Superfluid-insulator transition in a commensurate one-dimensional bosonic system with off-diagonal disorder

We study the nature of the superfluid-insulator quantum phase transition in a one-dimensional system of lattice bosons with off-diagonal disorder in the limit of a large integer filling factor. Monte Carlo simulations of two strongly disordered models show that the universality class of the transition in question is the same as that of the superfluid-Mott-insulator transition in a pure system. This result can be explained by disorder self-averaging in the superfluid phase and the applicability of the standard quantum hydrodynamic action. We also formulate the necessary conditions which should be satisfied by the stong-randomness universality class, if one exists.     

Some generic aspects of bosonic excitations in disordered systems

We consider noninteracting bosonic excitations in disordered systems, emphasizing generic features of quadratic Hamiltonians in the absence of Goldstone modes. We discuss relationships between such Hamiltonians and the symmetry classes established for fermionic systems. We examine the density rho(omega) of excitation frequencies omega, showing how the universal behavior rho(omega) approximately omega(4) for small omega can be obtained both from general arguments and by detailed calculations for one-dimensional models.     

Commensurate-incommensurate transition in one-dimensional disordered systems

Commensurate-incommensurate transition in the one-dimensional disordered system is investigated and the soliton density near commensurability at high and low temperatures is obtained.     

Localization-delocalization transition in non-hermitian disordered systems

Using the supersymmetry technique, we study the localization-delocalization transition in quasi-one-dimensional non-Hermitian systems with a direction. In contrast to chains, our model captures the diffusive character of carriers' motion at short distances. We calculate the joint probability of complex eigenvalues and some other correlation functions. We find that the transition is abrupt and it is due to an interplay between two saddle points in the free energy functional.     

Shape transition of state density for bosonic systems

For a finite m boson system, the ensemble-averaged state density has been computed with respect to the body interaction rank k. The shape of such a state density changes from Gaussian to semicircle as the body rank of the interaction increases. This state density is expressed as a linear superposition of Gaussian and semicircular states. The nearest-neighbour spacing distribution (NNSD), which is one of the most important spectral properties of a system, is studied. The NNSDs are rather independent of body rank k and show a Wigner distribution throughout.     

Superfluid-insulator transition in a periodically driven optical lattice

We demonstrate that the transition from a superfluid to a Mott insulator in the Bose-Hubbard model can be induced by an oscillating force through an effective renormalization of the tunneling matrix element. The mechanism involves adiabatic following of Floquet states, and can be tested experimentally with Bose-Einstein condensates in periodically driven optical lattices. Its extension from small to very large systems yields nontrivial information on the condensate dynamics.     

Superfluid-insulator transition in a moving system of interacting bosons

We analyze the stability of superfluid currents in a system of strongly interacting ultracold atoms in an optical lattice. We show that such a system undergoes a dynamic, irreversible phase transition at a critical phase gradient that depends on the interaction strength between atoms. At commensurate filling, the phase boundary continuously interpolates between the classical modulation instability of a weakly interacting condensate and the equilibrium quantum phase transition into a Mott insulator state at which the critical current vanishes. We argue that quantum fluctuations smear the transition boundary in low dimensional systems. Finally we discuss the implications to realistic experiments.     

Short range order and the metal-insulator transition in disordered systems

The effect of short range order on the electronic density of states, the conductivity, and localization is calculated for a model binary alloy in the simple cubic configuration using a cluster extension of CPA. In the presence of short range order a metal insulator transition takes place as the concentration passes through a critical range.     

Thermoelectric transport properties in disordered systems near the Anderson transition

We study the thermoelectric transport properties in the three-dimensional Anderson model of localization near the metal-insulator transition (MIT). In particular, we investigate the dependence of the thermoelectric power S, the thermal conductivity K, and the Lorenz number L₀ on temperature T. We first calculate the T dependence of the chemical potential μ from the number density n of electrons at the MIT using an averaged density of states obtained by diagonalization. Without any additional approximation, we determine from the behavior of S, K and L₀ at low T as the MIT is approached. We find that and K decrease to zero at the MIT as and show that S does not diverge. Both S and L₀ become temperature independent at the MIT and depend only on the critical behavior of the conductivity. Received 5 February 1999     

Superfluid-insulator transition of strongly interacting fermi gases in optical lattices

We study a quantum phase transition between fermion superfluid (SF) and band insulator (BI) of fermions in optical lattices. The destruction of the band insulator is driven by the energy gain in promoting fermions from valance band to various conducting bands to form Cooper pairs. We show that the transition must take place in lattice height Vo/ER between 2.23 and 4.14. The latter is the prediction of mean-field theory while the former is the value for opening a band gap. As one moves across resonance to the molecule side, the SF-BI transition evolves into the SF-Mott-insulator transition of bosonic molecules. We shall also present the global phase diagram for SF-insulator transition for the BCS-BEC family.     

Hidden supersymmetry in quantum bosonic systems

We show that some simple well-studied quantum mechanical systems without fermion (spin) degrees of freedom display, surprisingly, a hidden supersymmetry. The list includes the bound state Aharonov-Bohm, the Dirac delta and the Pöschl-Teller potential problems, in which the unbroken and broken N = 2 supersymmetry of linear and nonlinear (polynomial) forms is revealed.     

Solitons and (spin-)Peierls transition in disordered quasi-one-dimensional systems

We study the (spin-)Peierls transition in quasione- dimensional disordered systems, treating the lattice classically. The role of kinks, induced thermally and by disorder, is emphasized. For weak interchain interaction the kinks destroy the coherence between different chains at a temperature significantly lower than the mean-field Peierls transition temperature. We formulate the effective Ising model, which describes such a transition, investigate the doping dependence of the (spin-)Peierls transition temperature and discuss several implications of the picture developed. The results are compared with the properties of the spin-Peierls system CuGeO₃.     

Delocalization transition of two-dimensional disordered systems in a strong magnetic field

The delocalization transition in two-dimensional systems and a strong magnetic field is investigated with respect to its dependence on the Landau band indexj and on the type of disorder. The generation of random potentials according to a given correlation functionf and for a chosen correlation lengthd is described. The spectral properties of random eigenvalue sequences are examined as measures for the extension of wavefunctions and indicate a nonuniversal delocalization behaviour in higher Landau bands for short ranged correlated potentials. The critical exponents of the localization length of wavefunctions are determined for rapidly varying potentials in the second lowest Landau band (j=1) and depend on the correlation lengthd of the disorder. This different critical behaviour compared to that in the lowest band is confirmed by calculations for the density-density correlations of wavefunctions at the centers of the Landau levels. Calculations in different geometries also show that the critical systems of delocalized states are conformal invariant in the case of the nonuniversal delocalization transition (dl ₀), whereas such local rescaling properties cannot be expected for slowly varying potentials.