# Critical colored-RVB states in the frustrated quantum Heisenberg model on the square lattice

## TL;DR

This paper introduces colored-RVB states within PEPS to model the quantum disordered phase of the frustrated J1-J2 Heisenberg model, revealing critical correlations near a potential RK point.

## Contribution

It constructs a family of SU(2)-symmetric PEPS for the J1-J2 model, showing critical dimer correlations and short spin correlations near an RK point.

## Key findings

- Critical algebraic dimer-dimer correlations at J2/J1~0.55
- Short spin-spin correlation length in the same regime
- Evidence for a spin liquid or weak Valence Bond Crystal phase

## Abstract

We consider a family of SU(2)-symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining colored-Resonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1-J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimer-dimer correlations -- typical of Rokhsar-Kivelson (RK) points of quantum dimer models on bipartite lattices -- while, simultaneously, the spin-spin correlation length remains short. Our findings are consistent with a spin liquid or a weak Valence Bond Crystal in the neighborhood of an RK point.