# Gapless Kitaev Spin Liquid to Classical String Gas through Tensor Networks

## TL;DR

This paper introduces a tensor network framework for the gapless Kitaev spin liquid, revealing its hidden string gas structure and accurately modeling its properties without Majorana fermions.

## Contribution

It presents a novel tensor network approach that captures key features of the Kitaev spin liquid, including symmetries, gauge structure, and phase transitions, with minimal parameters.

## Key findings

- Achieves a highly accurate KSL ansatz with bond dimension D=8
- Reveals the hidden string gas structure of the KSL
- Provides insights into gap opening and non-Abelian phases under magnetic field

## Abstract

We provide a framework for understanding the gapless Kitaev spin liquid (KSL) in the language of tensor network(TN). Without introducing Majorana fermion, most of the features of the KSL including the symmetries, gauge structure, criticality and vortex-freeness are explained in a compact TN representation. Our construction reveals a hidden string gas structure of the KSL. With only two variational parameters to adjust, we obtain an accurate KSL ansatz with the bond dimension D = 8 in a compact form, where the energy is about 0.007% higher than the exact one. In addition, the opening of gap and non-Abelian phase driven by a magnetic field are naturally understood in our construction.