Entanglement entropy in quantum spin chains with broken reflection symmetry

TL;DR

This paper analyzes how reflection symmetry breaking affects entanglement entropy in quantum spin chains, providing analytical and numerical results that reveal criticality conditions and asymptotic behaviors.

Contribution

It derives the large block size asymptotics of entanglement entropy for general and specific non-gauge-invariant models, extending previous symmetric case analyses.

Findings

Reflection symmetry in ground states is broken only at quantum critical points.

Asymptotic entropy behavior matches Calabrese-Cardy formula in large chains.

Anomalies in saturation entropy occur near critical lines for non-critical Hamiltonians.

Abstract

We investigate the entanglement entropy of a block of L sites in quasifree translation-invariant spin chains concentrating on the effect of reflection symmetry breaking. The majorana two-point functions corresponding to the Jordan-Wigner transformed fermionic modes are determined in the most general case; from these it follows that reflection symmetry in the ground state can only be broken if the model is quantum critical. The large L asymptotics of the entropy is calculated analytically for general gauge-invariant models, which has, until now, been done only for the reflection symmetric sector. Analytical results are also derived for certain non-gauge-invariant models, e.g., for the Ising model with Dzyaloshinskii-Moriya interaction. We also study numerically finite chains of length N with a non-reflection-symmetric Hamiltonian and report that the reflection symmetry of the entropy of the first L spins is violated but the reflection-symmetric Calabrese-Cardy formula is recovered asymptotically. Furthermore, for non-critical reflection-symmetry-breaking Hamiltonians, we find an anomaly in the behavior of the "saturation entropy" as we approach the critical line. The paper also provides a concise but extensive review of the block entropy asymptotics in translation invariant quasifree spin chains with an analysis of the nearest neighbor case and the enumeration of the yet unsolved parts of the quasifree landscape.