# Competing Spin Liquid Phases in the S=$\frac{1}{2}$ Heisenberg Model on the Kagome Lattice

### Submission summary

 As Contributors: Shenghan Jiang Arxiv Link: https://arxiv.org/abs/1610.02024v2 Date submitted: 2019-04-24 Submitted by: Jiang, Shenghan Submitted to: SciPost Physics Domain(s): Theor. & Comp. Subject area: Condensed Matter Physics - Computational

### Abstract

The properties of ground state of spin-$\frac{1}{2}$ kagome antiferromagnetic Heisenberg (KAFH) model have attracted considerable interest in the past few decades, and recent numerical simulations reported a spin liquid phase. The nature of the spin liquid phase remains unclear. For instance, the interplay between symmetries and $Z_2$ topological order leads to different types of $Z_2$ spin liquid phases. In this paper, we develop a numerical simulation method based on symmetric projected entangled-pair states (PEPS), which is generally applicable to strongly correlated model systems in two spatial dimensions. We then apply this method to study the nature of the ground state of the KAFH model. Our results are consistent with that the ground state is a $U(1)$ Dirac spin liquid rather than a $Z_2$ spin liquid.

###### Current status:
Editor-in-charge assigned

### Submission & Refereeing History

Submission 1610.02024v2 on 24 April 2019

## Reports on this Submission

### Strengths

The Kagome HAFM is one of the hardest problem in frustrated quantum magnetism. The authors use state-of-the-art, recently developed, reliable tensor network (TN) techniques to investigate the nature of the spin liquid ground-state, obtaining convincing results in favor of a critical Dirac spin liquid.

### Weaknesses

Naively, one may think this paper is a bit outdated, considering the fact that more recent work on the topic, reaching similar conclusions, have been published as e.g. Liao et al., Phys. Rev. Lett. 118, 137202 (2017) by the group of Professor Tao Xiang (see comment below).

### Report

Considering the two remarks above, my overall opinion about the paper is very positive and I think it should be published because:

i) it was initially submitted on arXiv at the same time (even a week before) as the above mentioned PRL, while drawing similar strong conclusions.

ii) it follows a different route, using state-of-the-art tensor symmetry analysis, enabling to construct fully SU(2)-symmetric ansatz while in the non-symmetric TN version a spurious finite 120-degrees magnetic order at all finite D (the tensor bond dimension) values appears.

• validity: top
• significance: high
• originality: top
• clarity: high
• formatting: excellent
• grammar: perfect