887 research outputs found
Failure of Mean Field Theory at Large N
We study strongly coupled lattice QCD with colors of staggered fermions
in 3+1 dimensions. While mean field theory describes the low temperature
behavior of this theory at large , it fails in the scaling region close to
the finite temperature second order chiral phase transition. The universal
critical region close to the phase transition belongs to the 3d XY universality
class even when becomes large. This is in contrast to Gross-Neveu models
where the critical region shrinks as (the number of flavors) increases and
mean field theory is expected to describe the phase transition exactly in the
limit of infinite . Our work demonstrates that close to second order phase
transitions infrared fluctuations can sometimes be important even when is
strictly infinite.Comment: 4 pages, 3 figure
A Class of Parameter Dependent Commuting Matrices
We present a novel class of real symmetric matrices in arbitrary dimension
, linearly dependent on a parameter . The matrix elements satisfy a set
of nontrivial constraints that arise from asking for commutation of pairs of
such matrices for all , and an intuitive sufficiency condition for the
solvability of certain linear equations that arise therefrom. This class of
matrices generically violate the Wigner von Neumann non crossing rule, and is
argued to be intimately connected with finite dimensional Hamiltonians of
quantum integrable systems.Comment: Latex, Added References, Typos correcte
The Origin of Degeneracies and Crossings in the 1d Hubbard Model
The paper is devoted to the connection between integrability of a finite
quantum system and degeneracies of its energy levels. In particular, we analyze
in detail the energy spectra of finite Hubbard chains. Heilmann and Lieb
demonstrated that in these systems there are crossings of levels of the same
parameter independent symmetry. We show that this apparent violation of the
Wigner-von Neumann noncrossing rule follows directly from the existence of
nontrivial conservation laws and is a characteristic signature of quantum
integrability. The energy spectra of Hubbard chains display many instances of
permanent (at all values of the coupling) twofold degeneracies that cannot be
explained by parameter independent symmetries. We relate these degeneracies to
the different transformation properties of the conserved currents under spatial
reflections and the particle-hole transformation and estimate the fraction of
doubly degenerate states. We also discuss multiply degenerate eigenstates of
the Hubbard Hamiltonian. The wave functions of many of these states do not
depend on the coupling, which suggests the existence of an additional parameter
independent symmetry.Comment: 25 pages, 12 figure
Three-dimensional ultrasound-guided biopsy of breast lesion: a new diagnostic support in the preoperative diagnosis
Scattering Matrix and Excitation Spectrum of the Hubbard Model
We consider the one-dimensional Hubbard model at half filling. We show that
both excitation spectrum and S-matrix are determined by the SO(4) symmetry of
the model. The complete set of excitations is given by the scattering states
four elementary excitations, which form the fundamental representation of
SO(4). We evaluate the exact S-matrix, which satisfies the Yang-Baxter
relation. The results for the repulsive and attractive Hubbard model are
related by an interchange of spin and charge degrees of freedom.Comment: 8 pages, jyTeX (macro included - just TeX the file) ITP-SB-93-4
Direct Observation of Field-Induced Incommensurate Fluctuations in a One-Dimensional S=1/2 Antiferromagnet
Neutron scattering from copper benzoate, Cu(C6D5COO)2 3D2O, provides the
first direct experimental evidence for field-dependent incommensurate low
energy modes in a one-dimensional spin S = 1/2 antiferromagnet. Soft modes
occur for wavevectors q=\pi +- dq(H) where dq(H) ~ 2 \pi M(H)/g\mu_B as
predicted by Bethe ansatz and spinon descriptions of the S = 1/2 chain.
Unexpected was a field-induced energy gap , where
as determined from specific heat measurements. At H = 7 T
(g\mu_B H/J = 0.52), the magnitude of the gap varies from 0.06 - 0.3 J
depending on the orientation of the applied field.Comment: 11 pages, 5 postscript figures, LaTeX, Submitted to PRL 3/31/97,
e-mail comments to [email protected]
A note on density correlations in the half-filled Hubbard model
We consider density-density correlations in the one-dimensional Hubbard model
at half filling. On intuitive grounds one might expect them to exhibit an
exponential decay. However, as has been noted recently, this is not obvious
from the Bethe Ansatz/conformal field theory (BA/CFT) approach. We show that by
supplementing the BA/CFT analysis with simple symmetry arguments one can easily
prove that correlations of the lattice density operators decay exponentially.Comment: 3 pages, RevTe
Irreducibility criterion for a finite-dimensional highest weight representation of the sl(2) loop algebra and the dimensions of reducible representations
We present a necessary and sufficient condition for a finite-dimensional
highest weight representation of the loop algebra to be irreducible. In
particular, for a highest weight representation with degenerate parameters of
the highest weight, we can explicitly determine whether it is irreducible or
not. We also present an algorithm for constructing finite-dimensional highest
weight representations with a given highest weight. We give a conjecture that
all the highest weight representations with the same highest weight can be
constructed by the algorithm. For some examples we show the conjecture
explicitly. The result should be useful in analyzing the spectra of integrable
lattice models related to roots of unity representations of quantum groups, in
particular, the spectral degeneracy of the XXZ spin chain at roots of unity
associated with the loop algebra.Comment: 32 pages with no figure; with corrections on the published versio
New integrable extension of the Hubbard chain with variable range hopping
New integrable variant of the one-dimensional Hubbard model with
variable-range correlated hopping is studied. The Hamiltonian is constructed by
applying the quantum inverse scattering method on the infinite interval at zero
density to the one-parameter deformation of the L-matrix of the Hubbard model.
By construction, this model has Y(su(2))Y(su(2)) symmetry in the
infinite chain limit. Multiparticle eigenstates of the model are investigated
through this method.Comment: 25 pages, LaTeX, no figure
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