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arXiv:0706.1609

Phase transitions in coupled two dimensional XY systems with spatial anisotropy

Cenke Xu

Published Jun 12, 2007• 1 citation
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Abstract

We study phase transitions of coupled two dimensional XY systems with spatial anisotropy and $U(1) \times \mathbb{Z}_2$ symmetry, motivated by spinless bosonic atoms trapped in square optical lattice on the metastable first excited $p-$level orbitals with anisotropic hopping amplitudes. The phase transitions of the system are generally split into an Ising transition and an XY transition, but the sequence and the nature of the transitions depend on the ratio between the anisotropic couplings. In the isotropic limit the XY variables are expected to be disordered before the Ising variables when thermal or quantum fluctuations are turned on gradually. In the anisotropic limit with zero perpendicular hoppings, the finite temperature transition is a Kosterlitz-Thouless transition driven by proliferation of hybrid half vortices, and the zero temperature quantum phase transition is split into a bond order transition and a 3D XY transition, which can be driven by the condensation of either single vortices or half vortices. After the condensation of half vortices the resultant state is a Mott Insulator of paired bosons. A small perpendicular hopping $J_b$ leads to a 2D Ising transition at low temperature and a 2+1d quantum Ising transition with a small charging energy at zero temperature. Global phase diagrams for both classical and quantum phase transitions are drawn. The analytical results obtained in this work are expected to be checked both numerically and experimentally.

DOI
10.48550/arxiv.0706.1609

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The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72 053604 (2005)] and [arXiv: 0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY-type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent and reliable results. Furthermore, we observed first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The critical exponents of different types of phase transitions are reasonably fitted. The results are useful to help cold atom experiments explore the half-vortex topological phase.