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.
Highlights
Landau’s Fermi liquid theory is one of the cornerstones of condensed matter physics and is remarkably successful in describing conventional metallic phases of interacting electrons
In particular we argue that the Fermi surface in the Z2-FL* phase of the triangular lattice dimer model consists of small hole pockets centered at the M points of the Brillouin zone
The Fermi-pockets at the three distinct M points should give rise to an additional three-fold degeneracy of the Landau-levels, which is not observed in experiments. This could be due to two reasons: either the Fermi surface undergoes an additional reconstruction in the presence of a strong magnetic field, or our simple estimate of the dimer hopping amplitudes from a single-band, nearest-neighbor triangular tight-binding model does not hold for twisted bilayer graphene (TBG) and the dispersion minimum is at the Γ point
Summary
Landau’s Fermi liquid theory is one of the cornerstones of condensed matter physics and is remarkably successful in describing conventional metallic phases of interacting electrons. In this work we present exctly solvable, two-dimensional lattice models that exhibit metallic ground states with Z2 topological order These models are defined on the non-bipartite triangular and kagome lattices and are generalizations of a quantum dimer model introduced in Ref. [20] is defined on the bipartite square lattice and only allows for nearest neighbor dimers, a fractionalized Fermi liquid ground state without broken symmetries only appears by fine-tuning to the special RK-point, where the bosonic dimers form a U(1) spin liquid This is not a stable phase of matter, as the U(1) spin liquid is considered to be confining at large length scales [24, 25]. In the appendix we briefely present a construction of exact ground states for analogous dimer models on the kagome lattice
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