Finite size scaling in crossover among different random matrix ensembles in microscopic lattice models

Using numerical diagonalization we study the crossover among different random matrix ensembles [Poissonian, Gaussian Orthogonal Ensemble (GOE), Gaussian Unitary Ensemble (GUE) and Gaussian Symplectic Ensemble (GSE)] realized in two different microscopic models. The specific diagnostic tool used to study the crossovers is the level spacing distribution. The first model is a one dimensional lattice model of interacting hard core bosons (or equivalently spin 1/2 objects) and the other a higher dimensional model of non-interacting particles with disorder and spin orbit coupling. We find that the perturbation causing the crossover among the different ensembles scales to zero with system size as a power law with an exponent that depends on the ensembles between which the crossover takes place. This exponent is independent of microscopic details of the perturbation. We also find that the crossover from the Poissonian ensemble to the other three is dominated by the Poissonian to GOE crossover which introduces level repulsion while the crossover from GOE to GUE or GOE to GSE associated with symmetry breaking introduces a subdominant contribution. We also conjecture that the exponent is dependent on whether the system contains interactions among the elementary degrees of freedom or not and is independent of the dimensionality of the system.Comment: 15 pages, 8 figure

Many body localization in the presence of a single particle mobility edge

In one dimension, noninteracting particles can undergo a localization-delocalization transition in a quasiperiodic potential. Recent studies have suggested that this transition transforms into a many-body localization (MBL) transition upon the introduction of interactions. It has also been shown that mobility edges can appear in the single particle spectrum for certain types of quasiperiodic potentials. Here, we investigate the effect of interactions in two models with such mobility edges. Employing the technique of exact diagonalization for finite-sized systems, we calculate the level spacing distribution, time evolution of entanglement entropy, optical conductivity, and return probability to detect MBL. We find that MBL does indeed occur in one of the two models we study, but the entanglement appears to grow faster than logarithmically with time unlike in other MBL systems.Comment: 5 pages, 6 figure

Anisotropic merging and splitting of dipolar Bose-Einstein condensates

We study the merging and splitting of quasi-two-dimensional Bose-Einstein condensates with strong dipolar interactions. We observe that if the dipoles have a non-zero component in the plane of the condensate, the dynamics of merging or splitting along two orthogonal directions, parallel and perpendicular to the projection of dipoles on the plane of the condensate are different. The anisotropic merging and splitting of the condensate is a manifestation of the anisotropy of the roton-like mode in the dipolar system. The difference in dynamics disappears if the dipoles are oriented at right angles to the plane of the condensate as in this case the Bogoliubov dispersion, despite having roton-like features, is isotropic.Comment: 9 pages and 9 figure

Thermopower of the Hubbard model: Effects of multiple orbitals and magnetic fields in the atomic limit

We consider strongly-correlated systems described by the multi-orbital Hubbard model in the atomic limit and obtain exact expressions for the chemical potential and thermopower. We show that these expressions reduce to the Heikes formula in the appropriate limits ($k_BT \gg U$) and ($k_BT \ll U$) and obtain the full temperature dependence in between these regimes. We also investigate the effect of a magnetic field introduced through a Zeeman term and observe that the thermopower of the multi-orbital Hubbard model displays spikes as a function of magnetic field at certain special values of the field. This effect might be observable in experiments for materials with a large magnetic coupling.Comment: 8 pages, 4 figures Typos in eqns. 3 and 4 and reference 17 correcte

Luminosity and cooling suppression in magnetized white dwarfs

We investigate the luminosity and cooling of highly magnetized white dwarfs where cooling occurs by the diffusion of photons. We solve the magnetostatic equilibrium and photon diffusion equations to obtain the temperature and density profiles in the surface layers of these white dwarfs. With increase in field strength, the degenerate core shrinks in volume with a simultaneous increase in the core temperature. For a given white dwarf age and for a fixed interface radius or temperature, the luminosity decreases significantly from $\sim 10^{-6}\, L_{\odot}$ to $10^{-9}\, L_{\odot}$ as the field strength increases from $\sim 10^9$ to $10^{12}\,$G in the surface layers. This is remarkable as it argues that magnetized white dwarfs can remain practically hidden in an observed H--R diagram. We also find that the cooling rates for these highly magnetized white dwarfs are suppressed significantly.Comment: 6 pages including 3 figures; Proceedings of the 21st European Workshop on White Dwarfs held July 23-27, 2018 in Austin, TX, US

Doping dependence of thermopower and thermoelectricity in strongly correlated systems

The search for semiconductors with high thermoelectric figure of merit has been greatly aided by theoretical modeling of electron and phonon transport, both in bulk materials and in nanocomposites. Recent experiments have studied thermoelectric transport in ``strongly correlated'' materials derived by doping Mott insulators, whose insulating behavior without doping results from electron-electron repulsion, rather than from band structure as in semiconductors. Here a unified theory of electrical and thermal transport in the atomic and ``Heikes'' limit is applied to understand recent transport experiments on sodium cobaltate and other doped Mott insulators at room temperature and above. For optimal electron filling, a broad class of narrow-bandwidth correlated materials are shown to have power factors (the electronic portion of the thermoelectric figure of merit) as high at and above room temperature as in the best semiconductors.Comment: 4 pages, 4 figure

Universal power law in crossover from integrability to quantum chaos

We study models of interacting fermions in one dimension to investigate the crossover from integrability to non-integrability, i.e., quantum chaos, as a function of system size. Using exact diagonalization of finite-sized systems, we study this crossover by obtaining the energy level statistics and Drude weight associated with transport. Our results reinforce the idea that for system size $L \to \infty$ non-integrability sets in for an arbitrarily small integrability-breaking perturbation. The crossover value of the perturbation scales as a power law $\sim L^{-3}$ when the integrable system is gapless and the scaling appears to be robust to microscopic details and the precise form of the perturbation. We conjecture that the exponent in the power law is characteristic of the random matrix ensemble describing the non-integrable system. For systems with a gap, the crossover scaling appears to be faster than a power law.Comment: 5 pages, 7 figure

Transport, multifractality, and the breakdown of single-parameter scaling at the localization transition in quasiperiodic systems

There has been a revival of interest in localization phenomena in quasiperiodic systems with a view to examining how they differ fundamentally from such phenomena in random systems. Mo- tivated by this, we study transport in the quasiperiodic, one-dimentional (1d) Aubry-Andre model and its generalizations to 2d and 3d. We study the conductance of open systems, connected to leads, as well as the Thouless conductance, which measures the response of a closed system to boundary perturbations. We find that these conductances show signatures of a metal-insulator transition from an insulator, with localized states, to a metal, with extended states having (a) ballistic transport (1d), (b) superdiffusive transport (2d), or (c) diffusive transport (3d); precisely at the transition, the system displays sub-diffusive critical states. We calculate the beta function $\beta(g) = dln(g)/dln(L)$ and show that, in 1d and 2d, single-parameter scaling is unable to describe the transition. Further- more, the conductances show strong non-monotonic variations with L and an intricate structure of resonant peaks and subpeaks. In 1d the positions of these peaks can be related precisely to the prop- erties of the number that characterizes the quasiperiodicity of the potential; and the L-dependence of the Thouless conductance is multifractal. We find that, as d increases, this non-monotonic de- pendence of g on L decreases and, in 3d, our results for $\beta(g)$ are reasonably well approximated by single-parameter scaling.Comment: 13 pages, 6 figure