Correlated metallic state in honeycomb lattice: Orthogonal Dirac semimetal

TL;DR

This paper introduces the orthogonal Dirac semimetal, a novel gapped metallic state with topological order in honeycomb lattices, characterized by fractionalized excitations and a quantum phase transition with 2+1D Ising universality.

Contribution

It proposes the orthogonal Dirac semimetal state using $Z_{2}$ slave-spin representation, analyzes its quantum criticality, and constructs a path integral formalism for this approach.

Findings

Orthogonal Dirac semimetal has the same thermodynamic and transport properties as Dirac semimetal.

The quantum phase transition belongs to the 2+1D Ising universality class.

A large anomalous dimension for the physical electron is observed at the quantum critical point.

Abstract

A novel gapped metallic state coined orthogonal Dirac semimetal is proposed in the honeycomb lattice in terms of $Z_{2}$ slave-spin representation of Hubbard model. This state corresponds to the disordered phase of slave-spin and has the same thermaldynamical and transport properties as usual Dirac semimetal but its singe-particle excitation is gapped and has nontrivial topological order due to the $Z_{2}$ gauge structure. The quantum phase transition from this orthogonal Dirac semimetal to usual Dirac semimetal is described by a mean-field decoupling with complementary fluctuation analysis and its criticality falls into the universality class of 2+1D Ising model while a large anomalous dimension for the physical electron is found at quantum critical point (QCP), which could be considered as a fingerprint of our fractionalized theory when compared to other non-fractionalized approaches. As byproducts, a path integral formalism for the $Z_{2}$ slave-spin representation of Hubbard model is constructed and possible relations to other approaches and the sublattice pairing states, which has been argued to be a promising candidate for gapped spin liquid state found in the numerical simulation, are briefly discussed. Additionally, when spin-orbit coupling is considered, the instability of orthogonal Dirac semimetal to the fractionalized quantum spin Hall insulator (fractionalized topological insulator) is also expected. We hope the present work may be helpful for future studies in $Z_{2}$ slave-spin theory and related non-Fermi liquid phases in honeycomb lattice.