Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1009.0043 · Physical Review Letters

Phase Diagram of Two-Dimensional Polar Condensates in a Magnetic Field

A. J. A. James, Austen Lamacraft

Published Apr 6, 2011• 33 citations
arXivHTMLPDF

Abstract

Spin-1 condensates in the polar (antiferromagnetic) phase in two dimensions are shown to undergo a transition of the Ising type, in addition to the expected Kosterlitz-Thouless (KT) transition of half-vortices, due to the quadratic Zeeman effect. We establish the phase diagram in terms of temperature and the strength of the Zeeman effect using Monte Carlo simulations. When the Zeeman effect is sufficiently strong, the Ising and KT transitions meet. For very strong Zeeman field the remaining transition is of the familiar integer KT type.

DOI
10.1103/physrevlett.106.140402

Related papers

Phase transitions of S=1 spinor condensates in an optical lattice

Daniel K. Podolsky, Shailesh Chandrasekharan A, Ashvin Vishwanath

We study the phase diagram of spin-one polar condensates in a two-dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase transitions. These include Kosterlitz-Thouless-like transitions with a superfluid stiffness jump that can be experimentally tuned to take a continuous set of values, and a cascaded Kosterlitz-Thouless transition, characterized by two divergent length scales. For higher integer spin bosons $S$, the thermal phase transition out of the planar polar phase is strongly affected by the parity of $S$.

arXiv:0707.0695•Physical Review B•Dec 9, 2009•36 citations

Berezinskii–Kosterlitz–Thouless Transition of Spin-1 Spinor Bose Gases in the Presence of the Quadratic Zeeman Effect

Michikazu Kobayashi

We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group $\mathbb{Z}$, and $\mathbb{Z}_2$ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.

arXiv:1902.00210•Journal of the Physical Society of Japan•Aug 7, 2019•15 citations

Topological Defects and the Superfluid Transition of the s=1 Spinor Condensate in Two Dimensions

Subroto Mukerjee, Cenke Xu, Joel E. Moore

The s=1 spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We analyze the topological defects of the polar condensate, correcting previous studies, and show that the polar condensate in two dimensions is unstable at any finite temperature; instead, there is a nematic or paired superfluid phase with algebraic order in exp(2itheta), where theta is the superfluid phase, and no magnetic order. The Kosterlitz-Thouless transition out of this phase is driven by unbinding of half-vortices (the spin-disordered version of the combined spin and phase defects found by Zhou), and the anomalous universal 8T(c)/pi stiffness jump at the transition is confirmed in numerical simulations. The anomalous stiffness jump is a clear experimental signature of this phase and the corresponding phase transition.

arXiv:cond-mat/0605102•Physical Review Letters•Sep 20, 2006•102 citations

Monte Carlo Study of a Triangular Ising Lattice. II. Occurrence of the Kosterlitz-Thouless-Like Phase Transition

Hajime Takayama, Kazuyuki Matsumoto, Hideaki Kawahara +1 more

A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.

Journal of the Physical Society of Japan•Aug 1, 1983•65 citations

Phase diagrams of antiferromagnetic spin-1 bosons on a square optical lattice with the quadratic Zeeman effect

Laurent de Forges de Parny, V. G. Rousseau

We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean-field treatment. The QZE imbalances the populations of the magnetic sublevels $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ and $\ensuremath{\sigma}=0$, and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the $z$ axis is found in the odd Mott lobes and in the superfluid phase for energetically favored $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ states. In the superfluid phase with even filling, the $xy$ components of the nematic director remain finite only for moderate QZE.

arXiv:1801.00449•Physical Review A•Feb 21, 2018•7 citations

Monte Carlo Simulations of the Quantum XXZ Model in Two Dimensions

Eugene Loh, Douglas J. Scalapino, Paul Michael Grant

The XXZ spin Hamitonian H = - ( S i x S j x + S i y S j y + λ S i z S j z ) is simulated for quantum spins. The XY model (λ = 0) has a Kosterlitz- Thouless Phase transition T KT = 0.45 ± 0.05, slightly above which the specific heat has a finite peak. The vortex density has a non-zero value in the low-temperature limit, probably due to quantum fluctuations. The critical temperature holds up at least to λ = -0.8. The Ising transition temperature T Ising is measured for Ising-like antiferromagnets λ < -1 and is found to drop off to zero in a manner consistent with the reciprocal-logarithmic behavior T c α-1/log|-λ-1|, as proposed for the classical model.

