The spin-1/2 square-lattice J_1-J_2 model: The spin-gap issue

TL;DR

This study uses the coupled cluster method to analyze the ground state and spin gap of the spin-1/2 J_1-J_2 model on a square lattice, suggesting a gapless spin-liquid phase between certain coupling ratios.

Contribution

It provides high-precision calculations of phase transition points and the nature of the spin gap, supporting the existence of a gapless spin-liquid phase in the model.

Findings

Transition points at J_2^{c1}=0.454J_1 and J_2^{c2}=0.588J_1

Spin gap is zero in the accessible parameter region

Supports a gapless spin-liquid ground state

Abstract

We use the coupled cluster method to high orders of approximation in order to calculate the ground-state energy, the ground-state magnetic order parameter, and the spin gap of the spin-1/2 J_1-J_2 model on the square lattice. We obtain values for the transition points to the magnetically disordered quantum paramagnetic phase of J_2^{c1}=0.454J_1 and J_2^{c2}= 0.588 J_1. The spin gap is zero in the entire parameter region accessible by our approach, i.e. for J_2 \le 0.49J_1 and J_2 > 0.58J_1. This finding is in favor of a gapless spin-liquid ground state in this parameter regime.