Low-energy singlet sector in spin-$\frac{1}{2}$ $J_1$--$J_2$ Heisenberg model on square lattice

TL;DR

This study uses a specialized plaquette expansion to analyze the low-energy singlet spectrum of the spin-1/2 $J_1$--$J_2$ Heisenberg model on a square lattice, revealing phase transitions and the nature of non-magnetic phases.

Contribution

It introduces a novel operator construction via plaquette expansion to investigate the low-energy singlet spectrum and phase transitions in the $J_1$--$J_2$ model.

Findings

First-order quantum phase transition at $J_2\,\approx 0.64J_1$ from non-magnetic to N\'eel phase.

Large gap in singlet spectrum excludes gapless spin-liquid state in the non-magnetic phase.

Another first-order transition at $J_2\approx 0.55J_1$ between two non-magnetic phases.

Abstract

Based on a special variant of plaquette expansion, an operator is constructed whose eigenvalues give the low-energy singlet spectrum of spin-$\frac12$ Heisenberg antiferromagnet on square lattice with nearest- and frustrating next-nearest-neighbor exchange couplings $J_1$ and $J_2$. It is well known that a non-magnetic phase arises in this model at $0.4\lesssim J_2/J_1\lesssim 0.6$ sandwiched by two N\'eel ordered phases. In agreement with previous results, we observe a first-order quantum phase transition (QPT) at $J_2\approx 0.64J_1$ from the non-magnetic phase to the N\'eel one. Large gap ($\gtrsim0.4J_1$) is found in the singlet spectrum at $J_2<0.64J_1$ that excludes a gapless spin-liquid state at $0.4\lesssim J_2/J_1\lesssim 0.6$ and the deconfined quantum criticality scenario for the QPT to another N\'eel phase. We observe a first-order QPT at $J_2\approx 0.55J_1$ presumably between two non-magnetic phases.