Phase transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: A Monte Carlo simulation

Capriotti, Luca; Vaia, Ruggero; Cuccoli, Alessandro; Tognetti, V.

doi:10.1103/physrevb.58.273

Cited by 57 publications

(66 citation statements)

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“…The phase defined by this types of symmetry breaking is a novel one in quantum systems, while it has been studied quite intensively in various frustrated classical systems. 21,22,23,24,25,26,27,28,29, 30, 31) It is thus interesting to further investigate the properties of the chiral phases in frustrated quantum systems.In order to determine the phase diagram, we numerically calculate the correlation functions associated with the order parameters, m(q), O κ , and O str , for open chains, using the infinitesystem density-matrix renormalization-group (DMRG) method. Examining the behavior of these correlation functions at long distance, we find the following six phases , the Haldane, gapped and gapless chiral, DH, Néel, and DN phases, in the region where j ≥ 0 and ∆ ≥ 0.…”

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Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

et al. 2000

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The ground-state phase diagram of frustrated S = 1 XXZ spin chains with the competing nearest-and next-nearest-neighbor antiferromagnetic couplings is studied using the infinitesystem density-matrix renormalization-group method. We find six different phases, namely, the Haldane, gapped chiral, gapless chiral, double Haldane, Néel, and double Néel (uudd) phases. The gapped and gapless chiral phases are characterized by the spontaneous breaking of parity, in which the long-range order parameter is a chirality, κ l =S , whereas the spin correlation decays either exponentially or algebraically. These chiral ordered phases appear in a broad region in the phase diagram for ∆ < 0.95, where ∆ is an exchange-anisotropy parameter. The critical properties of phase transitions are also studied.KEYWORDS: frustration, spin-1 chain, ground-state phase diagram, density-matrix renormalization-group method, chiral ordering §1. Introduction Frustrated antiferromagnetic quantum spin systems have attracted considerable attention over the decades since they exhibit a wealth of fascinating phenomena in their ground states and lowlying excitations. In general, frustration supresses antiferromagnetic correlations and the tendency towards the Néel order. Classical systems, for example, often show a helical ordered state in their ground states in the presence of strong frustration. In quantum systems, the interplay of frustration and quantum fluctuations plays an important role which causes exotic phenomena, e.g., a spin-liquid state and a novel type of spontaneous symmetry breaking.In this paper, we study a one-dimensional anisotropic spin system with the antiferromagnetic nearest-neighbor coupling J 1 and the frustrating next-nearest-neighbor coupling J 2 . The model is * E-mail address: hikihara@phys03.phys.sci.kobe-u.ac. where S l is a spin-S spin operator at site l and ∆ ≥ 0 represents an exchange anisotropy. Hereafter, we put j ≡ J 2 /J 1 (j ≥ 0).In the classical limit, S → ∞, the system exhibits a magnetic long-range order (LRO) characterized by a wavenumber q. The order parameter is defined bywhere L is the total number of spins. While the magnetic LRO is of the Néel-type (q = π) when j is smaller than a critical value, j ≤ 1/4, it becomes of helical-type for j > 1/4 with q = cos −1 (−1/4j).It should be noticed that both the time-reversal and parity symmetries are broken in this helical ordered state. When the system has an XY -like anisotropy (∆ < 1), the helical ordered state possesses a two-fold discrete degeneracy according as the helix is either right-or left-handed, in addition to a continuous degeneracy associated with the original U (1) symmetry of the XY spin.This discrete degeneracy is characterized by mutually opposite signs of the total chirality definedNote that this chirality is distinct from the scalar chirality of the Heisenberg spin often discussed in the literature 2) defined by χ l = S l−1 · S l × S l+1 : The chirality O κ changes its sign under the parity operation but is invariant under the time-reversal op...

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Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

et al. 2000

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“…For the XY anisotropy (λ < 1), it is known that both BKT and chiral transitions occur at different but very close temperatures. 15,16 On the other hand, for the Ising anisotropy (λ > 1), it is known that two different BKT transitions occur separately for the longitudinal S z and the transverse (S x , S y ) components. 17,18 It is, however, still controversial how these four transitions behave as the system approaches the isotropic Heisenberg point λ = 1.…”

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Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Misawa

