Soluble limit and criticality of fermions in Z2 gauge theories

Abstract

Quantum information theory and strongly correlated electron systems share a common theme of macroscopic quantum entanglement. In both topological error correction codes and theories of quantum materials (spin liquid, heavy fermion and high-$T_c$ systems) entanglement is implemented by means of an emergent gauge symmetry. Inspired by these connections, we introduce a simple model for fermions moving in the deconfined phase of a ${\mathbb{Z}}_2$ gauge theory, by coupling Kitaev's toric code to mobile fermions. This permits us to exactly solve the ground state of this system and map out its phase diagram. Reversing the sign of the plaquette term in the toric code, permits us to tune the groundstate between an orthogonal metal and an orthogonal semimetal, in which gapless quasiparticles survive despite a gap in the spectrum of original fermions. The small-to-large Fermi surface transition between these two states occurs in a stepwise fashion with multiple intermediate phases. By using a novel diagrammatic technique we are able to explore physics beyond the integrable point, to examine various instabilities of the deconfined phase and to derive the critical theory at the transition between deconfined and confined phases. We outline how the fermionic toric code can be implemented as a quantum circuit thus providing an important link between quantum materials and quantum information theory.

6 pages with 6 figures + Appendix. Main update since v1: Proposal for a quantum emulator for fermions in ${\mathbb{Z}}_2$ gauge theories. Main update since v2: Extended discussion of orthogonal semimetal-metal transition. v2 is accepted for publication in Phys.Rev.B

References in corpus (13)

• Heavy Fermions and Quantum Phase Transitions
• Fractionalized Fermi liquids
• Orbital selective Mott transition in multi-band systems: slave-spin representation and dynamical mean-field theory
• Breakdown of a topological phase: Quantum phase transition in a loop gas model with tension
• Topological Kondo effect with Majorana fermions
• Quantum Oscillations of Electrical Resistivity in an Insulator
• Digital quantum simulation of ${\mathbb{Z}}_2$ lattice gauge theories with dynamical fermionic matter
• Charged fermions coupled to ${\mathbb{Z}}_2$ gauge fields: Superfluidity, confinement and emergent Dirac fermions
• Orbital-selective Mott transitions: Heavy fermions and beyond
• A simple fermionic model of deconfined phases and phase transitions
• Simple ${\mathbb{Z}}_2$ lattice gauge theories at finite fermion density
• Strongly coupled quantum criticality with a Fermi surface in two dimensions: fractionalization of spin and charge collective modes
• Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal

Cited by in corpus (12)

• Quantum phases of two-dimensional ${\mathbb{Z}}_2$ gauge theory coupled to single-component fermion matter
• Spin-liquid insulators can be Landau's Fermi liquids
• Topological Green's function zeros in an exactly solved model and beyond
• Synthetic ${\mathbb{Z}}_2$ gauge theories based on parametric excitations of trapped ions
• Frustrated Kondo impurity triangle: A simple model of deconfinement
• Spinless fermions in a ${\mathbb{Z}}_2$ gauge theory on the triangular ladder
• Topological Kondo effect with spinful Majorana fermions
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Obstructed Atomic Insulators and Superfluids of Fermions Coupled to ${\mathbb{Z}}_2$ Gauge Fields
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Triplet resonating valence bond theory and transition metal chalcogenides
• Critical States of Fermions with ${\mathbb{Z}}_2$ Flux Disorder