4,745 research outputs found
Solutions to the Multi-Component 1/R Hubbard Model
In this work we introduce one dimensional multi-component Hubbard model of
1/r hopping and U on-site energy. The wavefunctions, the spectrum and the
thermodynamics are studied for this model in the strong interaction limit
. In this limit, the system is a special example of Luttinger
liquids, exhibiting spin-charge separation in the full Hilbert space.
Speculations on the physical properties of the model at finite on-site energy
are also discussed.Comment: 9 pages, revtex, Princeton-May1
Exact Drude weight for the one-dimensional Hubbard model at finite temperatures
The Drude weight for the one-dimensional Hubbard model is investigated at
finite temperatures by using the Bethe ansatz solution. Evaluating finite-size
corrections to the thermodynamic Bethe ansatz equations, we obtain the formula
for the Drude weight as the response of the system to an external gauge
potential. We perform low-temperature expansions of the Drude weight in the
case of half-filling as well as away from half-filling, which clearly
distinguish the Mott-insulating state from the metallic state.Comment: 9 pages, RevTex, To appear in J. Phys.
Renormalized Harmonic-Oscillator Description of Confined Electron Systems with Inverse-Square Interaction
An integrable model for SU() electrons with inverse-square interaction
is studied for the system with confining harmonic potential. We develop a new
description of the spectrum based on the {\it renormalized
harmonic-oscillators} which incorporate interaction effects via the repulsion
of energy levels. This approach enables a systematic treatment of the
excitation spectrum as well as the ground-state quantities.Comment: RevTex, 7 page
Entropy and Barrier-Hopping Determine Conformational Viscoelasticity in Single Biomolecules
Biological macromolecules have complex and non-trivial energy landscapes,
endowing them a unique conformational adaptability and diversity in function.
Hence, understanding the processes of elasticity and dissipation at the
nanoscale is important to molecular biology and also emerging fields such as
nanotechnology. Here we analyse single molecule fluctuations in an atomic force
microscope (AFM) experiment using a generic model of biopolymer viscoelasticity
that importantly includes sources of local `internal' conformational
dissipation. Comparing two biopolymers, dextran and cellulose, polysaccharides
with and without the well-known `chair-to-boat' transition, reveals a signature
of this simple conformational change as minima in both the elasticity and
internal friction around a characteristic force. A calculation of two-state
populations dynamics offers a simple explanation in terms of an elasticity
driven by the entropy, and friction by barrier-controlled hopping, of
populations on a landscape. The microscopic model, allows quantitative mapping
of features of the energy landscape, revealing unexpectedly slow dynamics,
suggestive of an underlying roughness to the free energy.Comment: 25 pages, 7 figures, naturemag.bst, modified nature.cls
(naturemodified.cls
On Models with Inverse-Square Exchange
A one-dimensional quantum N-body system of either fermions or bosons with
colors interacting via inverse-square exchange is presented in this
article. A class of eigenstates of both the continuum and lattice version of
the model Hamiltonians is constructed in terms of the Jastrow-product type wave
function. The class of states we construct in this paper corresponds to the
ground state and the low energy excitations of the model that can be described
by the effective harmonic fluid Hamiltonian. By expanding the energy about the
ground state we find the harmonic fluid parameters (i.e. the charge, spin
velocities, etc.), explicitly. The correlation exponent and the compressibility
of are also found. As expected the general harmonic relation(i.e.
) is satisfied among the charge and spin velocities.Comment: 26 page
Spectrum and Thermodynamics of the one-dimensional supersymmetric t-J model with exchange and hopping
We derive the spectrum and the thermodynamics of the one-dimensional
supersymmetric t-J model with long range hopping and spin exchange using a set
of maximal-spin eigenstates. This spectrum confirms the recent conjecture that
the asymptotic Bethe-ansatz spectrum is exact. By empirical determining the
spinon degeneracies of each state, we are able to explicitly construct the free
energy.Comment: 13 pages, Latex, (published in PRB46, 6639 (1992)
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
Invariants of the Haldane-Shastry Chain
Using a formalism developed by Polychronakos, we explicitly construct a set
of invariants of the motion for the Haldane-Shastry chain.Comment: 11 pages, UVA-92-0
Exact solution and spectral flow for twisted Haldane-Shastry model
The exact solution of the spin chain model with exchange is found for
twisted boundary conditions. The spectrum thus obtained can be reproduced by
the asymptotic Bethe ansatz. The spectral flow of each eigenstate is determined
exactly as a function of the twist angle. We find that the period for
the ground state nicely fits in with the notion of fractional exclusion
statistics.Comment: 4 pages, revtex, 1 figure available on request, to appear in PR
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
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