Luttinger liquid physics from infinite-system DMRG

We study one-dimensional spinless fermions at zero and finite temperature T using the density matrix renormalization group. We consider nearest as well as next-nearest neighbor interactions; the latter render the system inaccessible by a Bethe ansatz treatment. Using an infinite-system alogrithm we demonstrate the emergence of Luttinger liquid physics at low energies for a variety of static correlation functions as well as for thermodynamic properties. The characteristic power law suppression of the momentum distribution n(k) function at T=0 can be directly observed over several orders of magnitude. At finite temperature, we show that n(k) obeys a scaling relation. The Luttinger liquid parameter and the renormalized Fermi velocity can be extracted from the density response function, the specific heat, and/or the susceptibility without the need to carry out any finite-size analysis. We illustrate that the energy scale below which Luttinger liquid power laws manifest vanishes as the half-filled system is driven into a gapped phase by large interactions

Approaching Many-Body Localization from Disordered Luttinger Liquids via the Functional Renormalization Group

We study the interplay of interactions and disorder in a one-dimensional fermion lattice coupled adiabatically to infinite reservoirs. We employ both the functional renormalization group (FRG) as well as matrix product state techniques, which serve as an accurate benchmark for small systems. Using the FRG, we compute the length- and temperature-dependence of the conductance averaged over $10^4$ samples for lattices as large as $10^{5}$ sites. We identify regimes in which non-ohmic power law behavior can be observed and demonstrate that the corresponding exponents can be understood by adapting earlier predictions obtained perturbatively for disordered Luttinger liquids. In presence of both disorder and isolated impurities, the conductance has a universal single-parameter scaling form. This lays the groundwork for an application of the functional renormalization group to the realm of many-body localization

Finite temperature dynamical DMRG and the Drude weight of spin-1/2 chains

We propose an easily implemented approach to study time-dependent correlation functions of one dimensional systems at finite temperature T using the density matrix renormalization group. The entanglement growth inherent to any time-dependent calculation is significantly reduced if the auxiliary degrees of freedom which purify the statistical operator are time evolved with the physical Hamiltonian but reversed time. We exploit this to investigate the long time behavior of current correlation functions of the XXZ spin-1/2 Heisenberg chain. This allows a direct extraction of the Drude weight D at intermediate to large T. We find that D is nonzero -- and thus transport is dissipationless -- everywhere in the gapless phase. At low temperatures we establish an upper bound to D by comparing with bosonization

Reducing the numerical effort of finite-temperature density matrix renormalization group transport calculations

Finite-temperature transport properties of one-dimensional systems can be studied using the time dependent density matrix renormalization group via the introduction of auxiliary degrees of freedom which purify the thermal statistical operator. We demonstrate how the numerical effort of such calculations is reduced when the physical time evolution is augmented by an additional time evolution within the auxiliary Hilbert space. Specifically, we explore a variety of integrable and non-integrable, gapless and gapped models at temperatures ranging from T=infty down to T/bandwidth=0.05 and study both (i) linear response where (heat and charge) transport coefficients are determined by the current-current correlation function and (ii) non-equilibrium driven by arbitrary large temperature gradients. The modified DMRG algorithm removes an 'artificial' build-up of entanglement between the auxiliary and physical degrees of freedom. Thus, longer time scales can be reached

Luttinger liquid universality in the time evolution after an interaction quench

We provide strong evidence that the relaxation dynamics of one-dimensional, metallic Fermi systems resulting out of an abrupt amplitude change of the two-particle interaction has aspects which are universal in the Luttinger liquid sense: The leading long-time behavior of certain observables is described by universal functions of the equilibrium Luttinger liquid parameter and the renormalized velocity. We analytically derive those functions for the Tomonaga-Luttinger model and verify our hypothesis of universality by considering spinless lattice fermions within the framework of the density matrix renormalization group

Transport properties of the one-dimensional Hubbard model at finite temperature

We study finite-temperature transport properties of the one-dimensional Hubbard model using the density matrix renormalization group. Our aim is two-fold: First, we compute both the charge and the spin current correlation function of the integrable model at half filling. The former decays rapidly, implying that the corresponding Drude weight is either zero or very small. Second, we calculate the optical charge conductivity sigma(omega) in presence of small integrability-breaking next-nearest neighbor interactions (the extended Hubbard model). The DC conductivity is finite and diverges as the temperature is decreased below the gap. Our results thus suggest that the half-filled, gapped Hubbard model is a normal charge conductor at finite temperatures. As a testbed for our numerics, we compute sigma(omega) for the integrable XXZ spin chain in its gapped phase

Understanding the Josephson current through a Kondo-correlated quantum dot

We study the Josephson current 0-$\pi$ transition of a quantum dot tuned to the Kondo regime. The physics can be quantitatively captured by the numerically exact continuous time quantum Monte Carlo method applied to the single-impurity Anderson model with BCS superconducting leads. For a comparison to an experiment the tunnel couplings are determined by fitting the normal-state linear conductance. Excellent agreement for the dependence of the critical Josephson current on the level energy is achieved. For increased tunnel couplings the Kondo scale becomes comparable to the superconducting gap and the regime of the strongest competition between superconductivity and Kondo correlations is reached; we predict the gate voltage dependence of the critical current in this regime.Comment: 5 pages, 3 figure