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Physical Review Letters

Computer Simulations of SU(N)⊗SU(N) Spin Systems in Two Dimensions

John B. Kogut, M. Snow, Michael Stone

Published Dec 21, 1981• 14 citations
Publisher

Abstract

$\mathrm{SU}(N)\ensuremath{\bigotimes}\mathrm{SU}(N)$ spin systems in two dimensions are studied for $N=2, 3, \mathrm{and} 4$ on 10\ifmmode\times\else\texttimes\fi{}10, 20\ifmmode\times\else\texttimes\fi{}20, and 30\ifmmode\times\else\texttimes\fi{}30 lattices with use of Monte Carlo methods. Variant forms of the action are considered. In addition to crossover phenomena, unexpected first-order transitions in multidimensional phase diagrams are discovered. These transitions are related to the presence of ${Z}_{N}$ vortices which experience short-range interactions. Contrasts with $\mathrm{SU}(N)$ gauge theories in four dimensions are drawn.

DOI
10.1103/physrevlett.47.1767

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SU(N)\ensuremath⨂SU(N)\mathrm{SU}(N)\ensuremath{\bigotimes}\mathrm{SU}(N)SU(N)\ensuremath⨂SU(N) spin systems in two dimensions are studied for N=2,3,and4N=2, 3, \mathrm{and} 4N=2,3,and4 on 10\ifmmode\times\else\texttimes\fi{}10, 20\ifmmode\times\else\texttimes\fi{}20, and 30\ifmmode\times\else\texttimes\fi{}30 lattices with use of Monte Carlo methods. Variant forms of the action are considered. In addition to crossover phenomena, unexpected first-order transitions in multidimensional phase diagrams are discovered. These transitions are related to the presence of ZN{Z}_{N}ZN​ vortices which experience short-range interactions. Contrasts with SU(N)\mathrm{SU}(N)SU(N) gauge theories in four dimensions are drawn.
Spin systems are a fundamental concept in condensed matter and statistical physics. Here, the authors provide the very first computation of the spin-SSS SU(N) antiferromagnet in a representation amenable to negative sign free fermion Monte Carlo simulations. They offer a numerical proof of the seminal works of Read and Sachdev. It highlights the close connection between topology and the melting of the quantum antiferromagnet, with the Berry phase explaining the various states observed in the vicinity of the quantum antiferromagnet.
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Consequences of explicit symmetry breaking in a physically motivated model of SU(N)SU(N)SU(N) antiferromagnet in spatial dimensions one and two are studied. It is shown that the case N=3N=3N=3, which can be realized in spin-1 cold atom systems, displays special properties distinctly different from those for $N\ensuremath{\ge}4$. Qualitative form of the phase diagram depending on the model parameters is given.
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