Slave spins away from half filling: Cluster mean-field theory of the Hubbard and extended Hubbard models

Abstract

A new slave-spin representation of fermion operators has recently been proposed for the half-filled Hubbard model. We show that with the addition of a gauge variable, the formalism can be extended to finite doping. The resulting spin problem can be solved using the cluster mean-field approximation. This approximation takes short-range correlations into account by exact diagonalization on the cluster, whereas long-range correlations beyond the size of clusters are treated at the mean-field level. In the limit where the cluster has only one site and the interaction strength U is infinite, this approach reduces to the Gutzwiller approximation. There are some qualitative differences when the size of the cluster is finite. We first compute the critical U for the Mott transition as a function of a frustrating second-neighbor interaction on lattices relevant for various correlated systems, namely the cobaltites, the layered organic superconductors and the high-temperature superconductors. For the triangular lattice, we also study the extended Hubbard model with nearest-neighbor repulsion. In additionto a uniform metallic state, we find a p (3) × p (3) charge density wave in a broad doping regime, including commensurate ones. We find that in the large U limit, intersite Coulomb repulsion V strongly suppresses the single-particle weight of the metallic state.

Orthogonal metals: The simplest non-Fermi liquids

“…[2][3][4]. Specifically these papers introduced a separate slave spin for each orbital and considered mean field states where the slave spins associated with some orbitals were disordered while other slave spins stay ordered.…”

“…Unlike the more traditional 'slave boson' representations, which have a U(1) gauge redundancy, and hence require introducing a compact U(1) gauge field 7 , the slave spin representation has only a Z 2 gauge redundancy. A 'slave spin representation' of this type was first introduced to study the multi-orbital Hubbard model [2][3][4][5] and the possibility of orbital selective Mott transitions in such models. The slave spin formulation has gained in popularity over the last few years, and has been employed to describe correlation effects in multiband metals such as the iron pnictides, and also to investigate non-equilibirum physics in quantum quenches 6 .…”

Metals Get an Awkward Cousin

“…Similar numbers were obtained through cluster dynamical mean-field-theory calculations. 5 Since three spatial dimensions represent the highest experimentally relevant dimensionality, it follows that the suppression factor 1/ τ x i τ x j ≈ 10 should be taken as the upper limit for the suppression of the Drude weight at the slave-spin ordering transition.…”

“…[3][4][5], the disordering of the slave spin of some orbital signals a fractionalization of the electrons corresponding to that orbital into a charged fermion and a gapped Ising variable. The resulting charged fermion continues to be gapless and contributes to thermodynamics and transport just as in a Fermi liquid.…”

“…Unlike the more traditional "slave-boson" representations, which have a U(1) gauge redundancy, and hence require introducing a compact U(1) gauge field, 2 the slave-spin representation has only a Z 2 gauge redundancy. A "slave-spin representation" of this type was first introduced to study the multiorbital Hubbard model [3][4][5][6] and the possibility of orbital selective Mott transitions in such models. The slave-spin formulation has gained in popularity over the last few years, and has been employed to describe correlation effects in multiband metals such as the iron pnictides, and also to investigate nonequilibrium physics in quantum quenches.…”