We review the physics of many-body localization in models with incommensurate potentials. In particular, we consider one-dimensional quasiperiodic models with single-particle mobility edges. Although a conventional perspective suggests that delocaliz
ed states act as a thermalizing bath for the localized states in the presence of of interactions, there is evidence that such systems can display non-ergodicity. This is in part due to the fact that the delocalized states do not have any kind of protection due to symmetry or topology and are thus susceptible to localization. A study of non-interacting incommensurate models shows that they admit extended, partially extended, and fully localized many-body states. These models cannot thermalize dynamically and remain localized upon the introduction of interactions. In particular, for a certain range of energy, the system can host a non-ergodic extended (i.e. metallic) phase in which the energy eigenstates violate the eigenstate thermalization hypothesis (ETH) but the entanglement entropy obeys volume-law scaling. The level statistics and entanglement growth also indicate the lack of ergodicity in these models. The phenomenon of localization and non-ergodicity in a system with interactions despite the presence of single-particle delocalized states is closely related to the so-called many-body proximity effect and can also be observed in models with disorder coupled to systems with delocalized degrees of freedom. Many-body localization in systems with incommensurate potentials (without single-particle mobility edges) have been realized experimentally, and we show how this can be modified to study the the effects of such mobility edges. Demonstrating the failure of thermalization in the presence of a single-particle mobility edge in the thermodynamic limit would indicate a more robust violation of the ETH.
We calculate the thermopower of monolayer graphene in various circumstances. First we show that experiments on the thermopower of graphene can be understood quantitatively with a very simple model of screening in the semiclassical limit. We can calcu
late the energy dependent scattering time for this model exactly. We then consider acoustic phonon scattering which might be the operative scattering mechanism in free standing films, and predict that the thermopower will be linear in any induced gap in the system. Further, the thermopower peaks at the same value of chemical potential (tunable by gate voltage) independent of the gap. Finally, we show that in the semiclassical approximation, the thermopower in a magnetic field saturates at high field to a value which can be calculated exactly and is independent of the details of the scattering. This effect might be observable experimentally.
We present an approach to tune the effective mass in an oxide semiconductor by a double doping mechanism. We demonstrate this in a model oxide system Sr$_{1-x}$La$_x$TiO$_{3-delta}$, where we can tune the effective mass ranging from 6--20$mathrm{m_e}
$ as a function of filling or carrier concentration and the scattering mechanism, which are dependent on the chosen lanthanum and oxygen vacancy concentrations. The effective mass values were calculated from the Boltzmann transport equation using the measured transport properties of thin films of Sr$_{1-x}$La$_x$TiO$_{3-delta}$. Our method, which shows that the effective mass decreases with carrier concentration, provides a means for understanding the nature of transport processes in oxides, which typically have large effective mass and low electron mobility, contrary to the tradional high mobility semiconductors.
Integrable and non-integrable systems have very different transport properties. In this work, we highlight these differences for specific one dimensional models of interacting lattice fermions using numerical exact diagonalization. We calculate the f
inite temperature adiabatic stiffness (or Drude weight) and isothermal stiffness (or ``Meissner stiffness) in electrical and thermal transport and also compute the complete momentum and frequency dependent dynamical conductivities $sigma(q,omega)$ and $kappa(q,omega)$. The Meissner stiffness goes to zero rapidly with system size for both integrable and non-integrable systems. The Drude weight shows signs of diffusion in the non-integrable system and ballistic behavior in the integrable system. The dynamical conductivities are also consistent with ballistic and diffusive behavior in the integrable and non-integrable systems respectively.
The $s=1$ spinor Bose condensate at zero temperature supports ferromagnetic and polar phases that combine magnetic and superfluid ordering. We investigate the formation of magnetic domains at finite temperature and magnetic field in two dimensions in
an optical trap. We study the general ground state phase diagram of a spin-1 system and focus on a phase that has a magnetic Ising order parameter and numerically determine the nature of the finite temperature superfluid and magnetic phase transitions. We then study three different dynamical models: model A, which has no conserved quantities, model F, which has a conserved second sound mode and the Gross-Pitaevskii (GP) equation which has a conserved density and magnetization. We find the dynamic critical exponent to be the same for models A and F ($z=2$) but different for GP ($z approx 3$). Externally imposed magnetization conservation in models A and F yields the value $z approx 3$, which demonstrates that the only conserved density relevant to domain formation is the magnetization density.
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 trans
port 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.
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 appro
priate 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.
