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arXiv:1708.08507 · Physical review. B./Physical review. B

Simple Z2 lattice gauge theories at finite fermion density

Christian G. Prosko, Shu-Ping Lee, Joseph Maciejko

Published Nov 2, 2017• 59 citations
arXivHTMLPDF

Abstract

Lattice gauge theories are a powerful language to theoretically describe a variety of strongly correlated systems, including frustrated magnets, high-${T}_{c}$ superconductors, and topological phases. However, in many cases gauge fields couple to gapless matter degrees of freedom, and such theories become notoriously difficult to analyze quantitatively. In this paper we study several examples of ${\mathbb{Z}}_{2}$ lattice gauge theories with gapless fermions at finite density, in one and two spatial dimensions, that are either exactly soluble or whose solution reduces to that of a known problem. We consider complex fermions (spinless and spinful) as well as Majorana fermions and study both theories where Gauss' law is strictly imposed and those where all background charge sectors are kept in the physical Hilbert space. We use a combination of duality mappings and the ${\mathbb{Z}}_{2}$ slave-spin representation to map our gauge theories to models of gauge-invariant fermions that are either free, or with on-site interactions of the Hubbard or Falicov-Kimball type that are amenable to further analysis. In 1D, the phase diagrams of these theories include free-fermion metals, insulators, and superconductors, Luttinger liquids, and correlated insulators. In 2D, we find a variety of gapped and gapless phases, the latter including uniform and spatially modulated flux phases featuring emergent Dirac fermions, some violating Luttinger's theorem.

DOI
10.1103/physrevb.96.205104

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Emergent superconformal symmetry in the phase diagram of a 1D Z2\mathbb{Z}_{2}Z2​ lattice gauge theory
We investigate the phase diagram and critical properties of a one-dimensional Z2\mathbb{Z}_{2}Z2​ lattice gauge theory describing an orthogonal metal, where spinless fermions and Ising spins are minimally coupled to a deconfined Z2\mathbb{Z}_{2}Z2​ gauge field. Working at half-filling of fermions, we derive an exact gauge-invariant formulation that maps the model onto decoupled XXZ and transverse-field Ising chains. This mapping enables a controlled low-energy field-theory description in terms of a perturbed Luttinger liquid and Ising conformal field theories. Combining analytical arguments with numerical simulations, we determine the full phase diagram and identify various critical and multi-critical regimes. Along a specific multi-critical line, where the fermionic and bosonic velocities coincide, we find strong evidence for an emergent superconformal symmetry. Our results establish a minimal lattice realization of emergent superconformal criticalities in a gauge-matter system and provide a route toward its exploration in quantum simulators.
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Fundamental forces of nature are described by field theories, also known as gauge theories, based on a local gauge invariance. The simplest of them is quantum electrodynamics (QED), which is an example of an Abelian gauge theory. Such theories describe the dynamics of massless photons and their coupling to matter. However, in two spatial dimensions (2D), they are known to exhibit gapped phases at low temperature. In the realm of quantum spin systems, it remains a subject of considerable debate if their low-energy physics can be described by emergent gauge degrees of freedom. Here we present a class of simple two-dimensional models that admit a low-energy description in terms of an Abelian gauge theory. We find rich phase diagrams for these models comprising exotic deconfined phases and gapless phases---a rare example for 2D Abelian gauge theories. The counterintuitive presence of gapless phases in 2D results from the emergence of additional symmetry in the models. Moreover, we propose schemes to realize our model with current experiments using ultracold bosonic atoms in optical lattices.