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

Physical Review Letters

Ground-State Symmetry in XY Model of Magnetism

Daniel Charles Mattis

Published Jun 4, 1979• 34 citations
Publisher

Abstract

Numerical studies by Betts and Oitmaa have led those authors to conjecture that in the $\mathrm{XY}$ model the ground-state magnetization ${M}_{z}$ is zero. This is a model of spins on a lattice with interactions $\ensuremath{-}J({{S}_{n}}^{x}{{S}_{m}}^{x}+{{S}_{n}}^{y}{{S}_{m}}^{y})$, that can also describe a hard-sphere boson fluid. In the present note I prove the conjecture for arbitrary spins $\mathcal{S}=\frac{1}{2}, 1, \frac{3}{2}, \dots{}$ for positive $J$, and treat various generalizations.

DOI
10.1103/physrevlett.42.1503

Related papers

The ground state of two quantum models of magnetism

J. Oitmaa, Donald D. Betts

The ground state energy and pair correlations have been computed exactly for the spin [Formula: see text] XY magnet and isotropic Heisenberg antiferromagnet, for a sequence of finite cells on the square and honeycomb lattices. Precise estimates of the ground state energy of the infinite lattices are obtained by extrapolation. It is predicted that the XY magnet has a non-zero transverse magnetization and the Heisenberg antiferromagnet has a non-zero staggered magnetization in the ground state.

Canadian Journal of Physics•Jul 1, 1978•353 citations

XY ring-exchange model on the triangular lattice

Leon Balents, Arun Paramekanti

We study ring-exchange models for bosons or $\mathrm{XY}$ spins on a triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbor exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin (superfluid) stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.

arXiv:cond-mat/0212589•Physical review. B, Condensed matter•Apr 28, 2003•21 citations

Variational study on the ground state of the spin XY magnet

Masuo Suzuki, Seiji Miyashita

An approximate wave function of the ground state of the spin [Formula: see text] XY magnet is derived using a variational method. This wave function yields estimates of the ground state energy and long-range order which agree very well with the results obtained by Betts and Oitmaa by a finite lattice method.

Canadian Journal of Physics•Jul 1, 1978•57 citations

Proof of phase transition in homogeneous systems of interacting bosons

András Sütö

Using the rigorous path integral formalism of Feynman and Kac we prove London's eighty years old conjecture that during the superfluid transition in liquid helium Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that at low enough temperatures macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We find also that in the limit of zero temperature the infinite cycles cover the whole system, while BEC remains partial. For the Bose-condensed fluid at rest we define a macroscopic wave function. Via the equivalence of 1/2 spins and hard-core bosons the method extends to lattice models. We show that at low enough temperatures the spin-1/2 axially anisotropic Heisenberg models, including the isotropic ferro- and antiferromagnet and the XY model, undergo magnetic ordering.

arXiv:1710.04441•Oct 12, 2017•0 citations

On the existence and uniqueness of ground states of a generalized spin$B!>(Bboson model

Asao Arai, Masao Hirokawa

Preprint Series of Department of Mathematics, Hokkaido University•Dec 1, 1996•1 citation

Spontaneous formation of a non-uniform chiral spin liquid in a "moat" lattice

Tigran Sedrakyan, L. I. Glazman, Alex Kamenev

A number of lattices exhibit moat-like band structures, i.e. a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to $s=1/2$ XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.

•Sep 25, 2014•0 citations
Numerical studies by Betts and Oitmaa have led those authors to conjecture that in the XY\mathrm{XY}XY model the ground-state magnetization Mz{M}_{z}Mz​ is zero. This is a model of spins on a lattice with interactions \ensuremath−J(SnxSmx+SnySmy)\ensuremath{-}J({{S}_{n}}^{x}{{S}_{m}}^{x}+{{S}_{n}}^{y}{{S}_{m}}^{y})\ensuremath−J(Sn​xSm​x+Sn​ySm​y), that can also describe a hard-sphere boson fluid. In the present note I prove the conjecture for arbitrary spins S=12,1,32,…\mathcal{S}=\frac{1}{2}, 1, \frac{3}{2}, \dots{}S=21​,1,23​,… for positive JJJ, and treat various generalizations.
We study ring-exchange models for bosons or XY\mathrm{XY}XY spins on a triangular lattice. A four-spin exchange leads to a manifold of ground states with gapless excitations and critical power-law correlations. With a nearest-neighbor exchange, fluctuations select a four-fold ferrimagnetically ordered ground state with a small spin (superfluid) stiffness which breaks the global U(1) and translational symmetry. We explore consequences for phase transitions at finite temperature and in an in-plane magnetic field.
Using the rigorous path integral formalism of Feynman and Kac we prove London's eighty years old conjecture that during the superfluid transition in liquid helium Bose-Einstein condensation (BEC) takes place. The result is obtained by proving first that at low enough temperatures macroscopic permutation cycles appear in the system, and then showing that this implies BEC. We find also that in the limit of zero temperature the infinite cycles cover the whole system, while BEC remains partial. For the Bose-condensed fluid at rest we define a macroscopic wave function. Via the equivalence of 1/2 spins and hard-core bosons the method extends to lattice models. We show that at low enough temperatures the spin-1/2 axially anisotropic Heisenberg models, including the isotropic ferro- and antiferromagnet and the XY model, undergo magnetic ordering.
A number of lattices exhibit moat-like band structures, i.e. a band with infinitely degenerate energy minima attained along a closed line in the Brillouin zone. If such a lattice is populated with hard-core bosons, the degeneracy prevents their condensation. At half-filling, the system is equivalent to s=1/2s=1/2s=1/2 XY model at zero magnetic field, while absence of condensation translates into the absence of magnetic order in the XY plane. Here we show that the ground state breaks the time-reversal as well as inversion symmetries. This state, which may be identified with the chiral spin liquid, has a bulk gap and chiral gapless edge excitations. The applications of the developed analytical theory include an explanation of recent numerical findings and a suggestion for the chiral spin liquid realizations in experiments with cold atoms in optical lattices.