Absence of spin liquid phase in the $J_1-J_2$ Heisenberg model on the square lattice

TL;DR

This study uses advanced numerical methods to thoroughly analyze the $J_1-J_2$ Heisenberg model on a square lattice, conclusively showing no intermediate spin liquid phase exists between the Néel AFM and VBS phases, and identifying the nature of phase transitions.

Contribution

The paper provides the first high-precision evidence against the existence of a spin liquid phase in the $J_1-J_2$ model, revealing a direct transition and characterizing its continuous nature.

Findings

No intermediate spin liquid phase found.

Identified a continuous transition at J2/J1=0.535(3).

Determined a first-order transition at J2/J1=0.610(5).

Abstract

We perform an in-depth investigation of the phase diagram of the $J_1-J_2$ Heisenberg model on the square lattice. We take advantage of Density Matrix Renormalization Group and Fully-Augmented Matrix Product States methods and reach unprecedented accuracy with large bond dimensions. We utilize excited-level crossing analysis to pinpoint the phase transition points. It was believed before that there exists a narrow spin liquid phase sandwiched by the N\'eel antiferromagnetic (AFM) and valence bond solid (VBS) phases. Through careful finite size scaling of the level crossing points, we find a direct phase transition between the N\'eel AFM and VBS phases at $J_2/J_1 = 0.535(3)$, suggesting the absence of an intermediate spin liquid phase. We also provide accurate results for ground state energies for a variety of sizes, from which we find that the transition between the N\'eel AFM and VBS phases is continuous. These results indicate the existence of a deconfined quantum critical point at $J_2/J_1 = 0.535(3)$ in the model. From the crossing of the first derivative of the energies with $J_2$ for different sizes, we also determine the precise location of the first order phase transition between the VBS and stripe AFM phases at $J_2/J_1=0.610(5)$.