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Quantum phases of two-dimensional $\mathbb{Z}_2$ gauge theory coupled to spinless fermion matter

Umberto Borla, Bhilahari Jeevanesan, Frank Pollmann, Sergej Moroz

Published Dec 17, 2020• 0 citations
OpenAlex

Abstract

We investigate the rich quantum phase diagram of Wegner's theory of discrete Ising gauge fields interacting with $U(1)$ symmetric single-component fermion matter hopping on a two-dimensional square lattice. In particular limits the model reduces to (i) pure $\mathbb{Z}_2$ even and odd gauge theories, (ii) free fermions in a static background of deconfined $\mathbb{Z}_2$ gauge fields, (iii) the kinetic Rokhsar-Kivelson quantum dimer model at a generic dimer filling. We develop a local transformation that maps the lattice gauge theory onto a model of $\mathbb{Z}_2$ gauge-invariant spin $1/2$ degrees of freedom. Using the mapping, we perform numerical density matrix renormalization group calculations that corroborate our understanding of the limits identified above. Moreover, in the absence of the magnetic plaquette term, we reveal signatures of topologically ordered Dirac semimetal and staggered Mott insulator phases at half-filling. At strong coupling, the lattice gauge theory displays fracton phenomenology with isolated fermions being completely frozen and dimers exhibiting restricted mobility. In that limit, we predict that in the ground state dimers form compact clusters, whose hopping is suppressed exponentially in their size. We determine the band structure of the smallest clusters numerically using exact diagonalization.

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Quantum phases of two-dimensional Z2\mathbb{Z}_2Z2​ gauge theory coupled to spinless fermion matter
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A study of spinless matter fermions coupled to a constrained Z2{\mathbb{Z}}_{2}Z2​ lattice gauge theory on a triangular ladder is presented. The triangular unit cell and the ladder geometry strongly modify the physics, as compared with a previous analysis on the square lattice. In the static case, the even and odd gauge theories for the empty and filled ladder are identical. The gauge field dynamics due to the electric coupling is drastically influenced by the absence of periodic boundary conditions, rendering the deconfinement-confinement process a crossover in general and a quantum phase transition (QPT) only for decorated couplings. At finite doping and in the static case, a staggered flux insulator at half-filling and vanishing magnetic energy competes with a uniform flux metal at elevated magnetic energy. As for the square lattice, a single QPT into a confined fermionic dimer gas is found vs electric coupling. Dimer resonances in the confined phase are, however, a second-order process only, likely reducing the tendency to phase separate for large magnetic energy. The results obtained employ a mapping to a pure spin model of Z2{\mathbb{Z}}_{2}Z2​ gauge-invariant moments, adapted from the square lattice, and density matrix renormalization group calculations thereof for numerical purposes. Global scans of the quantum phases in the intermediate coupling regime are provided.
We investigate a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field. The gauge field mediates long-range attraction between fermions resulting in their confinement into bosonic dimers. At strong coupling we develop an exactly solvable effective theory of such dimers with emergent constraints. Even at generic coupling and fermion density, the model can be rewritten as a local spin chain. Using the density matrix renormalization group the system is shown to form a Luttinger liquid, indicating the emergence of fractionalized excitations despite the confinement of lattice fermions. In a finite chain we observe the doubling of the period of Friedel oscillations which paves the way towards experimental detection of confinement in this system. We discuss the possibility of a Mott phase at the commensurate filling 2/3.
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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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