59 research outputs found
Spontaneous symmetry breaking of a hyperbolic sigma model in three dimensions
Non-linear sigma models that arise from the supersymmetric approach to
disordered electron systems contain a non-compact bosonic sector. We study the
model with target space H^2, the two-hyperboloid with isometry group SU(1,1),
and prove that in three dimensions moments of the fields are finite in the
thermodynamic limit. Thus the non-compact symmetry SU(1,1) is spontaneously
broken. The bound on moments is compatible with the presence of extended
states.Comment: 21 pages, dedicated to F.J. Dyson on the occasion of his 80th
birthda
Localization of quasiparticles in a disordered vortex
We study the diffusive motion of low-energy normal quasiparticles along the
core of a single vortex in a dirty, type-II, s-wave superconductor. The physics
of this system is argued to be described by a one-dimensional supersymmetric
nonlinear sigma model, which differs from the sigma models known for disordered
metallic wires. For an isolated vortex and quasiparticle energies less than the
Thouless energy, we recover the spectral correlations that are predicted by
random matrix theory for the universality class C. We then consider the
transport problem of transmission of quasiparticles through a vortex connected
to particle reservoirs at both ends. The transmittance at zero energy exhibits
a weak localization correction reminiscent of quasi-one-dimensional metallic
systems with symmetry index beta = 1. Weak localization disappears with
increasing energy over a scale set by the Thouless energy. This crossover
should be observable in measurements of the longitudinal heat conductivity of
an ensemble of vortices under mesoscopic conditions. In the regime of strong
localization, the localization length is shown to decrease by a factor of 8 as
the quasiparticle energy goes to zero.Comment: 38 pages, LaTeX2e + epsf, 4 eps figures, one reference adde
Symmetry classes of disordered fermions
Building upon Dyson's fundamental 1962 article known in random-matrix theory
as 'the threefold way', we classify disordered fermion systems with quadratic
Hamiltonians by their unitary and antiunitary symmetries. Important examples
are afforded by noninteracting quasiparticles in disordered metals and
superconductors, and by relativistic fermions in random gauge field
backgrounds.
The primary data of the classification are a Nambu space of fermionic field
operators which carry a representation of some symmetry group. Our approach is
to eliminate all of the unitary symmetries from the picture by transferring to
an irreducible block of equivariant homomorphisms. After reduction, the block
data specifying a linear space of symmetry-compatible Hamiltonians consist of a
basic vector space V, a space of endomorphisms in End(V+V*), a bilinear form on
V+V* which is either symmetric or alternating, and one or two antiunitary
symmetries that may mix V with V*. Every such set of block data is shown to
determine an irreducible classical compact symmetric space. Conversely, every
irreducible classical compact symmetric space occurs in this way.
This proves the correspondence between symmetry classes and symmetric spaces
conjectured some time ago.Comment: 52 pages, dedicated to Freeman J. Dyson on the occasion of his 80th
birthda
(1+1)-dimensional Baryons from the SU(N) Color-Flavor Transformation
The color-flavor transformation, an identity that connects two integrals,
each of which is over one of a dual pair of Lie groups acting in the fermionic
Fock space, is extended to the case of the special unitary group. Using this
extension, a toy model of lattice QCD is studied: N_f species of spinless
fermions interacting with strongly coupled SU(N_c) lattice gauge fields in 1+1
dimensions. The color-flavor transformed theory is expressed in terms of gauge
singlets, the meson fields, organized into sectors distinguished by the
distribution of baryonic flux. A comprehensive analytical and numerical search
is made for saddle-point configurations of the meson fields, with various
topological charges, in the vacuum and single-baryon sectors. Two definitions
of the static baryon on the square lattice, straight and zigzag, are
investigated. The masses of the baryonic states are estimated using the
saddle-point approximation for large N_c.Comment: LateX, 53 pages, 13 figure
Universal spectral statistics of Andreev billiards: semiclassical approach
The classification of universality classes of random-matrix theory has
recently been extended beyond the Wigner-Dyson ensembles. Several of the novel
ensembles can be discussed naturally in the context of superconducting-normal
hybrid systems. In this paper, we give a semiclassical interpretation of their
spectral form factors for both quantum graphs and Andreev billiards.Comment: final improved version (to be published in Physical Review E), 6
pages, revtex
Multifractality of wavefunctions at the quantum Hall transition revisited
We investigate numerically the statistics of wavefunction amplitudes
at the integer quantum Hall transition. It is demonstrated that
in the limit of a large system size the distribution function of is
log-normal, so that the multifractal spectrum is exactly parabolic.