Physica Scripta•Oct 1, 1985•12 citations
Spin-1 condensates in the polar (antiferromagnetic) phase in two dimensions are shown to undergo a transition of the Ising type, in addition to the expected Kosterlitz-Thouless (KT) transition of half-vortices, due to the quadratic Zeeman effect. We establish the phase diagram in terms of temperature and the strength of the Zeeman effect using Monte Carlo simulations. When the Zeeman effect is sufficiently strong, the Ising and KT transitions meet. For very strong Zeeman field the remaining transition is of the familiar integer KT type.
We study the phase diagram of spin-one polar condensates in a two-dimensional optical lattice with magnetic anisotropy. We show that the topological binding of vorticity to nematic disclinations allows for a rich variety of phase transitions. These include Kosterlitz-Thouless-like transitions with a superfluid stiffness jump that can be experimentally tuned to take a continuous set of values, and a cascaded Kosterlitz-Thouless transition, characterized by two divergent length scales. For higher integer spin bosons SSS, the thermal phase transition out of the planar polar phase is strongly affected by the parity of SSS.
We numerically study the Berezinskii-Kosterlitz-Thouless (BKT) transition of a spin-1 spinor Bose gas under the quadratic Zeeman effect. A calculation of the mass and spin superfluid densities shows that (i) the BKT transition occurs only when vortices are classified by the integer group Z\mathbb{Z}Z, and Z2\mathbb{Z}_2Z2​ vortices do not contribute to the BKT transition, (ii) the two BKT transition temperatures for mass and spin superfluid densities are different for a positive quadratic Zeeman effect and equal for a negative quadratic Zeeman effect, and (iii) the universal relation of the superfluid densities at the BKT transition temperature is changed when multiple kinds of vortices contribute to the transition. We have further found that (iv) spin-singlet pairs in non-magnetic states show the quasi-off-diagonal-long-range order at the different temperature lower than the BKT transition temperature, giving the new universal relation of the superfluid density.
The s=1 spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We analyze the topological defects of the polar condensate, correcting previous studies, and show that the polar condensate in two dimensions is unstable at any finite temperature; instead, there is a nematic or paired superfluid phase with algebraic order in exp(2itheta), where theta is the superfluid phase, and no magnetic order. The Kosterlitz-Thouless transition out of this phase is driven by unbinding of half-vortices (the spin-disordered version of the combined spin and phase defects found by Zhou), and the anomalous universal 8T(c)/pi stiffness jump at the transition is confirmed in numerical simulations. The anomalous stiffness jump is a clear experimental signature of this phase and the corresponding phase transition.
A two-dimensional triangular Ising lattice with the nearest-neighbor antiferromagnetic interaction J 1 and the next-nearest-neighbor ferromagnetic interaction - J 2 is studied by the Monte Carlo simulation. It is shown that the system with a finite J 2 undergoes the successive phase transition, paramagnetic→Kosterlitz-Thouless (KT)-like→ferrimagnetic phases, as temperature decreases. The sub-lattice switching phenomenon observed in our previous work is shown to be an intrinsic property inherent to the present system which has an XY character. The marginal exponent of the order-parameter correlation function at the KT-like transition point is seen to increase from 1/4 as the ratio J 2 / J 1 decreases, namely, it reveals a deviation from the universal behavior of a genuine XY model.
We study the quadratic Zeeman effect (QZE) in a system of antiferromagnetic spin-1 bosons on a square lattice and derive the ground-state phase diagrams by means of quantum Monte Carlo simulations and mean-field treatment. The QZE imbalances the populations of the magnetic sublevels $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ and $\ensuremath{\sigma}=0$, and therefore affects the magnetic and mobility properties of the phases. Both methods show that the tip of the even Mott lobes, stabilized by singlet state, is destroyed when turning on the QZE, thus leaving the space to the superfluid phase. Contrariwise, the tips of odd Mott lobes remain unaffected. Therefore, the Mott-superfluid transition with even filling strongly depends on the strength of the QZE, and we show that the QZE can act as a control parameter for this transition at fixed hopping. Using quantum Monte Carlo simulations, we elucidate the nature of the phase transitions and examine in detail the nematic order: the first-order Mott-superfluid transition with even filling observed in the absence of QZE becomes second order for weak QZE, in contradistinction to our mean-field results which predict a first-order transition in a larger range of QZE. Furthermore, a spin nematic order with director along the zzz axis is found in the odd Mott lobes and in the superfluid phase for energetically favored $\ensuremath{\sigma}=\ifmmode\pm\else\textpm\fi{}1$ states. In the superfluid phase with even filling, the xyxyxy components of the nematic director remain finite only for moderate QZE.
The XXZ spin Hamitonian H = - ( S i x S j x + S i y S j y + λ S i z S j z ) is simulated for quantum spins. The XY model (λ = 0) has a Kosterlitz- Thouless Phase transition T KT = 0.45 ± 0.05, slightly above which the specific heat has a finite peak. The vortex density has a non-zero value in the low-temperature limit, probably due to quantum fluctuations. The critical temperature holds up at least to λ = -0.8. The Ising transition temperature T Ising is measured for Ising-like antiferromagnets λ < -1 and is found to drop off to zero in a manner consistent with the reciprocal-logarithmic behavior T c α-1/log|-λ-1|, as proposed for the classical model.