Mott law as lower bound for a random walk in a random environment

We consider a random walk on the support of a stationary simple point process on $R^d$, $d\geq 2$ which satisfies a mixing condition w.r.t.the translations or has a strictly positive density uniformly on large enough cubes. Furthermore the point process is furnished with independent random bounded energy marks. The transition rates of the random walk decay exponentially in the jump distances and depend on the energies through a factor of the Boltzmann-type. This is an effective model for the phonon-induced hopping of electrons in disordered solids within the regime of strong Anderson localization. We show that the rescaled random walk converges to a Brownian motion whose diffusion coefficient is bounded below by Mott's law for the variable range hopping conductivity at zero frequency. The proof of the lower bound involves estimates for the supercritical regime of an associated site percolation problem

Weak disorder expansion for localization lengths of quasi-1D systems

A perturbative formula for the lowest Lyapunov exponent of an Anderson model on a strip is presented. It is expressed in terms of an energy-dependent doubly stochastic matrix, the size of which is proportional to the strip width. This matrix and the resulting perturbative expression for the Lyapunov exponent are evaluated numerically. Dependence on energy, strip width and disorder strength are thoroughly compared with the results obtained by the standard transfer matrix method. Good agreement is found for all energies in the band of the free operator and this even for quite large values of the disorder strength

Radiation induced zero-resistance states: a dressed electronic structure effect

Recent results on magnetoresistance in a two dimensional electron gas under crossed magnetic and microwave fields show a new class of oscillations, suggesting a new kind of zero-resistance states. A complete understanding of the effect is still lacking. We consider the problem from the point of view of the electronic structure dressed by photons due to a in plane linearly polarized ac field. The dramatic changes in the dressed electronic structure lead to a interpretation of the new magnetoresistance oscillations as a persistent-current like effect, induced by the radiation field.Comment: 5 pages, 5 figures, revtex4, changes in introduction and added reference

Stripes on a 6-Leg Hubbard Ladder

While DMRG calculations find stripes on doped n-leg t-J ladders, little is known about the possible formation of stripes on n-leg Hubbard ladders. Here we report results for a 7x6 Hubbard model with 4 holes. We find that a stripe forms for values of U/t ranging from 6 to 20. For U/t ~ 3-4, the system exhibits the domain wall feature of a stripe, but the hole density is very broadened.Comment: 4 pages, 5 figure

Weakly correlated electrons on a square lattice: a renormalization group theory

We study the weakly interacting Hubbard model on the square lattice using a one-loop renormalization group approach. The transition temperature T_c between the metallic and (nearly) ordered states is found. In the parquet regime, (T_c >> |mu|), the dominant correlations at temperatures below T_c are antiferromagnetic while in the BCS regime (T_c << |mu|) at T_c the d-wave singlet pairing susceptibility is most divergent.Comment: 12 pages, REVTEX, 3 figures included, submitted to Phys. Rev. Let

On the metal-insulator transition in the two-chain model of correlated fermions

The doping-induced metal-insulator transition in two-chain systems of correlated fermions is studied using a solvable limit of the t-J model and the fact that various strong- and weak-coupling limits of the two-chain model are in the same phase, i.e. have the same low-energy properties. It is shown that the Luttinger-liquid parameter K_\rho takes the universal value unity as the insulating state (half-filling) is approached, implying dominant d-type superconducting fluctuations, independently of the interaction strength. The crossover to insulating behavior of correlations as the transition is approached is discussed.Comment: 7 pages, 1 figur

Spin Gap and Superconductivity in Weakly Coupled Ladders: Interladder One-particle vs. Two-particle Crossover

Effects of the interladder one-particle hopping, $t_{\perp}$, on the low-energy asymptotics of a weakly coupled Hubbard ladder system have been studied, based on the perturbative renormalization-group approach. We found that for finite intraladder Hubbard repulsion, $U$, there exists a crossover value of the interladder one-particle hopping, $t_{\perp c}$. For $0<t_{\perp}<t_{\perp c}$, the spin gap metal (SGM) phase of the isolated ladder transits at a finite transition temperature, $T_{c}$, to the d-wave superconducting (SCd) phase via a two-particle crossover. In the temperature region, $T<T_{c}$, interladder coherent Josephson tunneling of the Cooper pairs occurs, while the interladder coherent one-particle process is strongly suppressed. For $t_{\perp c}<t_{\perp}$, around a crossover temperature, $T_{cross}$, the system crosses over to the two-dimensional (2D) phase via a one-particle crossover. In the temperature region, $T<T_{cross}$, the interladdercoherent band motion occurs.Comment: 4 pages, 5 eps figures, uses jpsj.st

Cold Attractive Spin Polarized Fermi Lattice Gases and the Doped Positive U Hubbard Model

Experiments on polarized fermion gases performed by trapping ultracold atoms in optical lattices, allow the study of an attractive Hubbard model for which the strength of the on site interaction is tuned by means of a Feshbach resonance. Using a well-known particle-hole transformation we discuss how results obtained for this system can be reinterpreted in the context of a doped repulsive Hubbard model. In particular we show that the Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) state corresponds to the striped state of the two-dimensional doped positive U Hubbard model. We then use the results of numerical studies of the striped state to relate the periodicity of the FFLO state to the spin polarization. We also comment on the relationship of the $d_{x^2-y^2}$ superconducting phase of the doped 2D repulsive Hubbard model to a d-wave spin density wave state for the attractive case.Comment: 4 pages, 2 figure

Columnar Fluctuations as a Source of Non-Fermi-Liquid Behavior in Weak Metallic Magnets

It is shown that columnar fluctuations, in conjunction with weak quenched disorder, lead to a T^{3/2} temperature dependence of the electrical resistivity. This is proposed as an explanation of the observed non-Fermi-liquid behavior in the helimagnet MnSi, with one possible realization of the columnar fluctuations provided by skyrmion lines that have independently been proposed to be present in this material.Comment: 4pp, 4 figure

Quantum J1J_1--J2J_2 antiferromagnet on the stacked square lattice: Influence of the interlayer coupling on the ground-state magnetic ordering

Using the coupled-cluster method (CCM) and the rotation-invariant Green's function method (RGM), we study the influence of the interlayer coupling $J_\perp$ on the magnetic ordering in the ground state of the spin-1/2 $J_1$-$J_2$ frustrated Heisenberg antiferromagnet ($J_1$-$J_2$ model) on the stacked square lattice. In agreement with known results for the $J_1$-$J_2$ model on the strictly two-dimensional square lattice ($J_\perp=0$) we find that the phases with magnetic long-range order at small $J_2< J_{c_1}$ and large $J_2> J_{c_2}$ are separated by a magnetically disordered (quantum paramagnetic) ground-state phase. Increasing the interlayer coupling $J_\perp>0$ the parameter region of this phase decreases, and, finally, the quantum paramagnetic phase disappears for quite small $J_\perp \sim 0.2 ... 0.3 J_1$.Comment: 4 pages, 3 figure