Constructing gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice

TL;DR

This paper constructs a gapless spin liquid state for the spin-1/2 J1-J2 Heisenberg model on a square lattice using PEPS and RVB wavefunctions, demonstrating topological sectors and critical correlations.

Contribution

It introduces a class of PEPS-based RVB wavefunctions with both short and long-range bonds, optimized for the J1-J2 model, revealing a gapless spin liquid phase.

Findings

Identifies a gapless spin liquid phase with power-law correlations.

Constructs four topological sectors with exponentially small energy splitting.

Finds lnL correction to entanglement entropy indicating criticality.

Abstract

We construct a class of projected entangled pair states (PEPS) which is exactly the resonating valence bond (RVB) wavefunctions endowed with both short range and long range valence bonds. With an energetically preferred RVB pattern, the wavefunction is simplified to live in a one parameter variational space. We tune this variational parameter to minimize the energy for the frustrated spin 1/2 J1-J2 antiferromagnetic Heisenberg model on the square lattice. Taking a cylindrical geometry, we are able to construct four topological sectors with even or odd number of fluxes penetrating the cylinder and even or odd number of spinons on the boundary. The energy splitting in different topological sectors is exponentially small with the cylinder perimeter. We find a power law decay of the dimer correlation function on a torus, and a lnL correction to the entanglement entropy, indicating a gapless spin liquid phase at the optimum parameter.