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Physical review. E

Incommensurability and phase transitions in two-dimensional XY models with Dzyaloshinskii-Moriya interactions

Huiping Liu, J. A. Plascak, D. P. Landau

Published May 15, 2018• 5 citations
Publisher

Abstract

The Dzyaloshinskii-Moriya (DM) interaction in magnetic models is the result of a combination of superexchange and spin-orbital coupling, and it can give rise to rich phase-transition behavior. In this paper, we study ferromagnetic XY models with the DM interaction on two-dimensional L×L square lattices using a hybrid Monte Carlo algorithm. To match the incommensurability between the resultant spin structure and the lattice due to the DM interaction, a fluctuating boundary condition is adopted. We also define a different kind of order parameter and use finite-size scaling to study the critical properties of this system. We find that a Kosterlitz-Thouless-like phase transition appears in this system and that the phase-transition temperature shifts toward higher temperature with increasing DM interaction strength.

DOI
10.1103/physreve.97.052118

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The Dzyaloshinskii-Moriya (DM) interaction in magnetic models is the result of a combination of superexchange and spin-orbital coupling, and it can give rise to rich phase-transition behavior. In this paper, we study ferromagnetic XY models with the DM interaction on two-dimensional L×L square lattices using a hybrid Monte Carlo algorithm. To match the incommensurability between the resultant spin structure and the lattice due to the DM interaction, a fluctuating boundary condition is adopted. We also define a different kind of order parameter and use finite-size scaling to study the critical properties of this system. We find that a Kosterlitz-Thouless-like phase transition appears in this system and that the phase-transition temperature shifts toward higher temperature with increasing DM interaction strength.
Using the density-matrix renormalization-group algorithm (DMRG) and a finite-size scaling analysis, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. The model shows a rich phase diagram: depending on the value of the coupling constants, the system can display different kinds of ferromagnetic order and Luttinger-liquid behavior. Transitions from ferromagnetic to Luttinger-liquid phases are first order. We thoroughly discuss the transition between different ferromagnetic phases, which, in the absence of DM interactions, belongs to the XX universality class. We provide evidence that the DM exchange term turns out to split this critical line into two separated Ising-like transitions and that in between a disordered phase may appear. Our study sheds light on the general problem of strongly-interacting spin-orbit-coupled bosonic gases trapped in an optical lattice and can be used to characterize the topological properties of superconducting nanowires in the presence of an imposed supercurrent and of interactions.
We investigate phase transitions of the XY model on a two-layer square lattice which consists of a Villain plane ( J ) and a ferromagnetic plane ( I ), using Monte Carlo simulations and a histogram method. Depending on the values of interaction parameters ( I , J ), the system presents three phases: namely, a Kosterlitz–Thouless (KT) phase in which the two planes are critical for I predominant over J , a chiral phase in which the two planes have a chiral order for J predominant over I and a new phase in which only the Villain plane has a chiral order and the ferromagnetic plane is paramagnetic with a small value of chirality. We clarify the nature of phase transitions by using a finite size scaling method. We find three different kinds of transitions according to the values of ( I , J ): the KT transition, the Ising transition and an XY -Ising transition with ν = 0.849(3). It turns out that the Ising or XY -Ising transition is associated with the disappearance of the chiral order in the Villain plane.
(1) Department of Physics, University of California, San Diego, La Jolla, CA 92093,USA(2) NEST, Scuola Normale Superiore and Istituto Nanoscienze-CNR, I-56126 Pisa,Italy(3) Dipartimento di Fisica dellUniversita di Pisa and INFN, Largo Pontecorvo 3,I-56127 Pisa, Italy(4) NEST, Istituto Nanoscienze-CNR and Scuola Normale Superiore, I-56126 Pisa(5) Center for Quantum Technologies, National University of Singapore, SingaporeAbstract. Using the density-matrix renormalization-group algorithm (DMRG)and nite-size-scaling, we study the properties of the one-dimensional completely-anisotropic spin-1/2 XYZ model with Dzyaloshinsky-Moriya (DM) interactions. Themodel shows a rich phase diagram: depending on the value of the coupling constants,the system can display di erent kinds of ferromagnetic order and Luttinger-liquidbehavior. Transitions from ferromagnetic to Luttinger-liquid phases are rst order.We thoroughly discuss the transition between di erent ferromagnetic phases, which,in the absence of DM interactions, belongs to the XX universality class; we provideevidence that in presence of DM it is split into two Ising-like transitions. In between,an interesting disordered phase appears. Our study sheds light on the general problemof strongly-interacting spin-orbit-coupled systems and is particularly useful to guidefuture experimental work on cold bosons loaded in optical lattices.
We have studied the phase diagram of the one dimensional XXZ model with Dzyaloshinskii-Moriya (DM) interaction. We have applied the quantum renormalization group (QRG) approach to get the stable fixed points, critical point and the scaling of coupling constants. This model has three phases, ferromagnetic, spin-fluid and Néel phases which are separated by a critical line which depends on the DM coupling constant. We have shown that the staggered magnetization is the order parameter of the system and investigated the influence of DM interaction on the chiral ordering as a helical magnetic order.
Results of Monte Carlo simulations of the ferromagnetic classical XXZ model on a square lattice are reported for interactions of the out of plane spin components \ensuremath{\lambda} varying between 0 and 0.99. For all the value of \ensuremath{\lambda} the signature of a Berezinskii-Kosterlitz-Thouless (BKT) phase transition was observed, and the corresponding critical temperature was located both by BKT fits and finite-size scaling methods. Data for in-plane and out of plane susceptibility, correlation length, specific heat, and internal energy are given in a broad range of temperature and for lattice sizes ranging from 32\ifmmode\times\else\texttimes\fi{}32 to 256\ifmmode\times\else\texttimes\fi{}256.
We study the quantum entanglement and quantum phase transition (QPT) of the anisotropic spin-1/21/21/2 XYXYXY model with staggered Dzyaloshinskii-Moriya (DM) interaction by means of the quantum renormalization group method. The scaling of coupling constants and the critical points of the system are obtained. It is found that when the number of renormalization group iterations tends to infinity, the system exhibit a QPT between the spin-fluid and N\'eel phases which correspond with two saturated values of the concurrence for a given value of the strength of DM interaction. The DM interaction can enhance the entanglement and influence the QPT of the system. To gain further insight, the first derivative of the entanglement exhibit a nonanalytic behavior at the critical point and it directly associates with the divergence of the correlation length. This shows that the correlation length exponent is closely related to the critical exponent, i.e., the scaling behaviors of the system.