61 research outputs found
Classical Dynamics of Anyons and the Quantum Spectrum
In this paper we show that (a) all the known exact solutions of the problem
of N-anyons in oscillator potential precisely arise from the collective degrees
of freedom, (b) the system is pseudo-integrable ala Richens and Berry. We
conclude that the exact solutions are trivial thermodynamically as well as
dynamically.Comment: 19 pages, ReVTeX, IMSc/93/0
Exclusion statistics for fractional quantum Hall states on a sphere
We discuss exclusion statistics parameters for quasiholes and quasielectrons
excited above the fractional quantum Hall states near . We
derive the diagonal statistics parameters from the (``unprojected'') composite
fermion (CF) picture. We propose values for the off-diagonal (mutual)
statistics parameters as a simple modification of those obtained from the
unprojected CF picture, by analyzing finite system numerical spectra in the
spherical geometry.Comment: 9 pages, Revtex, 4 Postscript figures. Universality of the statistics
parameters is stressed, 2 figs adde
Defect-unbinding transitions and inherent structures in two dimensions
We present a large-scale (36000-particle) computational study of the
"inherent structures" (IS) associated with equilibrium, two-dimensional,
one-component Lennard-Jones systems. Our results provide strong support both
for the inherent-structures theory of classical fluids, and for the KTHNY
theory of two-stage melting in two dimensions. This support comes from the
observation of three qualitatively distinct "phases" of inherent structures: a
crystal, a "hexatic glass", and a "liquid glass". We also directly observe, in
the IS, analogs of the two defect-unbinding transitions (respectively, of
dislocations, and disclinations) believed to mediate the two equilibrium phase
transitions. Each transition shows up in the inherent structures---although the
free disclinations in the "liquid glass" are embedded in a percolating network
of grain boundaries. The bond-orientational correlation functions of the
inherent structures show the same progressive loss of order as do the three
equilibrium phases: long-range to quasi-long-range to short-range.Comment: RevTeX, 8 pages, 15 figure
Time-dependent screening of a positive charge distribution in metals: Excitons on an ultra-short time scale
Experiments determining the lifetime of excited electrons in crystalline
copper reveal states which cannot be interpreted as Bloch states [S. Ogawa {\it
et al.}, Phys. Rev. B {\bf 55}, 10869 (1997)]. In this article we propose a
model which explains these states as transient excitonic states in metals. The
physical background of transient excitons is the finite time a system needs to
react to an external perturbation, in other words, the time which is needed to
build up a polarization cloud. This process can be probed with modern
ultra-short laser pulses. We calculate the time-dependent density-response
function within the jellium model and for real Cu. From this knowledge it is
possible within linear response theory to calculate the time needed to screen a
positive charge distribution and -- on top of this -- to determine excitonic
binding energies. Our results lead to the interpretation of the experimentally
detected states as transient excitonic states.Comment: 24 pages, 9 figures, to appear in Phys. Rev. B, Nov. 15, 2000, issue
2
Bosonic and fermionic single-particle states in the Haldane approach to statistics for identical particles
We give two formulations of exclusion statistics (ES) using a variable number
of bosonic or fermionic single-particle states which depend on the number of
particles in the system. Associated bosonic and fermionic ES parameters are
introduced and are discussed for FQHE quasiparticles, anyons in the lowest
Landau level and for the Calogero-Sutherland model. In the latter case, only
one family of solutions is emphasized to be sufficient to recover ES;
appropriate families are specified for a number of formulations of the
Calogero-Sutherland model. We extend the picture of variable number of
single-particle states to generalized ideal gases with statistical interaction
between particles of different momenta. Integral equations are derived which
determine the momentum distribution for single-particle states and distribution
of particles over the single-particle states in the thermal equilibrium.Comment: 6 pages, REVTE
Exclusonic Quasiparticles and Thermodynamics of Fractional Quantum Hall Liquids
Quasielectrons and quasiholes in the fractional quantum Hall liquids obey
fractional (including nontrivial mutual) exclusion statistics. Their statistics
matrix can be determined from several possible state-counting scheme, involving
different assumptions on statistical correlations. Thermal activation of
quasiparticle pairs and thermodynamic properties of the fractional quantum Hall
liquids near fillings ( odd) at low temperature are studied in the
approximation of generalized ideal gas. The existence of hierarchical states in
the fractional quantum Hall effect is shown to be a manifestation of the
exclusonic nature of the relevant quasiparticles. For magnetic properties, a
paramagnetism-diamagnetism transition appears to be possible at finite
temperature.Comment: latex209, REVTE
Chern_simons Theory of the Anisotropic Quantum Heisenberg Antiferromagnet on a Square Lattice
We consider the anisotropic quantum Heisenberg antiferromagnet (with
anisotropy ) on a square lattice using a Chern-Simons (or
Wigner-Jordan) approach. We show that the Average Field Approximation (AFA)
yields a phase diagram with two phases: a Ne{\`e}l state for
and a flux phase for separated by a
second order transition at . We show that this phase diagram does
not describe the regime of the antiferromagnet. Fluctuations around the
AFA induce relevant operators which yield the correct phase diagram. We find an
equivalence between the antiferromagnet and a relativistic field theory of two
self-interacting Dirac fermions coupled to a Chern-Simons gauge field. The
field theory has a phase diagram with the correct number of Goldstone modes in
each regime and a phase transition at a critical coupling . We identify this transition with the isotropic Heisenberg point. It
has a non-vanishing Ne{\` e}l order parameter, which drops to zero
discontinuously for .Comment: 53 pages, one figure available upon request, Revte
Separation of Spin and Charge Quantum Numbers in Strongly Correlated Systems
In this paper we reexamine the problem of the separation of spin and charge
degrees of freedom in two dimensional strongly correlated systems. We establish
a set of sufficient conditions for the occurence of spin and charge separation.
