Real space renormalization group study of the anisotropic quantum Heisenberg model on a square lattice

Drzewiński, Andrzej; Sznajd, J.

doi:10.1016/0375-9601(89)90880-3

Cited by 8 publications

(2 citation statements)

References 15 publications

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“…It is also known that quantum effects, despite being enhanced by the reduced dimensionality, do not substantially change the essential features of the above models, not even in the extreme S = 1/2 case, though evidently renormalizing their thermodynamic properties. This results from renormalization group 4,5 and semiclassical approaches 6,7 , as well as from quantum Monte Carlo (QMC) simulations 8,9,10,11,12 .…”

Section: Introductionmentioning

confidence: 85%

Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

et al. 2003

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We study the finite-temperature behaviour of two-dimensional S = 1/2 Heisenberg antiferromagnets with very weak easy-axis and easy-plane exchange anisotropies. By means of quantum Monte Carlo simulations, based on the continuous-time loop and worm algorithm, we obtain a rich set of data that allows us to draw conclusions about both the existence and the type of finite-temperature transition expected in the considered models. We observe that the essential features of the Ising universality class, as well as those of the Berezinskii-Kosterlitz-Thouless (BKT) one, are preserved even for anisotropies as small as 10 −3 times the exchange integral; such outcome, being referred to the most quantum case S = 1/2, rules out the possibility for quantum fluctuations to destroy the long or quasi-long range order, whose onset is responsible for the Ising or BKT transition, no matter how small the anisotropy. Besides this general issue, we use our results to extract, out of the isotropic component, the features which are peculiar to weakly anisotropic models, with particular attention for the temperature region immediately above the transition. By this analysis we aim to give a handy tool for understanding the experimental data relative to those real compounds whose anisotropies are too weak for a qualitative description to accomplish the goal of singling out the genuinely two-dimensional critical behaviour.

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Section: Introductionmentioning

confidence: 85%

Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

et al. 2003

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“…The exact diagonalization study of Tang on the anti-ferromagnetic XY model found isotropic staggered magnetization in the XY plane 7 . Drzewinsky and Sznajd used a block-spin renormalization group at finite temperatures to find a BKT transition temperature in this system 8 . The BKT transition for the 2DQXY was confirmed in quantum Monte Carlo studies [9][10][11][12] .…”

Section: Introductionmentioning

confidence: 99%

Topological phase transition of the anisotropic XY model with Dzyaloshinskii-Moriya interaction

Farajollahpour

Jafari

2018

Phys. Rev. B

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Within the real space renormalization group we obtain the phase portrait of the anisotropic quantum XY model on square lattice in presence of Dzyaloshinskii-Moriya (DM) interaction. The model is characterized by two parameters, λ corresponding to XY anisotropy, and D corresponding to the strength of DM interaction. The flow portrait of the model is governed by two global Ising-Kitaev attractors at (λ = ±1, D = 0) and a repeller line, λ = 0. Renormalization flow of concurrence suggests that the λ = 0 line corresponds to a topological phase transition. The gap starts at zero on this repeller line corresponding to super-fluid phase of underlying bosons; and flows towards a finite value at the Ising-Kitaev points. At these two fixed points the spin fields become purely classical, and hence the resulting Ising degeneracy can be interpreted as topological degeneracy of dual degrees of freedom. The state of affairs at the Ising-Kitaev fixed point is consistent with the picture of a p-wave pairing of strength λ of Jordan-Wigner fermions coupled with Chern-Simons gauge fields.

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On the real-space renormalization-group study of some 2D quantum spin systems

Drzewiński

Sznajd

1991

Physica A: Statistical Mechanics and its Applications

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Real space renormalization group study of the anisotropic quantum Heisenberg model on a square lattice

Cited by 8 publications

References 15 publications

Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

Quantum Monte Carlo study ofS=12weakly anisotropic antiferromagnets on the square lattice

Topological phase transition of the anisotropic XY model with Dzyaloshinskii-Moriya interaction

On the real-space renormalization-group study of some 2D quantum spin systems

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