3,173 research outputs found
Thermodynamics of an one-dimensional ideal gas with fractional exclusion statistics
We show that the particles in the Calogero-Sutherland Model obey fractional
exclusion statistics as defined by Haldane. We construct anyon number densities
and derive the energy distribution function. We show that the partition
function factorizes in the form characteristic of an ideal gas. The virial
expansion is exactly computable and interestingly it is only the second virial
coefficient that encodes the statistics information.Comment: 10pp, REVTE
Non-perturbative behavior of the quantum phase transition to a nematic Fermi fluid
We discuss shape (Pomeranchuk) instabilities of the Fermi surface of a
two-dimensional Fermi system using bosonization. We consider in detail the
quantum critical behavior of the transition of a two dimensional Fermi fluid to
a nematic state which breaks spontaneously the rotational invariance of the
Fermi liquid. We show that higher dimensional bosonization reproduces the
quantum critical behavior expected from the Hertz-Millis analysis, and verify
that this theory has dynamic critical exponent . Going beyond this
framework, we study the behavior of the fermion degrees of freedom directly,
and show that at quantum criticality as well as in the the quantum nematic
phase (except along a set of measure zero of symmetry-dictated directions) the
quasi-particles of the normal Fermi liquid are generally wiped out. Instead,
they exhibit short ranged spatial correlations that decay faster than any
power-law, with the law and we
verify explicitely the vanishing of the fermion residue utilizing this
expression. In contrast, the fermion auto-correlation function has the behavior
. In this regime we also find that, at
low frequency, the single-particle fermion density-of-states behaves as
, where is larger
than the free Fermi value, N(0), and is a constant. These results confirm
the non-Fermi liquid nature of both the quantum critical theory and of the
nematic phase.Comment: 20 pages, 2 figures, 1 table; new version with minor changes; new
subsection 3C2 added with an explicit calculation of the quasiparticle
residue at the nematic transition; minor typos corrected, new references;
general beautification of the text and figure
Universality Classes of Diagonal Quantum Spin Ladders
We find the classification of diagonal spin ladders depending on a
characteristic integer in terms of ferrimagnetic, gapped and critical
phases. We use the finite algorithm DMRG, non-linear sigma model and
bosonization techniques to prove our results. We find stoichiometric contents
in cuprate planes that allow for the existence of weakly interacting
diagonal ladders.Comment: REVTEX4 file, 3 color figures, 1 tabl
Semiclassical Solution of One Dimensional Model of Kondo Insulator
The model of Kondo chain with -fold degenerate band of conduction
electrons of spin 1/2 interacting with localized spins is studied for the
case when the electronic band is half filled. It is shown that the spectrum of
spin excitations in the continuous limit is described by the O(3) nonlinear
sigma model with the topological term with . For a case
(even) the system is an insulator and single electron excitations
at low energies are massive spin polarons. Otherwise the density of states has
a pseudogap and vanishes only at the Fermi level. The relevance of this picture
to higher dimensional Kondo insulators is discussed.Comment: 10 pages, LaTe
Low-Energy Properties of a One-dimensional System of Interacting bosons with Boundaries
The ground state properties and low-lying excitations of a (quasi)
one-dimensional system of longitudinally confined interacting bosons are
studied. This is achieved by extending Haldane's harmonic-fluid description to
open boundary conditions. The boson density, one-particle density matrix, and
momentum distribution are obtained accounting for finite-size and boundary
effects. Friedel oscillations are found in the density. Finite-size scaling of
the momentum distribution at zero momentum is proposed as a method to obtain
from the experiment the exponent that governs phase correlations. The strong
correlations between bosons induced by reduced dimensionality and interactions
are displayed by a Bijl-Jastrow wave function for the ground state, which is
also derived.Comment: Final published version. Minor changes with respect to the previous
versio
Laughlin State on Stretched and Squeezed Cylinders and Edge Excitations in Quantum Hall Effect
We study the Laughlin wave function on the cylinder. We find it only
describes an incompressible fluid when the two lengths of the cylinder are
comparable. As the radius is made smaller at fixed area, we observe a
continuous transition to the charge density wave Tao-Thouless state. We also
present some exact properties of the wave function in its polynomial form. We
then study the edge excitations of the quantum Hall incompressible fluid
modeled by the Laughlin wave function. The exponent describing the fluctuation
of the edge predicted by recent theories is shown to be identical with
numerical calculations. In particular, for , we obtain the occupation
amplitudes of edge state for 4-10 electron size systems. When plotted as
a function of the scaled wave vector they become essentially free of
finite-size effects. The resulting curve obtains a very good agreement with the
appropriate infinite-size Calogero-Sutherland model occupation numbers.
Finally, we numerically obtain of the edge excitations for some pairing
states which may be relevant to the incompressible Hall state.Comment: 25 pages revtex, 9 uuencoded figures, submitted separately, also
available from first author. CSULA-94-1
Universality relations in non-solvable quantum spin chains
We prove the exact relations between the critical exponents and the
susceptibility, implied by the Haldane Luttinger liquid conjecture, for a
generic lattice fermionic model or a quantum spin chain with short range weak
interaction. The validity of such relations was only checked in some special
solvable models, but there was up to now no proof of their validity in
non-solvable models
Critical exponents of the degenerate Hubbard model
We study the critical behaviour of the \SUN{} generalization of the
one-dimensional Hubbard model with arbitrary degeneracy . Using the
integrability of this model by Bethe Ansatz we are able to compute the spectrum
of the low-lying excitations in a large but finite box for arbitrary values of
the electron density and of the Coulomb interaction. This information is used
to determine the asymptotic behaviour of correlation functions at zero
temperature in the presence of external fields lifting the degeneracy. The
critical exponents depend on the system parameters through a
dressed charge matrix implying the relevance of the interaction of charge- and
spin-density waves.Comment: 18 page
Exact calculation of the ground-state dynamical spin correlation function of a S=1/2 antiferromagnetic Heisenberg chain with free spinons
We calculate the exact dynamical magnetic structure factor S(Q,E) in the
ground state of a one-dimensional S=1/2 antiferromagnet with gapless free S=1/2
spinon excitations, the Haldane-Shastry model with inverse-square exchange,
which is in the same low-energy universality class as Bethe's nearest-neighbor
exchange model. Only two-spinon excited states contribute, and S(Q,E) is found
to be a very simple integral over these states.Comment: 11 pages, LaTeX, RevTeX 3.0, cond-mat/930903
Charge-Spin Separation in 2D Fermi Systems: Singular Interactions as Modified Commutators, and Solution of 2D Hubbard Model in Bosonized Approximation
The general 2-dimensional fermion system with repulsive interactions
(typified by the Hubbard Model) is bosonized, taking into account the finite
on-shell forward scattering phase shift derived in earlier papers. By taking
this phase shift into account in the bosonic commutation relations a consistent
picture emerges showing the charge-spin separation and anomalous exponents of
the Luttinger liquid.Comment: Latex file 14 pages. email: [email protected]
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