231 research outputs found
Quantum Spin Formulation of the Principal Chiral Model
We formulate the two-dimensional principal chiral model as a quantum spin
model, replacing the classical fields by quantum operators acting in a Hilbert
space, and introducing an additional, Euclidean time dimension. Using coherent
state path integral techniques, we show that in the limit in which a large
representation is chosen for the operators, the low energy excitations of the
model describe a principal chiral model in three dimensions. By dimensional
reduction, the two-dimensional principal chiral model of classical fields is
recovered.Comment: 3pages, LATTICE9
From Spin Ladders to the 2-d O(3) Model at Non-Zero Density
The numerical simulation of various field theories at non-zero chemical
potential suffers from severe complex action problems. In particular, QCD at
non-zero quark density can presently not be simulated for that reason. A
similar complex action problem arises in the 2-d O(3) model -- a toy model for
QCD. Here we construct the 2-d O(3) model at non-zero density via dimensional
reduction of an antiferromagnetic quantum spin ladder in a magnetic field. The
complex action problem of the 2-d O(3) model manifests itself as a sign problem
of the ladder system. This sign problem is solved completely with a
meron-cluster algorithm.Comment: Based on a talk by U.-J. Wiese, 6 pages, 12 figures, to be published
in computer physics communication
A Multi-level Algorithm for Quantum-impurity Models
A continuous-time path integral Quantum Monte Carlo method using the
directed-loop algorithm is developed to simulate the Anderson single-impurity
model in the occupation number basis. Although the method suffers from a sign
problem at low temperatures, the new algorithm has many advantages over
conventional algorithms. For example, the model can be easily simulated in the
Kondo limit without time discretization errors. Further, many observables
including the impurity susceptibility and a variety of fermionic observables
can be calculated efficiently. Finally the new approach allows us to explore a
general technique, called the multi-level algorithm, to solve the sign problem.
We find that the multi-level algorithm is able to generate an exponentially
large number of configurations with an effort that grows as a polynomial in
inverse temperature such that configurations with a positive sign dominate over
those with negative signs. Our algorithm can be easily generalized to other
multi-impurity problems.Comment: 9 pages, 8 figure
Cluster Algorithms for Quantum Impurity Models and Mesoscopic Kondo Physics
Nanoscale physics and dynamical mean field theory have both generated
increased interest in complex quantum impurity problems and so have focused
attention on the need for flexible quantum impurity solvers. Here we
demonstrate that the mapping of single quantum impurity problems onto
spin-chains can be exploited to yield a powerful and extremely flexible
impurity solver. We implement this cluster algorithm explicitly for the
Anderson and Kondo Hamiltonians, and illustrate its use in the ``mesoscopic
Kondo problem''. To study universal Kondo physics, a large ratio between the
effective bandwidth and the temperature is required; our
cluster algorithm treats the mesoscopic fluctuations exactly while being able
to approach the large limit with ease. We emphasize that the
flexibility of our method allows it to tackle a wide variety of quantum
impurity problems; thus, it may also be relevant to the dynamical mean field
theory of lattice problems.Comment: 4 pages, 3 figure
Two dimensional SU(N) x SU(N) chiral models on the lattice
Lattice chiral models are analyzed by strong and weak
coupling expansions and by numerical simulations. order strong
coupling series for the free and internal energy are obtained for all . Three loop contributions to the internal energy and to the lattice
-function are evaluated for all and non-universal corrections to the
asymptotic parameter are computed in the ``temperature'' and the
``energy'' scheme. Numerical simulations confirm a faster approach to
asymptopia of the energy scheme. A phenomenological correlation between the
peak in the specific heat and the dip of the -function is observed.
Tests of scaling are performed for various physical quantities, finding
substantial scaling at . In particular, at three different
mass ratios are determined numerically and found in agreement, within
statistical errors of about 1\%, with the theoretical predictions from the
exact S-matrix theory.Comment: pre-print IFUP 29/93, revised version, 12 pages, 10 figures avaliable
on request by FAX or by mail. REVTE
Pions versus Magnons: From QCD to Antiferromagnets and Quantum Hall Ferromagnets
The low-energy dynamics of pions and magnons -- the Goldstone bosons of the
strong interactions and of magnetism -- are analogous in many ways. The
electroweak interactions of pions result from gauging an SU(2)_L x U(1)_Y
symmetry which then breaks to the U(1)_{em} gauge symmetry of electromagnetism.
The electromagnetic interactions of magnons arise from gauging not only
U(1)_{em} but also the SU(2)_s spin rotational symmetry, with the
electromagnetic fields E and B appearing as non-Abelian vector potentials.
