Low-energy singlet and triplet excitations in the spin-liquid phase of the two-dimensional J1-J2 model

TL;DR

This paper investigates the stability and excitations of the spin-liquid phase in the 2D J1-J2 Heisenberg model, revealing stable triplet and singlet modes and their behavior at phase transitions.

Contribution

It provides a detailed analysis of the low-energy excitations and the nature of the phase transition in the frustrated J1-J2 model, including exact diagonalization results.

Findings

Triplet excitation is stable for 0.38 < J2/J1 < 0.62.

A stable low-energy singlet mode is identified.

Dimerization vanishes at the transition point, correlating with the singlet gap.

Abstract

We analyze the stability of the spontaneously dimerized spin-liquid phase of the frustrated Heisenberg antiferromagnet - the J1-J2 model. The lowest triplet excitation, corresponding to breaking of a singlet bond, is found to be stable in the region 0.38 < J2/J1 < 0.62. In addition we find a stable low-energy collective singlet mode, which is closely related to the spontaneous violation of the discrete symmetry. Both modes are gapped in the quantum disordered phase and become gapless at the transition point to the Neel ordered phase (J2/J1=0.38). The spontaneous dimerization vanishes at the transition and we argue that the disappearance of dimer order is related to the vanishing of the singlet gap. We also present exact diagonalization data on a small (4x4) cluster which indeed show a structure of the spectrum, consistent with that of a system with a four-fold degenerate (spontaneously dimerized) ground state.