavy and light hardcore bosons.

The entanglement spectrum differs significantly from that of SU(2)-symmetric states.

Long-range hoppings of light particles are observed in the entanglement Hamiltonian.

Abstract

Two-dimensional Projected Entangled Pair States (PEPS) provide a unique framework giving access to detailed entanglement features of correlated (spin or electronic) systems. For a bi-partitioned quantum system, it has been argued that the Entanglement Spectrum (ES) is in a one-to-one correspondence with the physical edge spectrum on the cut and that the structure of the corresponding Entanglement Hamiltonian (EH) reflects closely bulk properties (finite correlation length, criticality, topological order, etc...). However, entanglement properties of systems with spontaneously broken continuous symmetry are still not fully understood. The spin-1/2 square lattice Heisenberg antiferromagnet provides a simple example showing spontaneous breaking of SU(2) symmetry down to U(1). The ground state can be viewed as a "quantum N\'eel state" where the classical (N\'eel) staggered magnetization is reduced by quantum fluctuations. Here I consider the (critical) Resonating Valence Bond state doped with spinons to describe such a state, that enables to use the associated PEPS representation (with virtual bond dimension $D=3$) to compute the EH and the ES for a partition of an (infinite) cylinder. In particular, I find that the EH is (almost exactly) a chain of a dilute mixture of heavy ($\downarrow$ spins) and light ($\uparrow$ spins) hardcore bosons, where light particles are subject to long-range hoppings. The corresponding ES shows drastic differences with the typical ES obtained previously for ground states with restored SU(2)-symmetry (on finite systems).