Pions couple to electromagnetism through a Goldstone-Wilczek current that
represents the baryon number of Skyrmions and gives rise to the decay \pi^0 to
\gamma \gamma. Similarly, magnons may couple to an analogue of the
Goldstone-Wilczek current for baby-Skyrmions which induces a magnon-two-photon
vertex. The corresponding analogue of photon-axion conversion is photon-magnon
conversion in an external magnetic field. The baryon number violating decay of
Skyrmions can be catalyzed by a magnetic monopole via the Callan-Rubakov
effect. Similarly, baby-Skyrmion decay can be catalyzed by a charged wire. For
more than two flavors, the Wess-Zumino-Witten term enters the low-energy pion
theory with a quantized prefactor N_c -- the number of quark colors. The magnon
analogue of this prefactor is the anyon statistics angle \theta which need not
be quantized.Comment: 34 pages, no figure
Two dimensional SU(N)xSU(N) Chiral Models on the Lattice (II): the Green's Function
Analytical and numerical methods are applied to principal chiral models on a
two-dimensional lattice and their predictions are tested and compared. New
techniques for the strong coupling expansion of SU(N) models are developed and
applied to the evaluation of the two-point correlation function. The
momentum-space lattice propagator is constructed with precision O(\beta^{10})
and an evaluation of the correlation length is obtained for several different
definitions. Three-loop weak coupling contributions to the internal energy and
to the lattice and functions are evaluated for all N, and the
effect of adopting the ``energy'' definition of temperature is computed with
the same precision. Renormalization-group improved predictions for the
two-point Green's function in the weak coupling ( continuum ) regime are
obtained and successfully compared with Monte Carlo data. We find that strong
coupling is predictive up to a point where asymptotic scaling in the energy
scheme is observed. Continuum physics is insensitive to the effects of the
large N phase transition occurring in the lattice model. Universality in N is
already well established for and the large N physics is well
described by a ``hadronization'' picture.Comment: Revtex, 37 pages, 16 figures available on request by FAX or mai
Classical integrability of Schrodinger sigma models and q-deformed Poincare symmetry
We discuss classical integrable structure of two-dimensional sigma models
which have three-dimensional Schrodinger spacetimes as target spaces. The
Schrodinger spacetimes are regarded as null-like deformations of AdS_3. The
original AdS_3 isometry SL(2,R)_L x SL(2,R)_R is broken to SL(2,R)_L x U(1)_R
due to the deformation. According to this symmetry, there are two descriptions
to describe the classical dynamics of the system, 1) the SL(2,R)_L description
and 2) the enhanced U(1)_R description. In the former 1), we show that the
Yangian symmetry is realized by improving the SL(2,R)_L Noether current. Then a
Lax pair is constructed with the improved current and the classical
integrability is shown by deriving the r/s-matrix algebra. In the latter 2), we
find a non-local current by using a scaling limit of warped AdS_3 and that it
enhances U(1)_R to a q-deformed Poincare algebra. Then another Lax pair is
presented and the corresponding r/s-matrices are also computed. The two
descriptions are equivalent via a non-local map.Comment: 20 pages, no figure, further clarification and references adde
Fermion-Boson Interactions and Quantum Algebras
Quantum Algebras (q-algebras) are used to describe interactions between
fermions and bosons. Particularly, the concept of a su_q(2) dynamical symmetry
is invoked in order to reproduce the ground state properties of systems of
fermions and bosons interacting via schematic forces. The structure of the
proposed su_q(2) Hamiltonians, and the meaning of the corresponding deformation
parameters, are discussed.Comment: 20 pages, 10 figures. Physical Review C (in press
Topological Lattice Actions
We consider lattice field theories with topological actions, which are
invariant against small deformations of the fields. Some of these actions have
infinite barriers separating different topological sectors. Topological actions
do not have the correct classical continuum limit and they cannot be treated
using perturbation theory, but they still yield the correct quantum continuum
limit. To show this, we present analytic studies of the 1-d O(2) and O(3)
model, as well as Monte Carlo simulations of the 2-d O(3) model using
topological lattice actions. Some topological actions obey and others violate a
lattice Schwarz inequality between the action and the topological charge Q.
Irrespective of this, in the 2-d O(3) model the topological susceptibility
\chi_t = \l/V is logarithmically divergent in the continuum limit.
Still, at non-zero distance the correlator of the topological charge density
has a finite continuum limit which is consistent with analytic predictions. Our
study shows explicitly that some classically important features of an action
are irrelevant for reaching the correct quantum continuum limit.Comment: 38 pages, 12 figure
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