Physics of the Pseudogap State: Spin-Charge Locking

The properties of the pseudogap phase above Tc of the high-Tc cuprate superconductors are described by showing that the Anderson-Nambu SU(2) spinors of an RVB spin gap 'lock' to those of the electron charge system because of the resulting improvement of kinetic energy. This enormously extends the range of the vortex liquid state in these materials. As a result it is not clear that the spinons are ever truly deconfined. A heuristic description of the electrodynamics of this pseudogap-vortex liquid state is proposed.Comment: Submitted to Phys Rev Letter

Random walk in a two-dimensional self-affine random potential : properties of the anomalous diffusion phase at small external force

We consider the random walk of a particle in a two-dimensional self-affine random potential of Hurst exponent $H=1/2$ in the presence of an external force $F$. We present numerical results on the statistics of first-passage times that satisfy closed backward master equations. We find that there exists a zero-velocity phase in a finite region of the external force $0<F<F_c$, where the dynamics follows the anomalous diffusion law $ x(t) \sim \xi(F) \ t^{\mu(F)} $. The anomalous exponent$0<\mu(F)<1$and the correlation length$\xi(F)$vary continuously with$F$. In the limit of vanishing force$F \to 0$, we measure the following power-laws : the anomalous exponent vanishes as$\mu(F) \propto F^a$with$a \simeq 0.6$(instead of$a=1$in dimension$d=1$), and the correlation length diverges as$\xi(F) \propto F^{-\nu}$with$\nu \simeq 1.29$(instead of$\nu=2$in dimension$d=1$). Our main conclusion is thus that the dynamics renormalizes onto an effective directed trap model, where the traps are characterized by a typical length$\xi(F)$along the direction of the force, and by a typical barrier$1/\mu(F)$. The fact that these traps are 'smaller' in linear size and in depth than in dimension$d=1$, means that the particle uses the transverse direction to find lower barriers.Comment: 10 pages, 8 figures, v2=final versio

Driven interfaces in random media at finite temperature : is there an anomalous zero-velocity phase at small external force ?

The motion of driven interfaces in random media at finite temperature $T$ and small external force $F$ is usually described by a linear displacement $h_G(t) \sim V(F,T) t$ at large times, where the velocity vanishes according to the creep formula as $V(F,T) \sim e^{-K(T)/F^{\mu}}$ for $F \to 0$. In this paper, we question this picture on the specific example of the directed polymer in a two dimensional random medium. We have recently shown (C. Monthus and T. Garel, arxiv:0802.2502) that its dynamics for F=0 can be analyzed in terms of a strong disorder renormalization procedure, where the distribution of renormalized barriers flows towards some "infinite disorder fixed point". In the present paper, we obtain that for small $F$, this "infinite disorder fixed point" becomes a "strong disorder fixed point" with an exponential distribution of renormalized barriers. The corresponding distribution of trapping times then only decays as a power-law $P(\tau) \sim 1/\tau^{1+\alpha}$, where the exponent $\alpha(F,T)$ vanishes as $\alpha(F,T) \propto F^{\mu}$ as $F \to 0$. Our conclusion is that in the small force region $\alpha(F,T)<1$, the divergence of the averaged trapping time $\bar{\tau}=+\infty$ induces strong non-self-averaging effects that invalidate the usual creep formula obtained by replacing all trapping times by the typical value. We find instead that the motion is only sub-linearly in time $h_G(t) \sim t^{\alpha(F,T)}$, i.e. the asymptotic velocity vanishes V=0. This analysis is confirmed by numerical simulations of a directed polymer with a metric constraint driven in a traps landscape. We moreover obtain that the roughness exponent, which is governed by the equilibrium value $\zeta_{eq}=2/3$ up to some large scale, becomes equal to $\zeta=1$ at the largest scales.Comment: v3=final versio

Intermittency of Height Fluctuations and Velocity Increment of The Kardar-Parisi-Zhang and Burgers Equations with infinitesimal surface tension and Viscosity in 1+1 Dimensions

