Using numerical diagonalization techniques we analyze the finite temperature/frequency conductance of a one-dimensional model of interacting spinless fermions. Depending on the interaction, the observed finite temperature charge stiffness and low-frequency conductance indicate a fundamental difference between integrable and nonintegrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The nonintegrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime. \textcopyright{} 1996 The American Physical Society.
Finite-temperature T>0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing in the metallic phases ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is an integrable system of wide physical interest. For electronic densities
n=1 it is an ideal conductor, with ballistic charge transport for T larger or equal to 0. In spite that it is solvable by the Bethe ansatz, at
n=1 its T>0 transport properties are a collective-behavior issue that remains poorly understood. Here we combine that solution with symmetry to show that for on-site repulsion U>0 the charge stiffness D (T) vanishes for T>0 in the thermodynamic limit. This absence of finite-temperature ballistic charge transport is an exact result that clarifies a long-standing open problem.
Finite-temperature T > 0 transport properties of integrable and nonintegrable one-dimensional (1D) many-particle quantum systems are rather different, showing ballistic and diffusive behavior, respectively. The repulsive 1D Hubbard model is a prominent example of an integrable correlated system. For electronic densities n ≠ 1 (and spin densities m ≠ 0) it is an ideal charge (and spin) conductor, with ballistic charge (and spin) transport for T ⩾ 0. In spite of the fact that it is solvable by the Bethe ansatz, at n = 1 (and m = 0) its T > 0 charge (and spin) transport properties are an issue that remains poorly understood. Here we combine this solution with symmetry and the explicit calculation of current-operator matrix elements between energy eigenstates to show that for on-site repulsion U > 0 and at n = 1 the charge stiffness D η ( T ) vanishes for T > 0 in the thermodynamic limit. A similar behavior is found by such methods for the spin stiffness D s ( T ) for U > 0 and T > 0, which vanishes at m = 0. This absence of finite temperature n = 1 ballistic charge transport and m = 0 ballistic spin transport are exact results that clarify long-standing open problems.
Combining the Bethe ansatz with a functional deviation expansion and using an asymptotic expansion of the Bethe ansatz equations, we compute the curvature of levels
Dn at any filling for the one-dimensional lattice spinless fermion model. We use these results to study the finite-temperature charge stiffness
D(T). We find that the curvature of the levels obeys, in general, the relation ${D}_{n}{=D}_{0}+\ensuremath{\delta}{D}_{n},$ where
D0 is the zero-temperature charge stiffness and $\ensuremath{\delta}{D}_{n}$ arises from excitations. Away from half-filling and for the low-energy (gapless) eigenstates, we find that the energy levels are, in general, flux dependent and, therefore, the system behaves as an ideal conductor, with
D(T) finite. We show that if gapped excitations are included the low-energy excitations feel an effective flux ${\ensuremath{\Phi}}^{\mathrm{eff}}$ which is different from what is usually expected. At half-filling, we prove, in the strong interacting limit and to order
1/V (V is the nearest-neighbor Coulomb interaction), that the energy levels are flux independent. This leads to a zero value for the curvature of levels
Dn and, as a consequence, to
D(T)=0, proving an earlier conjecture of Zotos and Prelov\ifmmode \check{s}\else \v{s}\fi{}ek [Phys. Rev. B 53, 983 (1996)].
Integrable and nonintegrable systems have very different transport properties. In this paper, we highlight these differences for specific one-dimensional models of interacting lattice fermions. The technique used is a finite temperature numerical calculation of the adiabatic stiffness (also called the Drude weight or charge stiffness) and isothermal stiffness (also called the ``Meissner'' stiffness) in electrical and energy transport, and the momentum dependent dynamical conductivities $\ensuremath{\sigma}(q,\ensuremath{\omega})$ and $\ensuremath{\kappa}(q,\ensuremath{\omega})$. We apply a flux twist to break the Kramers degeneracy; thus, allowing us to focus on the effect of the dynamical degeneracies in the integrable system. In this situation, we show that the isothermal stiffness goes to zero rapidly with the system size for both types of systems even at high temperatures; while the adiabatic stiffness appears to go to zero in the nonintegrable system and to a finite value in the integrable one. We analyze this difference in terms of the statistics of the current matrix elements and the degeneracies of the systems, and show that in the integrable system, despite the presence of degeneracies, the dominant contribution to the adiabatic stiffness comes from large-current-carrying nondegenerate states. We also show that energy transport at nonzero $\ensuremath{\omega}$ and
q occurs within a banded continuum in the integrable system indicative of ballistic transport while the nonintegrable system shows diffusion but with the existence of overdamped excitations at large values of momentum.