arXiv subjects
Publications and source records attributed to X. Zotos.
Recent developments in the analysis of finite temperature dissipationless transport in integrable quantum many body problems are presented. In particular, we will discuss: (i) the role played by the conservation laws in systems as the spin 1/2 Heisenberg chain and the one-dimensional Hubbard model, (ii) exact results obtained using the Bethe ansatz method on the long time decay of current correlations.
The cohesion and conductance of a point contact in a two-dimensional metallic nanowire are investigated in an independent-electron model with hard-wall boundary conditions. All properties of the nanowire are related to the Green's function of the electronic scattering problem, which is solved exactly via a modified recursive Green's function algorithm. Our results confirm the validity of a previous approach based on the WKB approximation for a long constriction, but find an enhancement of cohesion for shorter constrictions. Surprisingly, the cohesion persists even after the last conductance channel has been closed. For disordered nanowires, a statistical analysis yields well-defined peaks in the conductance histograms even when individual conductance traces do not show well-defined plateaus. The shifts of the peaks below integer multiples of $2e^2/h$, as well as the peak heights and widths, are found to be in excellent agreement with predictions based on random matrix theory, and are similar to those observed experimentally. Thus abrupt changes in the wire geometry are not necessary for reproducing the observed conductance histograms. The effect of disorder on cohesion is found to be quite strong and very sensitive to the particular configuration of impurities at the center of the constriction.
Extending the transfer matrix DMRG algorithm, we are able to calculate imaginary time spin autocorrelations with high accuracy (absolute error $<10^{-6}$) over a wide temperature range ($0<βJ<20$). After analytic continuation using the rules of probability theory along with the entropic prior (MaxEnt), we obtain real frequency spectra for the XY model, the isotropic Heisenberg and the gaped Heisenberg-Ising model. Available exact results in some limits allow for a critical evaluation of the quality of answers expected from this procedure. We find that high precision data are still insufficient for resolving specific lineshapes such as low frequency divergences. However, the method is appropriate for identifying low temperature gaps and peak positions.
Using the Bethe ansatz method, the zero frequency contribution (Drude weight) to the spin current correlations is analyzed for the easy plane antiferromagnetic Heisenberg model. The Drude weight is a monotonically decreasing function of temperature for all 0<Delta< 1, it approaches the zero temperature value with a power law and it appears to vanish for all finite temperatures at the isotropic Delta=1 point.
We study at the microscopic level the dynamics of a one-dimensional gravitationally interacting sticky gas. Initially, N identical particles of mass m with uncorrelated, randomly distributed velocities fill homogeneously a finite region of space. It is proved that at a characteristic time a single macroscopic mass is formed with certainty, surrounded by a dust of non extensive fragments. In the continuum limit this corresponds to a single shock creating a singular mass density. The statistics of the remaining fragments obeys the Poisson law at all times following the shock. Numerical simulations indicate that up to the moment of macroscopic aggregation the system remains internally homogeneous. At the short time scale a rapid decrease in the kinetic energy is observed, accompanied by the formation of a number sqrt(N) of aggregates with masses sqrt(N).
The t-J model with constant t and J between any pair of sites is studied by exploiting the symmetry of the Hamiltonian with respect to site permutations. For a given number of electrons and a given total spin the exchange term simply yields an additive constant. Therefore the real problem is to diagonalize the "t- model", or equivalently the infinite U Hubbard Hamiltonian. Using extensively the properties of the permutation group, we are able to find explicitly both the energy eigenvalues and eigenstates, labeled according to spin quantum numbers and Young diagrams. As a corollary we also obtain the degenerate ground states of the finite $U$ Hubbard model with infinite range hopping -t>0.
In this paper, we study the spin and energy dynamic correlations of the one dimensional spin 1/2 Heisenberg model, using mostly exact diagonalization numerical techniques. In particular, observing that the uniform spin and energy currents decay to finite values at long times, we argue for the absence of spin and energy diffusion in the easy plane anisotropic Heisenberg model.
We study the lowest order conservation laws in one-dimensional (1D) integrable quantum many-body models (IQM) as the Heisenberg spin 1/2 chain, the Hubbard and t-J model. We show that the energy current is closely related to the first conservation law in these models and therefore the thermal transport coefficients are anomalous. Using an inequality on the time decay of current correlations we show how the existence of conserved quantities implies a finite charge stiffness (weight of the zero frequency component of the conductivity) and so ideal conductivity at finite temperatures.
We study numerically the finite temperature and frequency mobility of a particle coupled by a local interaction to a system of spinless fermions in one dimension. We find that when the model is integrable (particle mass equal to the mass of fermions) the static mobility diverges. Further, an enhanced mobility is observed over a finite parameter range away from the integrable point. We present a novel analysis of the finite temperature static mobility based on a random matrix theory description of the many-body Hamiltonian.
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 non-integrable cases. The integrable systems behave as ideal conductors in the metallic regime and as ideal insulators in the insulating one. The non-integrable systems are, as expected, generic conductors in the metallic regime and activated ones in the insulating regime.
We analyse the finite temperature charge stiffness D(T>0), by a generalization of Kohn's method, for the problem of a particle interacting with a fermionic bath in one dimension. We present analytical evidence, using the Bethe ansatz method, that D(T>0) is finite in the integrable case where the mass of the particle equals the mass of the fermions and numerical evidence that it vanishes in the nonintegrable one of unequal masses. We conjecture that a finite D(T>0) is a generic property of integrable systems.
We study the level statistics of a non-integrable one dimensional interacting fermionic system characterized by the GOE distribution. We calculate numerically on a finite size system the level spacing distribution $P(s)$ and the Dyson-Mehta $Δ_3$ correlation. We observe that its low energy spectrum follows rather the Poisson distribution, characteristic of an integrable system, consistent with the fact that the low energy excitations of this system are described by the Luttinger model. We propose this Random Matrix Theory analysis as a probe for the existence and integrability of low energy effective Hamiltonians for strongly correlated systems.
Using the Bethe ansatz analysis as was reformulated by Edwards, we calculate the spectral properties of a particle interacting with a bath of fermions in one dimension for the case of equal particle-fermion masses. These are directly related to singularities apparent in optical experiments in one dimensional systems. The orthogonality catastrophe for the case of an infinite particle mass survives in the limit of equal masses. We find that the exponent $β$ of the quasiparticle weight, $Z\simeq N^{-β}$ is different for the two cases, and proportional to their respective phaseshifts at the Fermi surface; we present a simple physical argument for this difference. We also show that these exponents describe the low energy behavior of the spectral function, for repulsive as well as attractive interaction.
We use exact diagonalisation in order to study the infinite - $U$ limit of the two dimensional Hubbard model. As well as looking at single-particle correlations, such as $n_{{\bf k}σ}=\langle c^\dagger _{{\bf k}σ}c_{{\bf k}σ} \rangle $, we also study {\it N-particle correlation functions} which compare the relative positions of {\it all} the particles in different models. In particular we study 16 and 18-site clusters and compare the charge correlations in the Hubbard model with those of spinless fermions and hard-core bosons. We find that although low densities of holes favour a `locally-ferromagnetic' fermionic description, the correlations at larger densities resemble those of pure hard-core bosons surprisingly well .