12,223 research outputs found
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
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
Density Correlation Functions in Calogero Sutherland Models
Using arguments from two dimensional Yang-Mills theory and the collective
coordinate formulation of the Calogero-Sutherland model, we conjecture the
dynamical density correlation function for coupling and , where is
an integer. We present overwhelming evidence that the conjecture is indeed
correct.Comment: 12 pages phyzzx, CERN-TH/94.7243 One reference change
Correlations in an expanding gas of hard-core bosons
We consider a longitudinal expansion of a one-dimensional gas of hard-core
bosons suddenly released from a trap. We show that the broken translational
invariance in the initial state of the system is encoded in correlations
between the bosonic occupation numbers in the momentum space. The correlations
are protected by the integrability and exhibit no relaxation during the
expansion
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