arXiv subjects

Leon Balents

Publications and source records attributed to Leon Balents.

At least 235 records · Page 13Linked to original sources

arXiv1997

Delocalization Transition via Supersymmetry in one Dimension

We use supersymmetric (SUSY) methods to study the delocalization transition at zero energy in a one-dimensional tight-binding model of spinless fermions with particle-hole symmetric disorder. Like the McCoy-Wu random transverse-field Ising model to which it is related, the fermionic problem displays two different correlation lengths for typical and mean correlations. Using the SUSY technique, mean correlators are obtained as quantum mechanical expectation values for an U(2|1,1) ``superspin''. In the scaling limit, this quantum mechanics is closely related to a 0+1-dimensional Liouville theory, allowing an interpretation of the results in terms of simple properties of the zero-energy wavefunctions. Our primary results are the exact two-parameter scaling functions for the mean single-particle Green's functions. We also show how the Liouville quantum mechanics approach can be extended to obtain the full set of multifractal scaling exponents τ(q), y(q) at criticality. A thorough understanding of the unusual features of the present theory may be useful in applying SUSY to other delocalization transitions.

cond-mat.mes-hall↗

arXiv1996

Correlation Effects in Carbon Nanotubes

We consider the effects of Coulomb interactions on single-wall carbon nanotubes using an on-site Hubbard interaction, u. For the (N,N) armchair tubes the low energy theory is shown to be identical to a 2-chain Hubbard model at half-filling, with an effective interaction u_N = u/N. Umklapp scattering leads to gaps in the spectrum of charge and spin excitations which are exponentially small for large N. Above the gaps the intrinsic nanotube resistivity due to these scattering processes is linear in temperature, as observed experimentally. The presence of "d-wave" superconductivity in the 2-chain Hubbard model away from half-filling suggests that doped armchair nanotubes might exhibit superconductity with a purely electronic mechanism.

cond-mat.str-el↗

arXiv1996

Chiral Metal as a Ferromagnetic Super Spin Chain

The electrons on the surface of a disordered multi-layer integer quantum Hall system constitute an unusual chiral metal with ballistic motion transverse to the field, and diffusive motion parallel to it. We present a non-perturbative analytic treatment of an appropriate model, consisting of disordered chiral Fermions in two dimensions. A supersymmetric generating functional is set up for the correlation functions of this system. The strong disorder limit is mapped into a supersymmetric spin chain, with ferromagnetic exchange coupling, reflecting the electron's chiral motion. The ferromagnetic ground state and the spin wave excitations, corresponding to the diffusion modes of the chiral metal, are found exactly. The parametric density of states correlator in the ergodic limit is computed from a Boltzmann-weighted sum over low energy spin states. The result is of a universal form and coincides with that for a Hermitian random matrix.

cond-mat↗

arXiv1996

Critical Behavior of the Supersolid transition in Bose-Hubbard Models

We study the phase transitions of interacting bosons at zero temperature between superfluid (SF) and supersolid (SS) states. The latter are characterized by simultaneous off-diagonal long-range order and broken translational symmetry. The critical phenomena is described by a long-wavelength effective action, derived on symmetry grounds and verified by explicit calculation. We consider two types of supersolid ordering: checkerboard (X) and collinear (C), which are the simplest cases arising in two dimensions on a square lattice. We find that the SF--CSS transition is in the three-dimensional XY universality class. The SF--XSS transition exhibits non-trivial new critical behavior, and appears, within a $d=3-ε$ expansion to be driven generically first order by fluctuations. However, within a one--loop calculation directly in $d=2$ a strong coupling fixed point with striking ``non-Bose liquid'' behavior is found. At special isolated multi-critical points of particle-hole symmetry, the system falls into the 3d Ising universality class.

cond-mat↗

arXiv1996

Comment on "Moving Glass Phase of Driven Lattices"

We consider a periodic lattice rapidly driven through a quenched random potential as a model of a moving Abrikosov lattice. In addition to the transverse phonon displacements $u_y$, we consider the displacements $u_x$ along the direction of motion, which were assumed to be small in earlier treatments. We show that these displacements are in fact divergent even on large length scales and therefore lead to a breakdown of the elastic model along the direction of motion. We propose that the resulting phase is a moving "smectic" with translational order that is quasi-long-range transverse and liquid-like parallel to the direction of motion.

