Exact description of the magnetoelectric effect in the spin-1/2 XXZ-chain with Dzyaloshinskii-Moriya interaction

TL;DR

This paper provides an exact analytical description of the magnetoelectric effect in a spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction, revealing how magnetic and electric fields influence physical properties across temperatures.

Contribution

It introduces an exact solution for the magnetoelectric effect in an integrable spin chain model, connecting the Dzyaloshinskii-Moriya interaction to electric polarization and critical phenomena.

Findings

Multiple polarization regimes identified

Magnetic field can switch polarization states

Critical properties related to the magnetoelectric effect analyzed

Abstract

We consider a simple integrable model of a spin chain exhibiting the Magnetoelectric Effect (MEE). Starting from the periodic S=1/2 XXZ-chain with Dzyaloshinskii-Moriya terms, which we consider as a local electric polarization in the spirit of the Katsura-Nagaosa-Baladsky (KNB) mechanism, we perform the mapping onto the conventional XXZ-chain with twisted boundary conditions. Using the techniques of Quantum Transfer Matrix (QTM) and Non-Linear Integral Equations (NLIE) we obtain the magnetization, electric polarization and magnetoelectric tensor as functions of magnetic and electric field for arbitrary temperatures. We investigate these dependencies as well as the thermal behavior of the above mentioned physical quantities, especially in the low-temperature regime. We found several regimes of polarization. Adjusting the magnetic field one can switch the system from one regime to another. The features of the critical properties connected with the MEE are also illustrated.