# Possibility of Gapless Spin Liquid State by One-dimensionalization

## TL;DR

This paper investigates how frustration-induced one-dimensionalization in an anisotropic triangular lattice can lead to a gapless spin liquid state, providing insights into experimental observations in certain organic materials.

## Contribution

It demonstrates that frustration can cause a transition from 1D chains to a gapless spin liquid in a 2D Heisenberg model, using a resonating valence bond mean-field approach.

## Key findings

- Almost gapless excitations found across a wide anisotropy range.
- Frustration-induced one-dimensionalization is a plausible mechanism for gapless spin liquids.
- Supports experimental observations in organic triangular lattice materials.

## Abstract

Motivated by the observation of a gapless spin liquid state in $\kappa$-(BEDT-TTF)$_2$Cu$_2$(CN)$_3$, we analyze the anisotropic triangular lattice $S=1/2$ Heisenberg model with the resonating valence bond mean-field approximation. Paying attention to the small quasi-one-dimensional anisotropy of the material, we take an approach from one-dimensional (1D) chains coupled with frustrating zig-zag bonds. By calculating one-particle excitation spectra changing anisotropy parameter $J'/J$ from the decoupled 1D chains to the isotropic triangular lattice, we find almost gapless excitations in the wide range from the 1D limit. This one-dimensionalization by frustration is considered to be a candidate for the mechanism of the gapless spin liquid state.