2,998 research outputs found
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
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
New Types of Off-Diagonal Long Range Order in Spin-Chains
We discuss new possibilities for Off-Diagonal Long Range Order (ODLRO) in
spin chains involving operators which add or delete sites from the chain. For
the Heisenberg and Inverse Square Exchange models we give strong numerical
evidence for the hidden ODLRO conjectured by Anderson \cite{pwa_conj}. We find
a similar ODLRO for the XY model (or equivalently for free fermions in one
spatial dimension) which we can demonstrate rigorously, as well as numerically.
A connection to the singlet pair correlations in one dimensional models of
interacting electrons is made and briefly discussed.Comment: 13 pages, Revtex v3.0, 2 PostScript figures include
Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions
We study the Heisenberg spin chain with twisted boundary conditions, focusing
on the adiabatic flow of the energy spectrum as a function of the twist angle.
In terms of effective field theory for the nearest-neighbor model, we show that
the period 2 (in unit ) obtained by Sutherland and Shastry arises from
irrelevant perturbations around the massless fixed point, and that this period
may be rather general for one-dimensional interacting lattice models at half
filling. In contrast, the period for the Haldane-Shastry spin model with
interaction has a different and unique origin for the period, namely,
it reflects fractional statistics in Haldane's sense.Comment: 6 pages, revtex, 3 figures available on request, to appear in J.
Phys. Soc. Jp
Solution of Some Integrable One-Dimensional Quantum Systems
In this paper, we investigate a family of one-dimensional multi-component
quantum many-body systems. The interaction is an exchange interaction based on
the familiar family of integrable systems which includes the inverse square
potential. We show these systems to be integrable, and exploit this
integrability to completely determine the spectrum including degeneracy, and
thus the thermodynamics. The periodic inverse square case is worked out
explicitly. Next, we show that in the limit of strong interaction the "spin"
degrees of freedom decouple. Taking this limit for our example, we obtain a
complete solution to a lattice system introduced recently by Shastry, and
Haldane; our solution reproduces the numerical results. Finally, we emphasize
the simple explanation for the high multiplicities found in this model
Exclusion Statistics in Conformal Field Theory Spectra
We propose a new method for investigating the exclusion statistics of
quasi-particles in Conformal Field Theory (CFT) spectra. The method leads to
one-particle distribution functions, which generalize the Fermi-Dirac
distribution. For the simplest invariant CFTs we find a generalization
of Gentile parafermions, and we obtain new distributions for the simplest
-invariant CFTs. In special examples, our approach reproduces
distributions based on `fractional exclusion statistics' in the sense of
Haldane. We comment on applications to fractional quantum Hall effect edge
theories.Comment: 4 pages, 1 figure, LaTeX (uses revtex
A new class of exactly solvable interacting fermion models in one dimension
We investigate a model containing two species of one-dimensional fermions
interacting via a gauge field determined by the positions of all particles of
the opposite species. The model can be solved exactly via a simple unitary
transformation. Nevertheless, correlation functions exhibit nontrivial
interaction-dependent exponents. A similar model defined on a lattice is
introduced and solved. Various generalizations, e.g. to the case of internal
symmetries of the fermions, are discussed. The present treatment also clarifies
certain aspects of Luttinger's original solution of the ``Luttinger model''.Comment: 11 pages, revtex 3.0, no figures, some typos correcte
Stability of Chiral Luttinger Liquids and Abelian Quantum Hall States.
A criterion is given for topological stability of Abelian quantum Hall
states, and of Luttinger liquids at the boundaries between such states; this
suggests a selection rule on states in the quantum Hall hierarchy theory. The
linear response of Luttinger liquids to electromagnetic fields is described:
the Hall conductance is quantized, irrespective of whether edge modes propagate
in different directions.Comment: 12 pages, LaTeX (RevTeX 3.0
Band Structure of the Fractional Quantum Hall Effect
The eigenstates of interacting electrons in the fractional quantum Hall phase
typically form fairly well defined bands in the energy space. We show that the
composite fermion theory gives insight into the origin of these bands and
provides an accurate and complete microscopic description of the strongly
correlated many-body states in the low-energy bands. Thus, somewhat like in
Landau's fermi liquid theory, there is a one-to-one correspondence between the
low energy Hilbert space of strongly interacting electrons in the fractinal
quantum Hall regime and that of weakly interacting electrons in the integer
quantum Hall regime.Comment: 10 page
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