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Register a new userPersistent current and Drude weight for the one-dimensional Hubbard model from current lattice density functional theory
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The Bethe-Ansatz local density approximation (LDA) to lattice density functional theory (LDFT) for the one-dimensional repulsive Hubbard model is extended to current-LDFT (CLDFT). The transport properties of mesoscopic Hubbard rings threaded by a magnetic flux are then systematically investigated by this scheme. In particular we present calculations of ground state energies, persistent currents and Drude weights for both a repulsive homogeneous and a single impurity Hubbard model. Our results for the ground state energies in the metallic phase compares favorably well with those obtained with numerically accurate many-body techniques. Also the dependence of the persistent currents on the Coulomb and the impurity interaction strength, and on the ring size are all well captured by LDA-CLDFT. Our study demonstrates that CLDFT is a powerful tool for studying one-dimensional correlated electron systems with high accuracy and low computational costs.
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The frequency-dependent response of a one-dimensional fermion system is investigated using Current Density Functional Theory (CDFT) within the local approximation (LDA). DFT-LDA, and in particular CDFT-LDA, reproduces very well the dispersion of the collective excitations. Unsurprisingly, however, the approximation fails for details of the dynamic response for large wavevectors. In particular, we introduce CDFT for the one-dimensional spinless fermion model with nearest-neighbor interaction, and use CDFT-LDA plus exact (Bethe ansatz) results for the groundstate energy as function of particle density and boundary phase to determine the linear response. The successes and failures of this approach are discussed in detail.
We calculate the charge and spin Drude weight of the one-dimensional extended Hubbard model with on-site repulsion $U$ and nearest-neighbor repulsion $V$ at quarter filling using the density-matrix renormalization group method combined with a variational principle. Our numerical results for the Hubbard model (V=0) agree with exact results obtained from the Bethe ansatz solution. We obtain the contour map for both Drude weights in the $UV$-parameter space for repulsive interactions. We find that the charge Drude weight is discontinuous across the Kosterlitz-Thouless transition between the Luttinger liquid and the charge-density-wave insulator, while the spin Drude weight varies smoothly and remains finite in both phases. Our results can be generally understood using bosonization and renormalization group results. The finite-size scaling of the charge Drude weight is well fitted by a polynomial function of the inverse system size in the metallic region. In the insulating region we find an exponential decay of the finite-size corrections with the system size and a universal relation between the charge gap $Delta_c$ and the correlation length $xi$ which controls this exponential decay.
The solution of complex many-body lattice models can often be found by defining an energy functional of the relevant density of the problem. For instance, in the case of the Hubbard model the spin-resolved site occupation is enough to describe the system total energy. Similarly to standard density functional theory, however, the exact functional is unknown and suitable approximations need to be formulated. By using a deep-learning neural network trained on exact-diagonalization results we demonstrate that one can construct an exact functional for the Hubbard model. In particular, we show that the neural network returns a ground-state energy numerically indistinguishable from that obtained by exact diagonalization and, most importantly, that the functional satisfies the two Hohenberg-Kohn theorems: for a given ground-state density it yields the external potential and it is fully variational in the site occupation.
Motivated by the large interest in the non-equilibrium dynamics of low-dimensional quantum many-body systems, we present a fully-microscopic theoretical and numerical study of the charge and spin dynamics in a one-dimensional ultracold Fermi gas following a quench. Our approach, which is based on time-dependent current-density-functional theory, is applicable well beyond the linear-response regime and produces both spin-charge separation and spin-drag-induced broadening of the spin packets.
Using time-dependent density-matrix renormalization group, we study the time evolution of electronic wave packets in the one-dimensional extended Hubbard model with on-site and nearest neighbor repulsion, U and V, respectively. As expected, the wave packets separate into spin-only and charge-only excitations (spin-charge separation). Charge and spin velocities exhibit non-monotonic dependence on V. For small and intermediate values of V, both velocities increase with V. However, the charge velocity exhibits a stronger dependence than that of the spin, leading to a more pronounced spin-charge separation. Charge fractionalization, on the other hand, is weakly affected by V. The results are explained in terms of Luttinger liquid theory in the weak-coupling limit, and an effective model in the strong-coupling regime.
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