Drude and Superconducting Weights and Mott Transitions in Variation Theory

Abstract

Drude weight ($D$) is a useful measure to distinguish a metal from an insulator. However, $D$ has not been justifiably estimated by the variation theory for long, since Millis and Coppersmith [Phys. Rev. B 43 (1991) 13770] pointed out that a variational wave function ${\Psi }_Q$, which includes the key ingredient (doublon-holon binding effect) for a Mott transition, yields a positive $D$ (namely metallic) even in the Mott-insulating regime. We argue that, to obtain a correct $D$, an imaginary part must exist in the wave function. By introducing a configuration-dependent phase factor ${\mathcal{P}}_{\theta }$ to ${\Psi }_Q$, Mott transitions are successfully represented by $D$ ($D=0$ for $U>U_{\mathrm{c}}$) for a normal and $d$-wave pairing states; thereby, the problem of Millis and Coppersmith is settled. Generally, ${\mathcal{P}}_{\theta }$ plays a pivotal role in describing current-carrying states in regimes of Mott physics. On the other hand, we show using a perturbation theory, the one-body (mean-field) part of the wave function should be complex for band insulators such as antiferromagnetic states in hypercubic lattices.

11pages, 14figures

References in corpus (6)

• Orbital currents in extended Hubbard models of high-T${}_c$ cuprates
• Mott Transitions and d-wave Superconductivity in Half-Filled-Band Hubbard Model on Square Lattice with Geometric Frustration
• Crossover between BCS Superconductor and Doped Mott Insulator of d-wave Pairing State in Two-Dimensional Hubbard Model
• Superconductivity and a Mott Transition in a Hubbard Model on an Anisotropic Triangular Lattice
• Dynamical mean-field theory and numerical renormalization group study of superconductivity in the attractive Hubbard model
• Exact diagonalization study of optical conductivity in two-dimensional Hubbard model

Cited by in corpus (5)

• Local theory of the insulating state
• Staggered Flux State in Two-Dimensional Hubbard Models
• Loop Current and Antiferromagnetic States in Fermionic Hubbard Model with Staggered Flux at Half Filling
• Excited States beyond Mott Gap in Half-Filled-Band Hubbard Model
• Possibility of BCS-BEC crossover in $\kappa$-type organic superconductors