7,621 research outputs found
Crossover from Fermi Liquid to Non-Fermi Liquid Behavior in a Solvable One-Dimensional Model
We consider a quantum moany-body problem in one-dimension described by a
Jastrow type, characterized by an exponent and a parameter .
We show that with increasing , the Fermi Liquid state (
crosses over to non-Fermi liquid states, characterized by effective
"temperature".Comment: 8pp. late
GAPS IN THE HEISENBERG-ISING MODEL
We report on the closing of gaps in the ground state of the critical
Heisenberg-Ising chain at momentum . For half-filling, the gap closes at
special values of the anisotropy , integer. We explain
this behavior with the help of the Bethe Ansatz and show that the gap scales as
a power of the system size with variable exponent depending on . We use
a finite-size analysis to calculate this exponent in the critical region,
supplemented by perturbation theory at . For rational
fillings, the gap is shown to be closed for {\em all} values of and
the corresponding perturbation expansion in shows a remarkable
cancellation of various diagrams.Comment: 12 RevTeX pages + 4 figures upon reques
A Note on Dressed S-Matrices in Models with Long-Range Interactions
The {\sl dressed} Scattering matrix describing scattering of quasiparticles
in various models with long-range interactions is evaluated by means of
Korepin's method\upref vek1/. For models with -interactions
the S-matrix is found to be a momentum-independent phase, which clearly
demonstrates the ideal gas character of the quasiparticles in such models. We
then determine S-matrices for some models with -interaction
and find them to be in general nontrivial. For the -limit of the
-interaction we recover trivial S-matrices, thus exhibiting
a crossover from interacting to noninteracting quasiparticles. The relation of
the S-matrix to fractional statistics is discussed.Comment: 18 pages, jyTeX (macro included - just TeX the file) BONN-TH-94-13,
revised version: analysis of models with 1/sinh^2 interaction adde
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
Spectrum of a spin chain with inverse square exchange
The spectrum of a one-dimensional chain of spins positioned at the
static equilibrium positions of the particles in a corresponding classical
Calogero system with an exchange interaction inversely proportional to the
square of their distance is studied. As in the translationally invariant
Haldane--Shastry model the spectrum is found to exhibit a very simple structure
containing highly degenerate ``super-multiplets''. The algebra underlying this
structure is identified and several sets of raising and lowering operators are
given explicitely. On the basis of this algebra and numerical studies we give
the complete spectrum and thermodynamics of the system.Comment: 9 pages, late
Exact Solution of Heisenberg-liquid models with long-range coupling
We present the exact solution of two Heisenberg-liquid models of particles
with arbitrary spin interacting via a hyperbolic long-range potential. In
one model the spin-spin coupling has the simple antiferromagnetic Heisenberg
exchange form, while for the other model the interaction is of the
ferromagnetic Babujian-Takhatajan type. It is found that the Bethe ansatz
equations of these models have a similar structure to that of the
Babujian-Takhatajan spin chain. We also conjecture the integrability of a third
new spin-lattice model with long-range interaction.Comment: 7pages Revte
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
Exact operator solution of the Calogero-Sutherland model
The wave functions of the Calogero-Sutherland model are known to be
expressible in terms of Jack polynomials. A formula which allows to obtain the
wave functions of the excited states by acting with a string of creation
operators on the wave function of the ground state is presented and derived.
The creation operators that enter in this formula of Rodrigues-type for the
Jack polynomials involve Dunkl operators.Comment: 35 pages, LaTeX2e with amslate
Manipulation of the dynamics of many-body systems via quantum control methods
We investigate how dynamical decoupling methods may be used to manipulate the
time evolution of quantum many-body systems. These methods consist of sequences
of external control operations designed to induce a desired dynamics. The
systems considered for the analysis are one-dimensional spin-1/2 models, which,
according to the parameters of the Hamiltonian, may be in the integrable or
non-integrable limits, and in the gapped or gapless phases. We show that an
appropriate control sequence may lead a chaotic chain to evolve as an
integrable chain and a system in the gapless phase to behave as a system in the
gapped phase. A key ingredient for the control schemes developed here is the
possibility to use, in the same sequence, different time intervals between
control operations.Comment: 10 pages, 3 figure
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