Heisenberg spin- 12 XXZ chain in the presence of electric and magnetic fields

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 Néel 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 Néel 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.

Criticality and factorization in the Heisenberg chain with Dzyaloshinskii-Moriya interaction

“…To proceed, we examine the relation between the quantum-information quantifier with QPTs in the presence of anisotropy term ∆. For axial regime ∆ 1 (∆ −1), the system effectively stays in the Néel (fer- romagnetic) phase [26]. In the following, we concentrate on the planar regime (|∆| < 1).…”

“…The effects induced by external electric and magnetic fields have been of particular interest since the magnetic state can be qualitatively different depending on the magnitude and direction of the external fields. This has led to interest in the study of QPTs at finite fields [25][26][27].…”

Spin-1/2 XY chain magnetoelectric: Effect of zigzag geometry

“…[12,13] were further confirmed in Refs. [16,17]. The link between DM-terms and the quantum phase transitions of a generalized compass chain with staggered Dzyaloshinskii-Moriya interaction was also considered recently 18 .…”

“…However, by virtue of its complexity the model (1.2) allows only numerical treatment. Nevertheless, the exact solutions of the simplified spin models demonstrating the MEE due to KNB mechanism are very important as they can shed light on the general universal properties of the magnetoelectrics and offer a unique opportunity to figure out their general features analytically [12][13][14][15][16][17][18] . In one of the previous works the integrable model of the S = 1/2 XXZ chain with DMinteraction has been considered as a model of the linear spin-chain with the KNB mechanism 12 .…”

Influence of XY anisotropy on a magnetoelectric effect in spin-1/2 XY chain in a transverse magnetic field

“…The recent few years were marked by an interest toward exact and numerical investigation of onedimensional quantum spin models with KNB mechanism. Exact description (for some models supplemented with numerics) for the MEE is available so far only for simplified models, such as strictly linear integrable X X Z chain [23], the same system but in both longitudinal and transverse fields [24], spin-1/2 XY Z chain [25], the spin-1/2 XY chain with three-spin interaction [26][27][28], generalized quantum compass model with magnetoelectric coupling [30], spin-1/2 Heisenberg-Ising ladder [31]. However, exact results are very helpful for understanding the general features of the phenomena.…”