Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model

TL;DR

This paper uses advanced tensor network simulations to map the phase diagram of the spin-1/2 J1-J2 Heisenberg model on a square lattice, revealing a gapless quantum spin liquid phase and a narrow valence-bond solid region.

Contribution

First detailed comparison between PEPS and DMRG methods for this model, demonstrating PEPS's effectiveness in capturing long-range physics in frustrated quantum systems.

Findings

Identification of a gapless quantum spin liquid phase with power-law correlations

Discovery of a narrow valence-bond solid phase before the collinear antiferromagnetic phase

Validation of PEPS as a powerful tool for studying strongly correlated quantum systems

Abstract

The nature of the zero-temperature phase diagram of the spin-$1/2$ $J_1$-$J_2$ Heisenberg model on a square lattice has been debated in the past three decades, which may hold the key to understand high temperature superconductivity. By using the state-of-the-art tensor network method, specifically, the finite projected entangled pair state (PEPS) algorithm, to simulate the global phase diagram the $J_1$-$J_2$ Heisenberg model up to $24\times 24$ sites, we provide very solid evidences to show that the nature of the intermediate nonmagnetic phase is a gapless quantum spin liquid (QSL), whose spin-spin and dimer-dimer correlations both decay with a power law behavior. There also exists a valence-bond solid (VBS) phase in a very narrow region $0.56\lesssim J_2/J_1\leq0.61$ before the system enters the well known collinear antiferromagnetic phase. The physical nature of the discovered gapless QSL and potential experimental implications are also addressed. We stress that we make the first detailed comparison between the results of PEPS and the well-established density matrix renormalization group (DMRG) method through one-to-one direct benchmark for small system sizes, and thus give rise to a very solid PEPS calculation beyond DMRG. Our numerical evidences explicitly demonstrate the huge power of PEPS for precisely capturing long-range physcis for highly frustrated systems, and also demonstrate the finite PEPS method is a very powerful approach to study strongly corrleated quantum many-body problems.