Specifically, we discuss this issue in the context of the Heisenberg model for
spin-1/2 on a square lattice with nearest () and next-nearest ()
neighbor antiferromagnetic couplings. Our formulation makes explicit the
existence of a local SU(2) gauge symmetry once the spin-1/2 operators are
replaced by bound states of spinons. The mean-field theory for the spinons is
solved numerically as a function of the ratio for the so-called s-RVB
Ansatz. A second order phase transition exists into a novel flux state for
. We identify the range as the s-RVB phase. It is characterized by the existence of a finite gap
to the elementary excitations (spinons) and the breakdown of all the continuous
gauge symmetries. An effective continuum theory for the spinons and the gauge
degrees of freedom is constructed just below the onset of the flux phase. We
argue that this effective theory is consistent with the deconfinement of the
spinons carrying the fundamental charge of the gauge group. We contrast this
result with the study of the one dimensional quantum antiferromagnet within the
same approach. We show that in the one dimensional model, the spinons of the
gauge picture are always confined and thus cannot be identified with the
gapless spin-1/2 excitations of the quantum antiferromagnet Heisenberg model.Comment: 56 pages, RevteX 3.
The Role of Nonequilibrium Dynamical Screening in Carrier Thermalization
We investigate the role played by nonequilibrium dynamical screening in the
thermalization of carriers in a simplified two-component two-band model of a
semiconductor. The main feature of our approach is the theoretically sound
treatment of collisions. We abandon Fermi's Golden rule in favor of a
nonequilibrium field theoretic formalism as the former is applicable only in
the long-time regime. We also introduce the concept of nonequilibrium dynamical
screening. The dephasing of excitonic quantum beats as a result of
carrier-carrier scattering is brought out. At low densities it is found that
the dephasing times due to carrier-carrier scattering is in picoseconds and not
femtoseconds, in agreement with experiments. The polarization dephasing rates
are computed as a function of the excited carrier density and it is found that
the dephasing rate for carrier-carrier scattering is proportional to the
carrier density at ultralow densities. The scaling relation is sublinear at
higher densities, which enables a comparison with experiment.Comment: Revised version with additional refs. 12 pages, figs. available upon
request; Submitted to Phys. Rev.
W=0 pairing in Hubbard and related models of low-dimensional superconductors
Lattice Hamiltonians with on-site interaction have W=0 solutions, that
is, many-body {\em singlet} eigenstates without double occupation. In
particular, W=0 pairs give a clue to understand the pairing force in repulsive
Hubbard models. These eigenstates are found in systems with high enough
symmetry, like the square, hexagonal or triangular lattices. By a general
theorem, we propose a systematic way to construct all the W=0 pairs of a given
Hamiltonian. We also introduce a canonical transformation to calculate the
effective interaction between the particles of such pairs. In geometries
appropriate for the CuO planes of cuprate superconductors, armchair
Carbon nanotubes or Cobalt Oxides planes, the dressed pair becomes a bound
state in a physically relevant range of parameters. We also show that W=0 pairs
quantize the magnetic flux like superconducting pairs do. The pairing mechanism
breaks down in the presence of strong distortions. The W=0 pairs are also the
building blocks for the antiferromagnetic ground state of the half-filled
Hubbard model at weak coupling. Our analytical results for the
Hubbard square lattice, compared to available numerical data, demonstrate that
the method, besides providing intuitive grasp on pairing, also has quantitative
predictive power. We also consider including phonon effects in this scenario.
Preliminary calculations with small clusters indicate that vector phonons
hinder pairing while half-breathing modes are synergic with the W=0 pairing
mechanism both at weak coupling and in the polaronic regime.Comment: 42 pages, Topical Review to appear in Journal of Physics C: Condensed
Matte
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