The Heisenberg spin-1/2 XXZ chain in the presence of electric and magnetic fields

TL;DR

This paper investigates how electric and magnetic fields influence the phase diagram and order parameters of a one-dimensional Heisenberg spin-1/2 XXZ chain with Dzyaloshinskii-Moriya interaction, revealing tunable phase transitions and chiral order.

Contribution

It provides a detailed phase diagram of the XXZ chain under combined electric and magnetic fields using DMRG, highlighting the effects of these fields on phase boundaries and order parameters.

Findings

Electric field shifts phase boundaries without creating new phases.

Transverse magnetic field induces vector chiral order in the Néel phase.

External fields can tune between gapped and gapless phases.

Abstract

We study the interplay of electric and magnetic order in the one dimensional Heisenberg spin-1/2 XXZ chain with large Ising anisotropy in the presence of the Dzyaloshinskii-Moriya (D-M) interaction and with longitudinal and transverse magnetic fields, interpreting the D-M interaction as a coupling between the local electric polarization and an external electric field. We obtain the ground state phase diagram using the density matrix renormalization group method and compute various ground state quantities like the magnetization, staggered magnetization, electric polarization and spin correlation functions, etc. In the presence of both longitudinal and transverse magnetic fields, there are three different phases corresponding to a gapped N\'{e}el phase with antiferromagnetic (AF) order, gapped saturated phase and a critical incommensurate gapless phase. The external electric field modifies the phase boundaries but does not lead to any new phases. Both external magnetic fields and electric fields can be used to tune between the phases. We also show that the transverse magnetic field induces a vector chiral order in the N\'{e}el phase (even in the absence of an electric field) which can be interpreted as an electric polarization in a direction parallel to the AF order.