Phase transitions of the bilayered spin one XY model

Antonio S. T. Pires

Antonio S. T. Pires

Wei Liu, Pengwei Sun, Zhengxin Yan +1 more

Antonio S. T. Pires

Abstract The spin-one honeycomb bilayer XY antiferromagnet has been studied taking into account the effect of the next-near neighbor J2 exchange interactions and single-ion easy plane anisotropy, using a flavor wave theory. We found that, at a critical point α C = 13.8 , where α = J ⊥ / J 1 is the ratio between the interlayer J ⊥ to the intralayer near neighbor J1 exchange interaction, the system shows a quantum phase transition from an Neel ordered phase to a paramagnetic phase. The phase diagram at zero temperature is presented.

Jae-Kwon Kim

Feng-Feng Song, Guang-Ming Zhang

We study a bilayer system of coupled two-dimensional XY models by using tensor-network methods, showing that the inter-layer coupling can significantly alter the uncoupled topological Berezinskii-Kosterlizt-Thouless (BKT) transition. In the tensor-network representation, the partition function is mapped into a product of one-dimensional quantum transfer operator, whose eigen-equation can be accurately solved by an algorithm of matrix product states. The entanglement entropy of this one-dimensional quantum correspondence exhibits singularity, which can be used to determine various phase transitions. In the low temperature phase, an inter-layer Ising long-range order is developed,accompanying with vortex-antivortex bindings in both intra-layers and inter-layers. For two identical coupled layers, the Ising transition coincides with the BKT transition at a multi-critical point. For two inequivalent coupled layers, however, there emerges an intermediate quasi-long-range ordered phase, where vortex-antivortex bindings occur only in the layer with the larger intra-layer coupling but half-vortex pairs associated with topological strings emerge in the other layer. These results are supported by the correlation functions of the XY spins and nematic spins, and can be used to understand the novel properties in bilayer systems of superfluids, superconductors and quantum Hall systems.