The Kardar-Parisi-Zhang (KPZ) equation with infinitesimal surface tension, dynamically develops sharply connected valley structures within which the height derivative is not continuous. We discuss the intermittency issue in the problem of stationary state forced KPZ equation in 1+1--dimensions. It is proved that the moments of height increments $C_a =$ behave as $|x_1 -x_2|^{\xi_a}$ with $\xi_a = a$ for length scales $|x_1-x_2| << \sigma$. The length scale $\sigma$ is the characteristic length of the forcing term. We have checked the analytical results by direct numerical simulation.Comment: 13 pages, 9 figure

Replica symmetry breaking in long-range glass models without quenched disorder

We discuss mean field theory of glasses without quenched disorder focusing on the justification of the replica approach to thermodynamics. We emphasize the assumptions implicit in this method and discuss how they can be verified. The formalism is applied to the long range Ising model with orthogonal coupling matrix. We find the one step replica-symmetry breaking solution and show that it is stable in the intermediate temperature range that includes the glass state but excludes very low temperatures. At very low temperatures this solution becomes unstable and this approach fails.Comment: 6 pages, 2 figure

Universal temperature dependence of the conductivity of a strongly disordered granular metal

A disordered array of metal grains with large and random intergrain conductances is studied within the one-loop accuracy renormalization group approach. While at low level of disorder the dependence of conductivity on log T is nonuniversal (it depends on details of the array's geometry), for strong disorder this dependence is described by a universal nonlinear function, which depends only on the array's dimensionality. In two dimensions this function is found numerically. The dimensional crossover in granular films is discussed.Comment: 6 pages, 6 figures, submitted to JETP Letter

Degenerate Bose liquid in a fluctuating gauge field

We study the effect of a strongly fluctuating gauge field on a degenerate Bose liquid, relevant to the charge degrees of freedom in doped Mott insulators. We find that the superfluidity is destroyed. The resulting metallic phase is studied using quantum Monte Carlo methods. Gauge fluctuations cause the boson world lines to retrace themselves. We examine how this world-line geometry affects the physical properties of the system. In particular, we find a transport relaxation rate of the order of 2kT, consistent with the normal state of the cuprate superconductors. We also find that the density excitations of this model resemble that of the full tJ model.Comment: 4 pages. Uses RevTeX, epsf, multicols macros. 5 postscript figure

Two-loop approximation in the Coulomb blockade problem

We study Coulomb blockade (CB) oscillations in the thermodynamics of a metallic grain which is connected to a lead by a tunneling contact with a large conductance $g_0$ in a wide temperature range, $E_Cg_0^4 e^{-g_0/2}<T<E_C$, where $E_C$ is the charging energy. Using the instanton analysis and the renormalization group we obtain the temperature dependence of the amplitude of CB oscillations which differs from the previously obtained results. Assuming that at $T < E_Cg_0^4 e^{-g_0/2}$ the oscillation amplitude weakly depends on temperature we estimate the magnitude of CB oscillations in the ground state energy as $E_Cg_0^4 e^{-g_0/2}$.Comment: 10 pages, 3 figure

Low-frequency dynamics of disordered XY spin chains and pinned density waves: from localized spin waves to soliton tunneling

A long-standing problem of the low-energy dynamics of a disordered XY spin chain is re-examined. The case of a rigid chain is studied where the quantum effects can be treated quasiclassically. It is shown that as the frequency decreases, the relevant excitations change from localized spin waves to two-level systems to soliton-antisoliton pairs. The linear-response correlation functions are calculated. The results apply to other periodic glassy systems such as pinned density waves, planar vortex lattices, stripes, and disordered Luttinger liquids.Comment: (v2) Major improvements in presentation style. One figure added (v3) Another minor chang

Vortex-line liquid phases: Longitudinal superconductivity in the lattice London model

We study the vortex-line lattice and liquid phases of a clean type-II superconductor by means of Monte Carlo simulations of the lattice London model. Motivated by a recent controversy regarding the presence, within this model, of a vortex-liquid regime with longitudinal superconducting coherence over long length scales, we directly compare two different ways to calculate the longitudinal coherence. For an isotropic superconductor, we interpret our results in terms of a temperature regime within the liquid phase in which longitudinal superconducting coherence extends over length scales larger than the system thickness studied. We note that this regime disappears in the moderately anisotropic case due to a proliferation, close to the flux-line lattice melting temperature, of vortex loops between the layers.Comment: 8 pages, Revtex, with eps figures. To appear in Phys. Rev.