Exact treatment of magnetism-driven ferroelectricity in the one-dimensional compass model

TL;DR

This paper provides an exact analysis of magnetism-driven ferroelectricity in a one-dimensional compass model with Dzyaloshinskii-Moriya interaction, revealing complex phase behavior, entanglement features, and temperature-dependent magnetoelectric effects.

Contribution

It offers an exact solution of the 1D compass model with Dzyaloshinskii-Moriya interaction, detailing phase transitions, ground-state properties, and finite-temperature effects.

Findings

Three distinct phases identified: ferromagnetic, canted antiferromagnetic, and chiral.

Dzyaloshinskii-Moriya interaction induces electrical polarization in the chiral phase.

Unique specific-heat and polarization behaviors due to frustration.

Abstract

We consider a class of one-dimensional compass models with antisymmetric Dzyaloshinskii-Moriya exchange interaction in an external magnetic field. Based on the exact solution derived by means of Jordan-Wigner transformation, we study the excitation gap, spin correlations, ground-state degeneracy, and critical properties at phase transitions. The phase diagram at finite electric and magnetic field consists of three phases: ferromagnetic, canted antiferromagnetic, and chiral. Dzyaloshinskii-Moriya interaction induces an electrical polarization in the ground state of the chiral phase, where the nonlocal string order and special features of entanglement spectra arise, while strong chiral correlations emerge at finite temperature in the other phases and are controlled by a gap between the nonchiral ground state and the chiral excitations. We further show that the magnetoelectric effects in all phases disappear above a typical temperature corresponding to the total bandwidth of the effective fermionic model. To this end we explore the entropy, specific heat, magnetization, electric polarization, and the magnetoelectric tensor at finite temperature. We identify rather peculiar specific-heat and polarization behavior of the compass model which follows from highly frustrated interactions.