# Solvable lattice models for metals with Z2 topological order

### Submission summary

 As Contributors: Matthias Punk Arxiv Link: https://arxiv.org/abs/1908.00103v2 (pdf) Date accepted: 2019-11-26 Date submitted: 2019-10-23 02:00 Submitted by: Punk, Matthias Submitted to: SciPost Physics Academic field: Physics Specialties: Condensed Matter Physics - Theory Quantum Physics Approach: Theoretical

### Abstract

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

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Published as SciPost Phys. 7, 074 (2019)

We thank the referee for the very positive report and the helpful comments on our manuscript. Below we give a detailed response to the referee’s questions and comments. We updated our manuscript accordingly and hope this facilitates a timely publication of our work.

With many thanks and best regards, Brin Verheijden, Yuhao Zhao, Matthias Punk

# Response to referee’s requested changes:

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Response to referee’s requested changes:
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1.) So far we haven’t studied confinement transitions in our dimer model, but this is indeed a very interesting question. Such transitions would be manifest in the spontaneous breaking of lattice symmetries, leading to valence bond solid order for the purely bosonic RK model. In the presence of fermionic dimers we would expect a small Fermi surface which satisfies the conventional Luttinger count, since the Fermi surface is reconstructed due to the breaking of lattice symmetries. Unfortunatley we are not aware of definitive statements about the nature of confinement transitions between the Z2 fractionalized Fermi liquid studied in our work, and a confining phase in terms of an ordinary Fermi liquid with broken symmetries. However, related questions have been investigated recently in several numerical works, which studied square lattice models of fermionic matter coupled to Z2 gauge fields. We’ve added a corresponding comment in the discussion and conclusions section of our revised manuscript.

2.) We are not aware of a symmetry based argument which would explain why the dispersion minimum is at the M points of the Brillouin zone. Note, however, that a change of the sign of the dimer resonance amplitude delta t_1 shifts the position of the dispersion minimum back to the Gamma point. Moreover, a perturbation of the amplitude t_2 from the exactly solvable line (which we didn’t compute here, because we identified t_1 as the important perturbation) can shift the position of the dispersion minimum to the K points at the Brillouin zone corners. The position of the dispersion minima thus clearly depends on microscopic details.

3.) We want to emphasize that our model is at best a very simplistic toy model for the unconventional metallic state that has been observed in magic-angle twisted bilayer graphene (TBG) on the hole-doped side of the Mott-like insulator at a filling of nu = -2. Note that microscopic details of TBG are rather complex, as evidenced by the subtleties encountered in previous works that tried to construct a faithful tight-binding description. For this reason we wanted to refrain from making strong claims about the applicability of our model to TBG, besides pointing a few basic observations. As suggested by the referee, we now discuss relations to TBG in a new section of our manuscript, which contains an extended discussion of what was previously found in the conclusions section.

### List of changes

1.) New section 5 with an extended discussion of the relation of our results to TBG

2.) A new comment on confinement transitions in the Conclusions & Discussions section

3.) new references 34, 37, 38, 39, 40