# BKT-paired phase in coupled XY models

## TL;DR

This paper investigates how linear tunneling coupling between two 2D XY systems affects their topological phases, revealing a novel BKT-paired phase with unique correlation properties through numerical and theoretical analysis.

## Contribution

It introduces and characterizes a new BKT-paired phase in coupled XY models, supported by numerical simulations and renormalization group analysis.

## Key findings

- The BKT-paired phase exists at any finite interlayer coupling.
- In this phase, 1-body correlations decay exponentially, while 2-body correlations follow a power-law.
- Numerical simulations confirm the phase's presence across a range of couplings.

## Abstract

We study the effect of a linear tunneling coupling between 2D systems, each separately exhibiting the topological Berezinskii-Kosterlitz-Thouless (BKT) transition. In the uncoupled limit, there are two phases: one where the 1-body correlation functions are algebraically decaying and the other with exponential decay. When the linear coupling is turned on, a third BKT-paired phase emerges, in which 1-body correlations are exponentially decaying, while 2-body correlation functions exhibit power-law decay. We perform numerical simulations in the paradigmatic case of two coupled XY models at finite temperature, finding that for any finite value of the interlayer coupling, the BKT-paired phase is present. We provide a picture of the phase diagram using a renormalization group approach.