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Critical coloredRVB states in the frustrated quantum Heisenberg model on the square lattice
by Didier Poilblanc, Matthieu Mambrini, Sylvain Capponi
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Submission summary
Authors (as registered SciPost users):  Sylvain Capponi · Matthieu Mambrini · Didier Poilblanc 
Submission information  

Preprint Link:  https://arxiv.org/abs/1907.03678v1 (pdf) 
Date submitted:  20190711 02:00 
Submitted by:  Poilblanc, Didier 
Submitted to:  SciPost Physics 
Ontological classification  

Academic field:  Physics 
Specialties: 

Approach:  Theoretical 
Abstract
We consider a family of SU(2)symmetric Projected Entangled Paired States (PEPS) on the square lattice, defining coloredResonating Valence Bond (RVB) states, to describe the quantum disordered phase of the $J_1J_2$ frustrated Heisenberg model.For $J_2/J_1\sim 0.55$ we show the emergence of critical (algebraic) dimerdimer correlations  typical of RokhsarKivelson (RK) points of quantum dimer models on bipartite lattices  while, simultaneously, the spinspin 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.
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Reports on this Submission
Report #2 by Anonymous (Referee 2) on 2019828 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1907.03678v1, delivered 20190828, doi: 10.21468/SciPost.Report.1136
Strengths
study of an important model in the field
state of the art results
fresh insights for a new critical spin liquid phase
Weaknesses
 too technical for general audience
Report
The Authors report a numerical study of the spin1/2 J1J2 Heisenberg model on the square lattice, based on a family of variational, SU(2)symmetric PEPS wavefunctions. This model is one of the first and simplest frustrated models studied, with potential spin liquid states in the region J2~J1/2. Despite many studies, the nature of the ground state(s) in this region is still unsettled.
The Authors focus at the parameter point J2=0.55J1 and offer fresh insights for a possible critical phase, different from the one at J2=0.5J1. While these results do not settle the issue fully (the Authors point out possible connections to VBC phases reported previously), this study should be interesting for people working in this field and will motivate further investigations in this very old model. I would therefore recommend the article for publication.
The paper is well written, although a bit too technical for nonspecialists.
Report #1 by Anonymous (Referee 1) on 2019826 (Invited Report)
 Cite as: Anonymous, Report on arXiv:1907.03678v1, delivered 20190826, doi: 10.21468/SciPost.Report.1124
Strengths
1. Paper explores an interesting and longstanding problem regarding the nature of the quantum disordered region for the spin$1/2$ $J_1$$J_2$ Heisenberg model on the square lattice.
2. A rather careful variational wavefunction analysis is presented using the iPEPS method.
3. Signatures of an interesting state with shortranged spinspin correlations but critical dimerdimer correlations found for $J_2/J_1 \sim 0.55$.
Weaknesses
1. The technicalities related to the variational determination of the ground state using iPEPS are a bit difficult to follow.
Report
The properties of the ground state of the spin$1/2$ $J_1$$J_2$ Heisenberg model on the square lattice in its quantum disordered region (in the vicinity of $J_2/J_1 \sim 0.5$) has attracted considerable attention for several years now due to the interplay of strong quantum fluctuations and frustration. Despite this, the nature of the phase(s) in the quantum disordered region remains controversial.
Here, the authors consider a family of PEPS with the full space group symmetry of the lattice and the $SU(2)$ spin rotation symmetry incorporated in their calculations. Within this variational approach, they find an interesting RVBlike state with shortranged spinspin correlations but (almost) critical dimerdimer correlations for $J_2/J_1 \sim 0.55$. This state is rather different from a gapless spin liquid (where the spinspin correlations are also algebraic) obtained at $J_2/J_1=0.5$ using a similar framework.
Could the authors comment on the following? Can they detect some signatures of an enlarged symmetry (possibly $U(1)$) from the wavefunction at $J_2/J_1 \sim 0.55$, e.g., by looking at columnar and plaquette like dimer correlation functions as a function of $r$? Secondly, when they compute the dimerdimer correlations using long stripes, how do they take into account of the reduced lattice symmetry in their variational parameters?
The results presented here are definitely interesting and the numerics has been carefully done. After getting appropriate response from the authors to my questions above, I will be happy to recommend this manuscript for publication.
Requested changes
1. Few typos need to be corrected. E.g. Page 2, second paragraph>"which are specially designed to "describe" SU(2)invariant", Page 6, first paragraph>"Hence, we have "improved" the CTMRG", Page 11, last paragraph>"(at least) two "scenarios""