Finite-temperature charge transport in the one-dimensional Hubbard model

We study the charge conductivity of the one-dimensional repulsive Hubbard model at finite temperature using the method of dynamical quantum typicality, focusing at half filling. This numerical approach allows us to obtain current autocorrelation functions from systems with as many as 18 sites, way beyond the range of standard exact diagonalization. Our data clearly suggest that the charge Drude weight vanishes with a power law as a function of system size. The low-frequency dependence of the conductivity is consistent with a finite dc value and thus with diffusion, despite large finite-size effects. Furthermore, we consider the mass-imbalanced Hubbard model for which the charge Drude weight decays exponentially with system size, as expected for a non-integrable model. We analyze the conductivity and diffusion constant as a function of the mass imbalance and we observe that the conductivity of the lighter component decreases exponentially fast with the mass-imbalance ratio. While in the extreme limit of immobile heavy particles, the Falicov-Kimball model, there is an effective Anderson-localization mechanism leading to a vanishing conductivity of the lighter species, we resolve finite conductivities for an inverse mass ratio of $\eta \gtrsim 0.25$.Comment: 13 pages, 11 figure

A Measurement of Secondary Cosmic Microwave Background Anisotropies with Two Years of South Pole Telescope Observations

We present the first three-frequency South Pole Telescope (SPT) cosmic microwave background (CMB) power spectra. The band powers presented here cover angular scales 2000 < ℓ < 9400 in frequency bands centered at 95, 150, and 220 GHz. At these frequencies and angular scales, a combination of the primary CMB anisotropy, thermal and kinetic Sunyaev-Zel'dovich (SZ) effects, radio galaxies, and cosmic infrared background (CIB) contributes to the signal. We combine Planck/HFI and SPT data at 220 GHz to constrain the amplitude and shape of the CIB power spectrum and find strong evidence for nonlinear clustering. We explore the SZ results using a variety of cosmological models for the CMB and CIB anisotropies and find them to be robust with one exception: allowing for spatial correlations between the thermal SZ effect and CIB significantly degrades the SZ constraints. Neglecting this potential correlation, we find the thermal SZ power at 150 GHz and ℓ = 3000 to be 3.65 ± 0.69 μK^2, and set an upper limit on the kinetic SZ power to be less than 2.8 μK^2 at 95% confidence. When a correlation between the thermal SZ and CIB is allowed, we constrain a linear combination of thermal and kinetic SZ power: D^(tSZ)_(3000) + 0.5D^(kSZ)_(3000) = 4.60 ± 0.63 μK^2, consistent with earlier measurements. We use the measured thermal SZ power and an analytic, thermal SZ model calibrated with simulations to determine σ_8 = 0.807 ± 0.016. Modeling uncertainties involving the astrophysics of the intracluster medium rather than the statistical uncertainty in the measured band powers are the dominant source of uncertainty on σ_8. We also place an upper limit on the kinetic SZ power produced by patchy reionization; a companion paper uses these limits to constrain the reionization history of the universe

One-dimensional infinite component vector spin glass with long-range interactions

We investigate zero and finite temperature properties of the one-dimensional spin-glass model for vector spins in the limit of an infinite number m of spin components where the interactions decay with a power, \sigma, of the distance. A diluted version of this model is also studied, but found to deviate significantly from the fully connected model. At zero temperature, defect energies are determined from the difference in ground-state energies between systems with periodic and antiperiodic boundary conditions to determine the dependence of the defect-energy exponent \theta on \sigma. A good fit to this dependence is \theta =3/4-\sigma. This implies that the upper critical value of \sigma is 3/4, corresponding to the lower critical dimension in the d-dimensional short-range version of the model. For finite temperatures the large m saddle-point equations are solved self-consistently which gives access to the correlation function, the order parameter and the spin-glass susceptibility. Special attention is paid to the different forms of finite-size scaling effects below and above the lower critical value, \sigma =5/8, which corresponds to the upper critical dimension 8 of the hypercubic short-range model.Comment: 27 pages, 27 figures, 4 table

Thermal quenches in N=2* plasmas

We exploit gauge/gravity duality to study `thermal quenches' in a plasma of the strongly coupled N=2* gauge theory. Specifically, we consider the response of an initial thermal equilibrium state of the theory under variations of the bosonic or fermionic mass, to leading order in m/T<<1. When the masses are made to vary in time, novel new counterterms must be introduced to renormalize the boundary theory. We consider transitions the conformal super-Yang-Mills theory to the mass deformed gauge theory and also the reverse transitions. By construction, these transitions are controlled by a characteristic time scale \calt and we show how the response of the system depends on the ratio of this time scale to the thermal time scale 1/T. The response shows interesting scaling behaviour both in the limit of fast quenches with T\calt<<1 and slow quenches with T\calt>>1. In the limit that T\calt\to\infty, we observe the expected adiabatic response. For fast quenches, the relaxation to the final equilibrium is controlled by the lowest quasinormal mode of the bulk scalar dual to the quenched operator. For slow quenches, the system relaxes with a (nearly) adiabatic response that is governed entirely by the late time profile of the mass. We describe new renormalization scheme ambiguities in defining gauge invariant observables for the theory with time dependant couplings.Comment: 78 pages, 17 figure

Finite-Size Scaling Critical Behavior of Randomly Pinned Spin-Density Waves

We have performed Monte Carlo studies of the 3D $XY$ model with random uniaxial anisotropy, which is a model for randomly pinned spin-density waves. We study $L \times L \times L$ simple cubic lattices, using $L$ values in the range 16 to 64, and with random anisotropy strengths of $D / 2 J$ = 1, 2, 3, 6 and $\infty$. There is a well-defined finite temperature critical point, $T_c$, for each these values of $D / 2 J$. We present results for the angle-averaged magnetic structure factor, $S (k)$ at $T_c$ for $L = 64$. We also use finite-size scaling analysis to study scaling functions for the critical behavior of the specific heat, the magnetization and the longitudinal magnetic susceptibility. Good data collapse of the scaling functions over a wide range of $T$ is seen for $D / 2 J$ = 6 and $\infty$. For our finite values of $D / 2 J$ the scaled magnetization function increases with $L$ below $T_c$, and appears to approach an $L$-independent limit for large $L$. This suggests that the system is ferromagnetic below $T_c$.Comment: 21 pages in single column format, 20 .eps files, revised and expanded, errors corrected, submitted to PR