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arXiv:1405.1263 · Physical Review B

Slave rotor approach to dynamically screened Coulomb interactions in solids

Igor S. Krivenko, Silke Biermann

Published Apr 29, 2015• 9 citations
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Abstract

Recent studies of dynamical screening of the electronic Coulomb interactions in solids have revived interest in lattice models of correlated fermions coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We propose a new dynamical mean-field-based approach to dynamically screened Coulomb interactions. In the effective Anderson-Holstein model, a transformation to slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is performed to decouple the dynamical part of the interaction. This transformation allows for a systematic derivation and analysis of recently introduced approximate schemes for the solution of dynamical impurity problems, in particular, the Bose factor ansatz within the dynamic atomic limit approximation (DALA) with and without Lang-Firsov correction. More importantly still, it suggests an optimized choice for a Bose factor in the sense of the variational principle of Feynman and Peierls. We demonstrate the accuracy of our scheme and present a comparison to calculations within the DALA.

DOI
10.1103/physrevb.91.155149

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Recent studies of dynamical screening of the electronic Coulomb interactions in solids have revived interest in lattice models of correlated fermions coupled to bosonic degrees of freedom (Hubbard-Holstein-type models). We propose a new dynamical mean-field-based approach to dynamically screened Coulomb interactions. In the effective Anderson-Holstein model, a transformation to slave rotors [S. Florens and A. Georges, Phys. Rev. B 66, 165111 (2002)] is performed to decouple the dynamical part of the interaction. This transformation allows for a systematic derivation and analysis of recently introduced approximate schemes for the solution of dynamical impurity problems, in particular, the Bose factor ansatz within the dynamic atomic limit approximation (DALA) with and without Lang-Firsov correction. More importantly still, it suggests an optimized choice for a Bose factor in the sense of the variational principle of Feynman and Peierls. We demonstrate the accuracy of our scheme and present a comparison to calculations within the DALA.
Dynamical screening of the Coulomb interactions in correlated electron systems results in a low-energy effective problem with a dynamical Hubbard interaction $\mathcal{U}(\ensuremath{\omega})$. We propose a Green's function ansatz for the Anderson impurity problem with retarded interactions, in which the Green's function factorizes into a contribution stemming from an effective static-UUU problem and a bosonic high-energy part introducing collective plasmon excitations. Our approach relies on the scale separation of the low-energy properties, related to the instantaneous static UUU, from the intermediate- to high-energy features originating from the retarded part of the interaction. We argue that for correlated materials where retarded interactions arise from downfolding higher-energy degrees of freedom, the characteristic frequencies are typically in the antiadiabatic regime. In this case, accurate approximations to the bosonic factor are relatively easy to construct, with the most simple being the boson factor of the dynamical atomic-limit problem. We benchmark the quality of our method against numerically exact continuous-time quantum Monte Carlo results for the Anderson-Holstein model both at half- and quarter-filling. Furthermore, we study the Mott transition within the Hubbard-Holstein model within extended dynamical mean field theory. Finally, we apply our technique to a realistic three-band Hamiltonian for SrVO3{}_{3}3​. We show that our approach reproduces both the effective mass renormalization and the position of the lower Hubbard band by means of a dynamically screened UUU, previously determined ab initio within the constrained random phase approximation. Our approach could also be used within schemes beyond dynamical mean field theory, opening a quite general way of describing satellites and plasmon excitations in correlated materials.
Building on the work by Florens and Georges [Phys. Rev. B 70, 035114 (2004)], we formulate and study a self-consistent slave rotor mean-field theory for strongly correlated systems. This approach views the electron, in the strong correlation regime, as a composite of a neutral spinon and a charged rotor field. We solve the coupled spinon-rotor model self-consistently using a cluster mean-field theory for the rotors and various Ans\"atze for the spinon ground state. We illustrate this approach with a number of examples relevant to ongoing experiments in strongly correlated electronic systems such as (i) the phase diagram of the isotropic triangular lattice organic Mott insulators, (ii) quasiparticle excitations and tunneling asymmetry in the weakly doped cuprate superconductors, and (iii) the cyclotron mass of carriers in commensurate spin-density wave and U(1) staggered flux (or ddd-density wave) normal states of the underdoped cuprates. We compare the estimated cyclotron mass with results from recent quantum oscillation experiments on ortho-II YBa2Cu3O6.5\mathrm{Y}{\mathrm{Ba}}_{2}{\mathrm{Cu}}_{3}{\mathrm{O}}_{6.5}YBa2​Cu3​O6.5​ by Doiron-Leyraud et al. [Nature (London) 447, 565 (2007)] which appear to find Fermi pockets in the magnetic field induced normal state. We comment on the relation of this normal ground state to Fermi arcs seen in photoemission experiments above Tc{T}_{c}Tc​. This slave rotor mean-field theory can be generalized to study inhomogeneous states and strongly interacting models relevant to ultracold atoms in optical lattices.
We introduce a set of generalized slave-particle models for extended Hubbard models that treat localized electronic correlations using slave-boson decompositions. Our models automatically include two slave-particle methods of recent interest, the slave-rotor and slave-spin methods, as well as a ladder of new intermediate models where one can choose which of the electronic degrees of freedom (e.g., spin or orbital labels) are treated as correlated degrees of freedom by the slave bosons. In addition, our method removes the aberrant behavior of the slave-rotor model, where it systematically overestimates the importance of electronic correlation effects for weak interaction strength, by removing the contribution of unphysical states from the bosonic Hilbert space. The flexibility of our formalism permits one to separate and isolate the effect of correlations on the key degrees of freedom.
We consider slave boson formulations of the Hubbard model, the t–J model and the Anderson model, in which spin and charge fermion degrees of freedom are represented by Bose fields. The approach has been applied to the Hubbard model generalizing the formulation of Kotliar and Ruckenstein. There the Gutzwiller solution is recovered as a saddle point. The method allows to find other types of mean field solutions in a systematic way. Dynamical correlation functions in mean field approximation as well as fluctuation contributions are also calculated.
We introduce a representation of electron operators as a product of a spin-carrying fermion and of a phase variable dual to the total charge (slave quantum rotor). Based on this representation, a method is proposed for solving multiorbital Anderson quantum impurity models at finite interaction strength U. It consists in a set of coupled integral equations for the auxiliary field Green's functions, which can be derived from a controlled saddle point in the limit of a large number of field components. In contrast to some finite-UUU extensions of the noncrossing approximation, the method provides a smooth interpolation between the atomic limit and the weak-coupling limit, and does not display violation of causality at low frequency. We demonstrate that this impurity solver can be applied in the context of dynamical mean-field theory, at or close to half-filling. Good agreement with established results on the Mott transition is found, and large values of the orbital degeneracy can be investigated at low computational cost.
In this paper, we develop a new type of slave particle method which is similar to the slave rotor model except that the quantum rotor is substituted by a spin one slave particle. The spin-one slave particle itself can be represented in terms of Schwinger bosons/fermions. This approach is more conveniently applicable to the strongly correlated Hamiltonians with on-site Hubbard interaction and resolves the limitations of using the slave rotor model as well as the Anderson-Zou slave particle technique. For instance, the mean-field parameters of the slave spin method do not vanish above the Mott transition and this approach is smoothly connected to the non-interacting limit. As an example, we study the phase diagram of the Kane-Mele-Hubbard model using our current approach. In the absence of the spin-orbit interaction, the Mott transition occurs at Uc 3t1U_c ~ 3 t_1Uc​ 3t1​. Several aspects of the slave spin method, its gauge theory and various possible mean-field states associated with this approach have been discussed.