Neel-VBS phase boundary of the extended J_1-J_2 model with biquadratic interaction

TL;DR

This study investigates the phase boundary between N'eel and valence-bond-solid phases in an extended J_1-J_2 model with biquadratic interaction, using numerical diagonalization to identify continuous phase transitions and critical exponents.

Contribution

The paper provides the first numerical evidence of a continuous phase transition with unconventional critical indices in the extended J_1-J_2 model with biquadratic interaction.

Findings

Signature of continuous phase transition observed

Estimated correlation-length critical exponent =1.1(3)

Evaluation of Roomany-Wyld  function indicating non-local criticality

Abstract

The J_1-J_2 model with the biquadratic (plaquette-four-spin) interaction was simulated with the numerical-diagonalization method. Some limiting cases of this model have been investigated thoroughly. Taking the advantage of the extended parameter space, we survey the phase boundary separating the N'eel and valence-bond-solid phases. According to the deconfined-criticality scenario, the singularity of this phase boundary is continuous, accompanied with unconventional critical indices. Diagonalizing the finite-size cluster with N \le 36 spins, we observe a signature of continuous phase transition. Our tentative estimate for the correlation-length critical exponent is \nu=1.1(3). In order to elucidate a non-local character of criticality, we evaluated the Roomany-Wyld \beta function around the critical point.