The question of conductivity is revisited. Using the total momentum shift operator to construct the perturbed many-body Hamiltonian and ground state wave function the second derivative of the ground state energy with respect to the perturbing field is expressed in terms of the one and two-body momentum densities. The distinction between the adiabatic and envelope function derivatives, hence that between the Drude and superfluid weights, can be introduced in a straightforward manner. It is shown that a discontinuity in the momentum density leads to a contribution to the Drude weight, but not the superfluid weight, however a δ-function contribution in the two-body momentum density (such as in the BCS wave-funtion) contributes to both quantities. The connection between the discontinuity in the momentum density and localization is also demonstrated.
The question of conductivity is revisited. Using the total momentum shift operator to construct the perturbed many-body Hamiltonian and ground state wave function the second derivative of the ground state energy with respect to the perturbing field is expressed in terms of the one and two-body momentum densities. The distinction between the adiabatic and envelope function derivatives, hence that between the Drude and superfluid weights can be introduced in a straightforward manner. It is shown that a discontinuity in the momentum density leads to a contribution to the Drude weight, but not the superfluid weight, however a
δ-function contribution in the two-body momentum density (such as in the BCS wave-funtion) contributes to both quantities. The connection between the discontinuity in the momentum density and localization is also demonstrated.
We calculate the Drude weight in the superfluid (SF) and supersolid (SS) phases of the hard-core boson (HCB) model on a square lattice using stochastic series expansion (SSE). We demonstrate from our numerical calculations that the normal phase of HCBs in two dimensions can be an ideal conductor with dissipationless transport. In two dimensions, when the ground state is a SF, the superfluid stiffness drops to zero with a Kosterlitz-Thouless type transition at
TKT. The Drude weight, though is equal to the stiffness below
TKT, surprisingly, stays finite even for a range of temperatures above
TKT indicating the nondissipative transport in the normal state of this system. In contrast to this, in a three-dimensional SF phase, where the superfluid stiffness goes to zero continuously via a second-order phase transition at
Tc, the Drude weight goes to zero at
Tc, as expected. We also calculated the Drude weight in a two-dimensional SS phase, where the charge density wave (CDW) order coexists with superfluidity. For the SS phase we studied, superfluidity is lost via a Kosterlitz-Thouless transition at
TKT and the transition temperature for the CDW order is larger than
TKT. In striped SS phase where the CDW order breaks the rotational symmetry of the lattice, the system behaves like an ideal conductor for a range of temperatures above
TKT along the lattice direction parallel to the stripes, while along the direction perpendicular to the stripes it behaves like an insulator for all
T>TKT. In contrast to this, in the star-SS phase, the Drude weight along both lattice directions goes to zero along with the superfluid stiffness and for
T>TKT we have the finite temperature phase of a CDW insulator.
To distinguish a metal from an insulator, the Drude weight (D, zero-frequency component of conductivity) is a useful measure, as Kohn pointed out long ago: D > 0(=0) for a metal (insulator). Later, Millis and Coppersmith showed that a variational wave function ΨQ in which the key ingredient for a Mott transition (a doublon-holon binding effect) is introduced exhibits D > 0 (metallic) even for sufficiently large correlation strength, namely, a Mott transition is absent from. ΨQ In contrast, variational Monte Carlo studies using ΨQ confirmed, by studying relevant quantities such as doublon density d and a superconducting correlation function, Pd∞ that ΨQ undoubtedly raises a Mott transition. This contradiction has been a long-standing perplexing problem. We definitely settle this problem by adding ΨQ to a configuration-dependent phase factor Pθ, which has been hitherto overlooked. This factor appropriately picks out a negative counterpart in D for insulators, so that D vanishes. Because Pθ does not affect the quantities such as d and Pd∞, the previous results of ΨQ on the Mott transition remain intact for PθΨQ.
The Drude and superfluid weights are investigated in the context of variational theory. It is shown that a commonly applied procedure to obtain the Drude weight actually corresponds to the superfluid weight. This realization changes previous interpretations of conductivity for variational wavefunctions, one result being that the Gutzwiller wavefunction displays a finite superfluid weight at finite interaction. To gain insight into DC conductivity an expression for the current response in terms of a geometric phase is derived. Applying to the Gutzwiller wavefunction it is shown that for any value of the interaction the Gutzwiller wavefunction is a perfect conductor.