cond-mat↗

arXiv1996

Dynamical Transition in Sliding Charge-density Waves with Quenched Disorder

We have studied numerically the dynamics of sliding charge-density waves (CDWs) in the presence of impurities in d=1,2. The model considered exhibits a first order dynamical transition at a critical driving force $F_c$ between ``rough'' (disorder dominated) $(F F_c)$ sliding phases where disorder is washed out by the external drive. The effective model for the sliding CDWs in the presence of impurities can be mapped onto that of a magnetic flux line pinned by columnar defects and tilted by an applied field. The dynamical transition of sliding CDWs corresponds to the transverse Meissner effect of the tilted flux line.

cond-mat↗

arXiv1996

The Large Scale Energy Landscapes of Randomly Pinned Objects

We discuss the large scale effective potential for elastic objects (manifolds) in the presence of a random pinning potential, from the point of view of the Functional Renormalisation Group (FRG) and of the replica method. Both approaches suggest that the energy landscape at large scales is a succession of parabolic wells of random depth, matching on singular points where the effective force is discontinuous. These parabolas are themselves subdivided into smaller parabolas, corresponding to the motion of smaller length scales, in a hierarchical manner. Consequences for the dynamics of these pinned objects are underlined.

cond-mat↗

arXiv1995

Chiral Surface States in the Bulk Quantum Hall Effect

In layered samples which exhibit a bulk quantum Hall effect (QHE), a two-dimensional (2d) surface ``sheath" of gapless excitations is expected. These excitations comprise a novel 2d chiral quantum liquid which should dominate the low temperature transport along the field (z-axis). For the integer QHE, we show that localization effects are completely absent in the ``sheath", giving a metallic z-axis conductivity. For fractional filling $ν=1/3$, the ``sheath" is a 2d non-Fermi liquid, with incoherent z-axis transport and $σ_{zz} \sim T^3$. Experimental implications for the Bechgaard salts are discussed.

cond-mat↗

arXiv1995

Continuous 3d Freezing Transition in Layered Superconductors

We use Ginzburg-Landau theory to study the $H_{c2}$ transition in layered superconductors with field parallel to the layers, finding a continuous 3d freezing transition to a triangular vortex super-solid in the three-dimensional XY universality class. If screening effects are neglected, off--diagonal--long--range--order survives only for $d>d_{lc}=5/2$. The partial breaking of the lowest Landau level degeneracy induced by layering leads to a {\sl local} selection of a triangular lattice structure, in contrast to the {\sl global} free energy minimization in, e.g. Abrikosov's calculation. Our results are relevant to artificially layered superconductors and to strongly anisotropic high T$_c$ materials.

cond-mat↗

arXiv1995

Temporal Order in Dirty Driven Periodic Media

We consider the non--equilibrium steady states of a driven charge density wave in the presence of impurities and noise. In three dimensions at strong drive, a true dynamical phase transition into a temporally periodic state with quasi--long--range translational order is predicted. In two dimensions, impurity induced phase slips are argued to destroy the periodic ``moving solid'' phase. Implications for narrow band noise measurements and relevance to other driven periodic media, e.g. vortex lattices, are discussed.

cond-mat↗

arXiv1995

Quantum Smectic and Supersolid Order in Helium Films and Vortex Arrays

A flux liquid can condense into a smectic crystal in a pure layered superconductor with the magnetic field oriented nearly parallel to the layers. Similar order can arise in low temperature $^4$He films with a highly anisotropic periodic substrate potential. If the smectic order is commensurate with the layering, this periodic array is {\sl stable} to quenched random point--like disorder. By tilting and adjusting the magnitude of the applied field, both incommensurate and tilted smectic and crystalline phases are found for vortex arrays. Related variations are possible by changing the chemical potential in the helium system. We discuss transport near the second order smectic freezing transition, and show that permeation modes in superconductors lead to a small non--zero resistivity and a large but finite tilt modulus in the smectic crystal. In helium films, the theory predicts a nonzero superfluid density and propagating third sound modes, showing that the quantum smectic is always simultaneously crystalline and superfluid.

cond-mat↗

arXiv1995

Weak Coupling Phase Diagram of the Two Chain Hubbard Model

We present a general method for determining the phase diagram of systems of a finite number of one dimensional Hubbard--like systems coupled by single--particle hopping with weak interactions. The technique is illustrated by detailed calculations for the two--chain Hubbard model, providing the first controlled results for arbitrary doping and inter-chain hopping. Of nine possible states which could occur in such a spin--$1/2$ ladder, we find seven at weak coupling. We discuss the conditions under which the model can be regarded as a one--dimensional analog of a superconductor.

