We present results for the zero- and finite-temperature Drude weight
D(T) and for the Meissner fraction of the attractive and the repulsive Hubbard model, as well as for the model with next-nearest-neighbor repulsion. They are based on quantum Monte Carlo studies and on the Bethe ansatz. We show that the Drude weight is well defined as an extrapolation on the imaginary frequency axis, even for finite temperature. The temperature, filling, and system size dependence of D is obtained. We find counterexamples to a conjectured connection of dissipationless transport and integrability of lattice models.
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.
We study the superfluid density of hard-core bosons on quasi-one-dimensional lattices using the quantum Monte Carlo method. Because of phase slippage, the superfluid density drops quickly to zero at finite temperatures with increasing the system length $\ensuremath{\ell}$ and the superfluid transition temperature is zero in one spatial dimension and also in quasi-one dimension in the limit of $\ensuremath{\ell}\ensuremath{\rightarrow}\ensuremath{\infty}$. We calculate the superfluid density of a model where no phase slippage is allowed and show that the superfluid density remains finite at finite temperatures even in the one-dimensional limit. We also discuss how finite superfluid density can be observed in a quasi-one-dimensional system using a torsional oscillator.
A technique to determine accurately transport properties of integrable and nonintegrable quantum-spin chains at finite temperatures by quantum Monte Carlo is presented. The reduction of the Drude weight by interactions in the integrable gapless regime is evaluated. Evidence for the absence of Drude weight in the gapless regime of a nonintegrable system with longer-ranged interactions is presented. We estimate the effect of the nonintegrability on the transport properties and compare with recent experiments on one-dimensional quantum-spin chains.
A nonzero superfluid density is equivalent to the occurrence of a Meissner effect and therefore signals superconductivity. A recent theorem shows that in the case of a spectrum with a gap the superfluid density is equivalent to the Drude weight. This theorem is employed to compare approximate calculations of the superfluid density in the two-dimensional attractive Hubbard model using the Hartree-Fock approximation with exact diagonalization calculations of the Drude weight. Direct comparison of the approximate results with recent finite-temperature quantum Monte Carlo calculations is also made. The approximate results are found to be quantitatively accurate for all fillings, except close to half-filling.
We study the Drude weight D ( T ) at finite temperatures T of an integrable bosonic model where the particles interact via nearest-neighbour coupling on a chain. At low temperatures, D ( T ) is shown to be universal in the sense that this region is equivalently described by a Gaussian model. This low-temperature limit is also relevant for the integrable one-dimensional Bose gas. We then use the thermodynamic Bethe ansatz to confirm the low-temperature result, to obtain the high-temperature limit of D ( T ) and to calculate D ( T ) numerically.