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

### Submission summary

 As Contributors: Matthieu Mambrini · Didier Poilblanc Arxiv Link: https://arxiv.org/abs/1907.03678v2 (pdf) Date accepted: 2019-09-19 Date submitted: 2019-09-13 02:00 Submitted by: Poilblanc, Didier Submitted to: SciPost Physics Discipline: Physics Subject area: Condensed Matter Physics - Theory Approach: Theoretical

### 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.

### Ontology / Topics

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Published as SciPost Phys. 7, 041 (2019)

Dear Editor,

We would like to resubmit our manuscript to SciPost. Following the referees' comments we have slightly modified the manuscript and added one ref to a relevant very recent work.

Sincerely yours,

Didier Poilblanc, on behalf of the authors

### List of changes

1) We have rearranged a bit the presentation of the iPEPS method, to make it more accessible to non-expert (the more technical part has been left in the Appendix). In particular we have now two separate subsections, one on the real space RG method (CTMRG) used to contract the tensor network and one on the optimization procedure.

2) Following one referee's comment we have made clear that, "although we are using a strip geometry,the local tensor (and the corresponding environment tensorT) has been optimized for the fully rotationally invariant (infinite) lattice." Note that, currently, the method does not allow to measure correlations along some tilted direction with respect to the crystal axis (to capture e.g. some emergent U(1) symmetry).

3) a small number of typos have been corrected, and a reference added.