Layered XY-Models, Anyon Superconductors, and Spin-Liquids

TL;DR

This paper exactly computes the partition function of a double-layer XY model, revealing how layers lock or decouple through a BKT transition, with implications for anyon superconductors and spin-liquids in layered systems.

Contribution

It provides an exact analysis of layered XY models and extends the understanding of phase transitions in related dual systems like anyon superconductors and spin-liquids.

Findings

Layers lock via BKT transition in weak coupling limit

Layers decouple inside the normal phase

Results extend to finite layered systems

Abstract

The partition function of the double-layer $XY$ model in the (dual) Villain form is computed exactly in the limit of weak coupling between layers. Both layers are found to be locked together through the Berezinskii-Kosterlitz-Thouless transition, while they become decoupled well inside the normal phase. These results are recovered in the general case of a finite number of such layers. When re-interpreted in terms of the dual problems of lattice anyon superconductivity and of spin-liquids, they also indicate that the essential nature of the transition into the normal state found in two dimensions persists in the case of a finite number of weakly coupled layers.