Our findings lend strong support to a recent conjecture for a critical theory
of the quantum Hall transition.Comment: 4 pages Late
Conformal Current Algebra in Two Dimensions
We construct a non-chiral current algebra in two dimensions consistent with
conformal invariance. We show that the conformal current algebra is realized in
non-linear sigma-models on supergroup manifolds with vanishing dual Coxeter
number, with or without a Wess-Zumino term. The current algebra is computed
using two distinct methods. First we exploit special algebraic properties of
supergroups to compute the exact two- and three-point functions of the currents
and from them we infer the current algebra. The algebra is also calculated by
using conformal perturbation theory about the Wess-Zumino-Witten point and
resumming the perturbation series. We also prove that these models realize a
non-chiral Kac-Moody algebra and construct an infinite set of commuting
operators that is closed under the action of the Kac-Moody generators. The
supergroup models that we consider include models with applications to
statistical mechanics, condensed matter and string theory. In particular, our
results may help to systematically solve and clarify the quantum integrability
of PSU(n|n) models and their cosets, which appear prominently in string
worldsheet models on anti-deSitter spaces.Comment: 33 pages, minor correction
Dimensionality dependence of the wave function statistics at the Anderson transition
The statistics of critical wave functions at the Anderson transition in three
and four dimensions are studied numerically. The distribution of the inverse
participation ratios (IPR) is shown to acquire a scale-invariant form in
the limit of large system size. Multifractality spectra governing the scaling
of the ensemble-averaged IPRs are determined. Conjectures concerning the IPR
statistics and the multifractality at the Anderson transition in a high spatial
dimensionality are formulated.Comment: 4 pages, 4 figure
Localization and fluctuations of local spectral density on tree-like structures with large connectivity: Application to the quasiparticle line shape in quantum dots
We study fluctuations of the local density of states (LDOS) on a tree-like
lattice with large branching number . The average form of the local spectral
function (at given value of the random potential in the observation point)
shows a crossover from the Lorentzian to semicircular form at ,
where , is the typical value of the hopping matrix
element, and is the width of the distribution of random site energies. For
the LDOS fluctuations (with respect to this average form) are
weak. In the opposite case, , the fluctuations get strong and the
average LDOS ceases to be representative, which is related to the existence of
the Anderson transition at . On the localized side
of the transition the spectrum is discrete, and LDOS is given by a set of
-like peaks. The effective number of components in this regime is given
by , with being the inverse participation ratio. It is shown that
has in the transition point a limiting value close to unity, , so that the system undergoes a transition directly from the deeply
localized to extended phase. On the side of delocalized states, the peaks in
LDOS get broadened, with a width being exponentially small near the
transition point. We discuss application of our results to the problem of the
quasiparticle line shape in a finite Fermi system, as suggested recently by
Altshuler, Gefen, Kamenev, and Levitov.Comment: 12 pages, 1 figure. Misprints in eqs.(21) and (28) corrected, section
VII added. Accepted for publication in Phys. Rev.
Nonhermitian Supersymmetric Partition Functions: the case of one bosonic flavor
We discuss the supersymmetric formulation of the nonhermitian
random matrix partition function with one bosonic flavor. This partition
function is regularized by adding one conjugate boson and fermion each. A
supersymmetric nonlinear -model for the resulting Goldstone degrees of
freedom is obtained using symmetry arguments only. For a Gaussian probability
distribution the same results are derived using superbosonization and the
complex orthogonal polynomial method. The symmetry arguments apply to any model
with the same symmetries and a mass gap, and demonstrate the universality of
the nonlinear -model.Comment: 17 pages, 0 figures. Section II extended. Version to appear in
Nucl.Phys.
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