Motome

2010

J. Phys. Soc. Jpn.

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Effect of exchange anisotropy on the relaxation time of spin and vector chirality is studied for the antiferromagnetic classical Heisenberg model on the triangular lattice by using the nonequilibrium relaxation Monte Carlo method. We identify the Berezinskii-KosterlitzThouless (BKT) transition and the chiral transition in a wide range of the anisotropy, even for very small anisotropy of ∼ 0.01%. As the anisotropy decreases, both the critical temperatures steeply decrease, while the BKT critical region becomes divergently wide. We elucidate a sharp "V shape" of the phase diagram around the isotropic Heisenberg point, which suggests that the isotropic case is exceptionally singular and the associated Z2 vortex transition will be isolated from the BKT and chiral transitions. We discuss the relevance of our results to peculiar behavior of the spin relaxation time observed experimentally in triangular antiferromagnets.KEYWORDS: geometrical frustration, triangular lattice, Heisenberg model, nonequilibrium relaxation, BKT transition, chiral transition, Z2 vortex transitionAntiferromagnet on the two-dimensional triangular lattice has been intensively studied as one of the most fundamental models for the geometrically frustrated systems.1 For the isotropic Heisenberg model with nearestneighbor interactions, it is believed that the ground state of the system exhibits a three-sublattice 120• long-range order, 2 whereas the magnetic ordering is no longer retained against thermal fluctuations.3 Nevertheless, an interesting possibility was proposed by Kawamura and Miyashita, 4, 5 that is, an unconventional topological transition at a finite temperature (T ) -Z 2 vortex transition. From the symmetry point of view, the Z 2 vortex transition is different from the conventional BerezinskiiKosterlitz-Thouless (BKT) transition which occurs in the presence of anisotropy. 6,7 The relation between these two topological transitions, however, is not fully understood yet. In particular, it is still unclear how the system behaves in the region of vanishing anisotropy.Experimentally, several materials with triangular layered structure have been studied, and recently, the Z 2 vortex attracts renewed interests for understanding of their peculiar properties. One of the peculiar properties is anomalous enhancement of the spin relaxation time. Critical divergence of the relaxation time is observed in an anomalously wide range of T in many compounds, such as ACrO 2 (A=Li,H,Na), [8][9][10][11] Li 7 RuO 6 , 12and NiGa 2 S 4 . 13, 14 The critical behaviors are often argued to be a fingerprint of the Z 2 vortex transition. The Z 2 vortex, however, is a topological object specific to spin-rotational-invariant systems, and hence, it is not trivial whether its influence is observed in real compounds in which anisotropy exists.In this letter, to shed light on the origin of the anomalous critical behavior and its relation to the Z 2 vortex transition, we directly calculate the relaxation time in the antiferromagnetic Heisenberg model with classical spins ...

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“…It is also used to study systems such as films of superfluid helium, Josephsonjunctions, superconducting materials, fluctuating surfaces as well as certain magnetic, gaseous and liquid-crystal systems. Besides this model, transitions of the BKT type also exist in the ice-type F model [6], antiferromagnetic models [7], certain models with long-range interactions [8], lattice gauge theories [9] and in string theory [10] amongst others. Thus a thorough and quantitative understanding of the paradigmatic two-dimensional XY model is beneficial to a number of areas within theoretical physics.…”

Section: The Bkt Transition In the Xy And Step Modelsmentioning

confidence: 99%

“…The formulae (10) and (11) refer to thermal scaling on infinite lattices. Such systems are not [26] 2005 FSS −0.056 (7) amenable to computational techniques as one may only simulate finite-size systems. There, finitesize scaling (FSS) theory predicts that the role of the correlation length is played by the lattice extent L. For example, the susceptibility at criticality (t = 0) scales as [13] …”

Section: Bkt Scaling Behaviourmentioning

confidence: 99%

Homotopy in statistical physics

Kenna¹

2006

Condens. Matter Phys.

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In condensed matter physics and related areas, topological defects play important roles in phase transitions and critical phenomena. Homotopy theory facilitates the classification of such topological defects. After a pedagogic introduction to the mathematical methods involved in topology and homotopy theory, the role of the latter in a number of mainly low-dimensional statistical-mechanical systems is outlined. Some recent activities in this area are reviewed and some possible future directions are discussed.

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Phase transitions induced by easy-plane anisotropy in the classical Heisenberg antiferromagnet on a triangular lattice: A Monte Carlo simulation

Cited by 57 publications

References 29 publications

Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

Ground State Phase Diagram of Frustrated S = 1 XXZ chains: Chiral Ordered Phases

Nonequilibrium Relaxation Study of the Anisotropic Antiferromagnetic Heisenberg Model on the Triangular Lattice

Homotopy in statistical physics

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