We analyze the effects of the on-site Coulomb repulsion U on a band insulator using dynamical mean field theory (DMFT). We find the surprising result that the gap is suppressed to zero at a critical U c1 and remains zero within a metallic phase. At a larger U c2 there is a second transition from the metal to a Mott insulator, in which the gap increases with increasing U. These results are qualitatively different from Hartree-Fock theory which gives a monotonically decreasing but nonzero insulating gap for all finite U.

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We study the T = 0 crossover from the BCS superconductivity to Bose-Einstein condensation in the attractive Hubbard Model within dynamical mean field theory(DMFT) in order to examine the validity of Hartree-Fock-Bogoliubov (HFB) mean field theory, usually used to describe this crossover, and to explore physics beyond it. Quantum fluctuations are incorporated using iterated perturbation theory as the DMFT impurity solver. We find that these fluctuations lead to large quantitative effects in the intermediate coupling regime leading to a reduction of both the superconducting order parameter and the energy gap relative to the HFB results. A qualitative change is found in the single-electron spectral function, which now shows incoherent spectral weight for energies larger than three times the gap, in addition to the usual Bogoliubov quasiparticle peaks.

We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions or long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space, and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping (t(r) ∼ t0/r α with α < 2), there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with 1 < α < 2 delocalizes the system partially, with almost all the states extended for α ≤ 1. Even in a system which has single-particle mobility edges in the non-interacting limit, turning on long-range interactions does not cause delocalization.

We demonstrate in a simple model the surprising result that turning on an on-site Coulomb interaction U in a doped band insulator leads to the formation of a half-metallic state. In the undoped system, we show that increasing U leads to a first order transition at a finite value UAF between a paramagnetic band insulator and an antiferomagnetic Mott insulator. Upon doping, the system exhibits half-metallic ferrimagnetism over a wide range of doping and interaction strengths on either side of UAF. Our results, based on dynamical mean field theory, suggest a new route to half metallicity, and will hopefully motivate searches for new materials for spintronics.

We study the phase diagram of the ionic Hubbard model (IHM) at half-filling on a Bethe lattice of infinite connectivity using dynamical mean field theory (DMFT), with two impurity solvers, namely, iterated perturbation theory (IPT) and continuous time quantum Monte Carlo (CTQMC). The physics of the IHM is governed by the competition between the staggered ionic potential ∆ and the on-site Hubbard U . We find that for a finite ∆ and at zero temperature, long range antiferromagnetic (AFM) order sets in beyond a threshold U = UAF via a first order phase transition. For U smaller than UAF the system is a correlated band insulator. Both the methods show a clear evidence for a quantum transition to a half-metal phase just after the AFM order is turned on, followed by the formation of an AFM insulator on further increasing U . We show that the results obtained within both the methods have good qualitative and quantitative consistency in the intermediate to strong coupling regime at zero temperature as well as at finite temperature. On increasing the temperature, the AFM order is lost via a first order phase transition at a transition temperature TAF (U, ∆) (or, equivalently, on decreasing U below UAF (T, ∆)), within both the methods, for weak to intermediate values of U/t. In the strongly correlated regime, where the effective low energy Hamiltonian is the Heisenberg model, IPT is unable to capture the thermal (Neel) transition from the AFM phase to the paramagnetic phase, but the CTQMC does. At a finite temperature T , DMFT+CTQMC shows a second phase transition (not seen within DMFT+IPT) on increasing U beyond UAF . At UN > UAF , when the Neel temperature TN for the effective Heisenberg model becomes lower than T , the AFM order is lost via a second order transition. For2 ) where x = 2∆/U and thus TN increases with increase in ∆/U . In the 3-dimensional parameter space of (U/t, T /t and ∆/t), as T increases, the surface of first order transition at UAF (T, ∆) and that of the second order transition at UN (T, ∆) approach each other, shrinking the range over which the AFM order is stable. There is a line of tricritical points that separates the surfaces of first and second order phase transitions.

We show that in weakly disordered Luttinger liquids close to a commensurate filling the ratio of thermal conductivity kappa and electrical conductivity sigma can deviate strongly from the Wiedemann-Franz law valid for Fermi liquids scattering from impurities. In the regime where the umklapp scattering rate Gamma(U) is much larger than the impurity scattering rate Gamma(imp), the Lorenz number L = kappa/(sigmaT) rapidly changes from very large values L approximately Gamma(U)/Gamma(imp) >> 1 at the commensurate point to very small values L approximately Gamma(imp)/Gamma(U) << 1 for a slightly doped system. This surprising behavior is a consequence of approximate symmetries existing even in the presence of strong umklapp scattering.

We study many-body localization (MBL) in an interacting one-dimensional system with a deterministic aperiodic potential. Below the threshold potential h < hc, the non-interacting system has single particle mobility edges (MEs) at ±Ec while for h > hc all the single particle states are localized. We demonstrate that even in the presence of single particle MEs, interactions do not always delocalise the system and the interacting system can have MBL. Our numerical calculation of energy level spacing statistics, participation ratio in the Fock space and Shannon entropy shows that for some regime of particle densities, even for h < hc many-body states at the top (with E > E2) and the bottom of the spectrum (with E < E1) remain localized though states in the middle of the spectrum are delocalized. Variance of entanglement entropy (EE) also diverges at E1,2 indicating a transition from MBL to delocalized regime though transition from volume to area law scaling for EE and from thermal to non-thermal behavior occur inside the MBL regime much below E1 and above E2. Interplay of disorder and interactions in quantum systems is a topic of great interest in condensed matter physics. In a non-interacting system with random disorder, any small amount of disorder is sufficient to localize all the single particle states in one and two dimensions [1][2][3], except in systems where back scattering is suppressed e.g. in graphene [4,5], while in three dimensions (3-d) there occurs a single particle mobility edge (ME) leading to a metal-Anderson Insulator transition. The question of immense interest, that has remained unanswered for decades, is what happens to Anderson localization when both disorder and interactions are present in a system. Recently based on perturbative treatment of interactions for the case where all the single particle states are localised, it has been established that Anderson localization can survive interactions and disordered many-body eigenstates can be localized resulting in a many-body localized (MBL) phase, provided that interactions are sufficiently weak [6]. The question we want to answer in this work is what happens in the presence of interactions when the non-interacting system has single particle MEs? Conventional wisdom says that in the presence of interactions, localised states will get hybridised with the extended states resulting in delocalization. In this work based on exact diagonalisation (ED) study of an interacting model of spin-less fermions in the presence of a deterministic aperiodic potential, where the non-interacting system has MEs, we demonstrate that for some parameter regimes, many-body states at the top and the bottom of the spectrum remain localised even in the presence of interactions.The MBL phase and the MBL transition are unique for several reasons and challenge the basic foundations of quantum statistical physics [7,8]. In the MBL phase the system explores only an exponentially small fraction of the configuration space and local observables do not thermalize leading to violati...