Phase transitions in coupled two dimensional XY systems with spatial anisotropy

TL;DR

This paper investigates phase transitions in coupled 2D XY systems with spatial anisotropy, revealing complex behaviors including Ising and XY transitions, Kosterlitz-Thouless phenomena, and quantum phase transitions influenced by anisotropic couplings.

Contribution

It provides a comprehensive analysis of how spatial anisotropy affects phase transition sequences and nature in coupled XY systems, including both classical and quantum regimes.

Findings

Finite temperature transition is a Kosterlitz-Thouless transition driven by half vortices.

Zero temperature quantum transition splits into bond order and 3D XY transitions.

Small perpendicular hopping induces 2D and 2+1D Ising transitions.

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.