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Solvable lattice models for metals with Z2 topological order

by Brin Verheijden, Yuhao Zhao, Matthias Punk

This is not the current version.

Submission summary

As Contributors: Matthias Punk
Arxiv Link: (pdf)
Date submitted: 2019-08-02 02:00
Submitted by: Punk, Matthias
Submitted to: SciPost Physics
Discipline: Physics
Subject area: Condensed Matter Physics - Theory
Approach: Theoretical


We present quantum dimer models in two dimensions which realize metallic ground states with Z2 topological order. Our models are generalizations of a dimer model introduced in [PNAS 112, 9552-9557 (2015)] to provide an effective description of unconventional metallic states in hole-doped Mott insulators. We construct exact ground state wave functions in a specific parameter regime and show that the ground state realizes a fractionalized Fermi liquid. Due to the presence of Z2 topological order the Luttinger count is modified and the volume enclosed by the Fermi surface is proportional to the density of doped holes away from half filling. We also comment on possible applications to magic-angle twisted bilayer graphene.

Ontology / Topics

See full Ontology or Topics database.

Mott insulators Topological codes
Current status:
Has been resubmitted

Submission & Refereeing History

Resubmission 1908.00103v2 on 23 October 2019

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Submission 1908.00103v1 on 2 August 2019

Reports on this Submission

Anonymous Report 1 on 2019-10-2 Invited Report

  • Cite as: Anonymous, Report on arXiv:1908.00103v1, delivered 2019-10-02, doi: 10.21468/SciPost.Report.1207


1. New and exact results on a strongly-interacting topologically ordered model of fermions.
2. Concise and clear presentation of the results.


1. The physical discussion is restricted to a small range of physical parameters and phases.
2. Connection to twisted angle bilayer graphene physics is not sufficiently substantiated.


The authors study a lattice model of spin-singlets coupled to fermionic dimers, defined on the triangular lattice. Building on a previous study concerning a similar model on the square lattice, an exactly solvable point in parameter space is identified, and its physical properties are thoroughly analyzed. The resulting many-body state, known as a fractionalized Fermi-Liquid, violates Luttinger's theorem through the appearance of Z2 topological order. The exactly solvable point is massively degenerate due to its flat-band spectrum. Perturbing away from this point lifts the degeneracy, giving rise to a non-trivial dispersion. A crucial feature of the triangular lattice model, which distinguishes it from all previous studies, is the stability of a Z2 deconfined phase. This property is in sharp contrast to the finely-tuned RK point on the square lattice. The authors make some connections to recent experimental observations in twisted bilayer graphene. In the appendix, results for a similar model defined on the Kagome lattice are presented.

The paper is very well written and contains a concise yet self-contained presentation of the main results. Identifying an exactly solvable model exhibiting a topologically ordered metallic state is a fundamental topic with direct links to experiments in strongly correlated metals. Therefore, I recommend publication in SciPost.

Below, I list a few points which and I would like the authors to consider.

Requested changes

1. In contrast to the square lattice case that without fine-tuning is always confining, on a triangular lattice, a confinement-deconfinement transition is allowed. Could the authors comment on the nature of such a transition? In particular, its effect on the fermionic degrees of freedom.

2. Could the authors provide a physical understanding of the electronic dispersion? In particular, could the band minimum at the M point be explained through symmetry-based arguments?

3. I find that the discussion on possible connections to twisted to bi-layer graphene physics is slightly unclear. While I understand that inevitably such a link is heuristic, it might be worth devoting a full section to make the discussion more precise.

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

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