Gapless spin liquid and valence-bond solid in the $J_1-J_2$ Heisenberg model on the square lattice: insights from singlet and triplet excitations

TL;DR

This study uses advanced computational methods to identify a quantum phase transition in the $J_1-J_2$ Heisenberg model on the square lattice, revealing a transition from a gapless spin liquid to a valence-bond solid.

Contribution

It provides new evidence for a phase transition in the $J_1-J_2$ model using singlet and triplet excitation analysis, clarifying previous conflicting results.

Findings

Identification of a level crossing at J2/J1 ≈ 0.54

Evidence for a gapless spin liquid phase between J2/J1 ≈ 0.48 and 0.54

Detection of a valence-bond solid phase for J2/J1 > 0.54

Abstract

The spin-$1/2$ $J_1-J_2$ Heisenberg model on the square lattice represents one of the simplest examples in which the effets of magnetic interactions may suppress magnetic order, eventually leading to a pure quantum phase with no local order parameters. This model has been extensively studied in the last three decades, with conflicting results. Here, by using Gutzwiller-projected wave functions and recently developed methods to assess the low-energy spectrum, we show the existence of a level crossing between the lowest-energy triplet and singlet excitations for $J_2/J_1 \approx 0.54$. This fact supports the existence of a phase transition between a gapless spin liquid (which is stable for $0.48 \lesssim J_2/J_1 \lesssim 0.54$) and a valence-bond solid (for $0.54 \lesssim J_2/J_1 \lesssim 0.6$), even though no clear sign of dimer order is visible in the correlations functions. These results, which confirm recent density-matrix renormalization calculations on cylindrical clusters [L. Wang and A.W. Sandvik, Phys. Rev. Lett. 121, 107202 (2018)] reconcile the contraddicting results obtained within different approaches over the years.