Orbital-selective Mott transition in multiband systems: Slave-spin representation and dynamical mean-field theory

Abstract

We examine whether the Mott transition of a half-filled, two-orbital Hubbard model with unequal bandwidths occurs simultaneously for both bands or whether it is a two-stage process in which the orbital with narrower bandwith localizes first (giving rise to an intermediate 'orbital-selective' Mott phase). This question is addressed using both dynamical mean-field theory, and a representation of fermion operators in terms of slave quantum spins, followed by a mean-field approximation (similar in spirit to a Gutzwiller approximation). In the latter approach, the Mott transition is found to be orbital-selective for all values of the Coulomb exchange (Hund) coupling J when the bandwidth ratio is small, and only beyond a critical value of J when the bandwidth ratio is larger. Dynamical mean-field theory partially confirms these findings, but the intermediate phase at J = 0 is found to differ from a conventional Mott insulator, with spectral weight extending down to arbitrary low energy. Finally, the orbital-selective Mott phase is found, at zero-temperature, to be unstable with respect to an inter-orbital hybridization V , and replaced at small V by a state with a large effective mass (and a low quasiparticle coherence scale) for the narrower band.

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

“…29 We also note that since the original discussion of multiband Hubbard models of Ref. 3, many other studies have emerged where the slave-spin mean field has been employed and found regions of parameter space where the slave spins are disordered. We have emphasized that these should be interpreted as orthogonal metals or orbitally selective orthogonal metals.…”

“…[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.…”