cond-mat↗

arXiv1995

Spatially Ordered Fractional Quantum Hall States

Fractional quantum Hall liquids can accomodate various degrees of spatial ordering. The most likely scenarios are a Hall hexatic, Hall smectic, and Hall crystal, in which respectively orientational, one--dimensional translational, and two--dimensional translational symmetries are broken. I derive the long--wavelength properties of these phases and the transitions between them using the Chern--Simons Landau--Ginzburg mapping, which relates them to spatially ordered superfluids. The effects of coupling to a periodic or anisotropic ``substrate'' (e.g. a gate array) are also discussed.

cond-mat↗

arXiv1995

Problems With the Vortex-Boson Mapping in 1+1 Dimensions

Using the well known boson mapping, we relate the transverse magnetic susceptibility of a system of flux vortices in 1+1 dimensions to an appropriately defined conductivity of a one-dimensional boson system. The tilt response for a system free of disorder is calculated directly, and it is found that a subtle order of limits is required to avoid deceptive results.

cond-mat↗

arXiv1995

Commensurability Effects in Large Josephson Junctions

Two types of commensurability effects are possible in a large Josephson junction patterned with columnar defects. The first occurs for a periodic array of pins when the mean fluxon spacing (tuned by the magnitude of the applied in--plane magnetic field) is a rational fraction of the defect spacing. We show that this effect leads, under fairly general conditions, to a mapping of the behavior of the Josephson junction near the commensurate field values to that of a zero field junction with an effective Josephson penetration depth. The second occurs for more general arrangements of pinning sites, when the orientation of the Josephson vortex lattice (tuned by the direction of the applied field) nearly matches the orientation of the defects. We investigate this tilt response in the limit of a single Josephson vortex. The results are compared, where possible, to recent experiments. As an aside from our main analysis, we prove that, contrary to recent claims in the literature, the critical current density vanishes in the thermodynamic limit, even in the presence of (non--pathologically distributed) pinning disorder

cond-mat↗

arXiv1994

Fluctuations and Intrinsic Pinning in Layered Superconductors

A flux liquid can condense into a smectic crystal in a pure layered superconductors with the magnetic field oriented nearly parallel to the layers. If the smectic order is commensurate with the layering, this crystal is {\sl stable} to point disorder. By tilting and adjusting the magnitude of the applied field, both incommensurate and tilted smectic and crystalline phases are found. We discuss transport near the second order smectic freezing transition, and show that permeation modes lead to a small non--zero resistivity and large but finite tilt modulus in the smectic crystal.

cond-mat↗

arXiv1993

Localization of Elastic Layers by Correlated Disorder

The equilibrium behavior of a system of elastic layers under tension in the presence of correlated disorder is studied using functional renormalization group techniques. The model exhibits many of the features of the Bose glass phase of type II superconductors induced by columnar defects, but may be more directly applicable to charge density waves, incommensurate striped magnetic phases, stacked membranes under tension, vicinal crystal surfaces, or superconducting ``vortex--chains''. Below five dimensions, an epsilon expansion for the stable zero temperature fixed point yields the properties of the glassy phase. Transverse to the direction of correlation, the randomness induces logarithmic growth of displacements. Displacements are strongly localized in the correlation direction. The absence of a response to a weak applied transverse field (transverse Meissner effect) is demonstrated analytically. In this simple model, the localized phase is stable to point disorder, in contrast to the behavior in the presence of dislocations, in which the converse is believed to be true.

cond-mat↗

arXiv1993

Large N Expansion for 4-Epsilon Dimensional Oriented Manifolds in Random Media

The equilibrium statistical mechanics of a d dimensional ``oriented'' manifold in an N+d dimensional random medium are analyzed in d=4-epsilon dimensions. For N=1, this problem describes an interface pinned by impurities. For d=1, the model becomes identical to the directed polymer in a random medium. Here, we generalize the functional renormalization group method used previously to study the interface problem, and extract the behavior in the double limit epsilon small and N large, finding non-analytic corrections in 1/N. For short-range disorder, the interface width scales as a power law of the width. We calculate the roughness exponent characterizing this power law for small epsilon and large N, as well as other properties of the phase. We also analyze the behavior for disorder with long-range correlations, as is appropriate for interfaces in random field systems, and study the crossover between the two regimes.

cond-mat↗