Gapless spin liquid ground state of spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices

TL;DR

This study uses advanced tensor network methods to demonstrate that the spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices hosts a gapless spin liquid phase without magnetic or dimer order in a specific parameter range.

Contribution

The paper introduces a novel application of gradient-optimized PEPS combined with Monte Carlo sampling to accurately determine the ground state of the $J_1$-$J_2$ model, revealing a gapless spin liquid phase.

Findings

No magnetic, dimer, or plaquette order in the intermediate region.

Power-law decay of correlation functions indicating a gapless spin liquid.

Ground state energies competitive with the best existing results.

Abstract

The spin-1/2 $J_1$-$J_2$ Heisenberg model on square lattices are investigated via the finite projected entangled pair states (PEPS) method. Using the recently developed gradient optimization method combining with Monte Carlo sampling techniques, we are able to obtain the ground states energies that are competitive to the best results. The calculations show that there is no N\'eel order, dimer order and plaquette order in the region of 0.42 $\lesssim J_2/J_1\lesssim$ 0.6, suggesting a single spin liquid phase in the intermediate region. Furthermore, the calculated staggered spin, dimer and plaquette correlation functions all have power law decay behaviours, which provide strong evidences that the intermediate nonmagnetic phase is a single gapless spin liquid state.