Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions

Abstract

We consider a 2+1 dimensional model of charged fermions coupled to a ${\mathbb{Z}}_2$ gauge field, and study the confinement transition in this regime. To elucidate the phase diagram of this model, we introduce a method to handle the Gauss law constraint within sign problem free determinantal quantum Monte Carlo, at any charge density. For generic charge densities, ${\mathbb{Z}}_2$ gauge fluctuations mediate pairing and the ground state is a gapped superfluid. Superfluidity also appears in the confined phase. This is reminiscent of the BCS-BEC crossover, except that a true zero temperature transition occurs here, with the maximum $T_c$ achieved near the transition. At half-filling also one obtains a large Fermi surface which is gapped at zero temperature. However, on increasing fermion hopping a $\pi$-flux phase is spontaneously generated, with emergent Dirac fermions that are stable against pairing. In contrast to a Fermi liquid of electrons, the change in Fermi surface volumes of the ${\mathbb{Z}}_2$ fermions occurs without the breaking of translation symmetry. Unexpectedly, the numerics indicate a single continuous transition between the deconfined Dirac phase and the confined superfluid, in contrast to the naive expectation of a split transition, where a gap to fermions precedes confinement.

arXiv comment16 pages, 14 figures

References in corpus (24)

• Quantum Orders and Symmetric Spin Liquids
• Z_2 Gauge Theory of Electron Fractionalization in Strongly Correlated Systems
• Interactions and phase transitions on graphene's honeycomb lattice
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• The Flux-Phase of the Half-Filled Band
• Worm algorithms for classical statistical models
• Short-ranged RVB physics, quantum dimer models and Ising gauge theories
• On the stability of U(1) spin liquids in two dimensions
• BCS-BEC Crossover and the Unitary Fermi Gas
• Deviations from Fermi-liquid behavior above $T_c$ in 2D short coherence length superconductors
• Solving fermion sign problem in quantum Monte Carlo by Majorana representation
• Sign-problem-free quantum Monte Carlo of the onset of antiferromagnetism in metals
• BCS superconductivity of Dirac electrons in graphene layers
• What makes the Tc of monolayer FeSe on SrTiO3 so high: a sign-problem-free quantum Monte Carlo study
• Orthogonal Metals: The simplest non-Fermi liquids
• A quantum dimer model for the pseudogap metal
• Competing Orders in a Nearly Antiferromagnetic Metal
• Split orthogonal group: A guiding principle for sign-problem-free fermionic simulations
• Superconductivity of disordered Dirac fermions
• Magnetic field screening and mirroring in graphene
• Superconductivity and Nematic Fluctuations in a model of FeSe monolayers: A Determinant Quantum Monte Carlo Study
• Quantum electrodynamics in 2+1 dimensions, confinement, and the stability of U(1) spin liquids
• Spin density wave order, topological order, and Fermi surface reconstruction
• A cluster algorithm for Lattice Gauge Theories

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