107 research outputs found
Diagrammatic approach in the variational coupled-cluster method
Recently, as demonstrated by an antiferromagnetic spin-lattice application,
we have successfully extended the coupled-cluster method (CCM) to a variational
formalism in which two sets of distribution functions are introduced to
evaluate Hamiltonian expectation. We calculated these distribution functions by
employing an algebraic scheme. Here we present an alternative calculation based
on a diagrammatic technique. Similar to the method of correlated-basis
functionals (CBF), a generating functional is introduced and calculated by a
linked-cluster expansion in terms of diagrams which are categorized and
constructed according to a few simple rules and using correlation coefficients
and Pauli exclusion principle (or Pauli line) as basic elements. Infinite
resummations of diagrams can then be done in a straightforward manner. One such
resummation, which includes all so-called ring diagrams and ignores Pauli
exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond
SWT are also given. Interestingly, one such approximation including all
so-called super-ring diagrams by a resummation of infinite Pauli lines in
additional to resummations of ring diagrams produces a convergent, precise
number for the order-parameter of the one-dimensional isotropic model, contrast
to the well-known divergence of SWT. We also discuss the direct relation
between our variational CCM and CBF and discuss a possible unification of the
two theories.Comment: 18 pages, 9 figure
The permutation group S_N and large Nc excited baryons
We study the excited baryon states for an arbitrary number of colors Nc from
the perspective of the permutation group S_N of N objects. Classifying the
transformation properties of states and quark-quark interaction operators under
S_N allows a general analysis of the spin-flavor structure of the mass operator
of these states, in terms of a few unknown constants parameterizing the unknown
spatial structure. We explain how to perform the matching calculation of a
general two-body quark-quark interaction onto the operators of the 1/Nc
expansion. The inclusion of core and excited quark operators is shown to be
necessary. Considering the case of the negative parity L=1 states transforming
in the MS of S_N, we discuss the matching of the one-gluon and the
Goldstone-boson exchange interactions.Comment: 38 pages. Final version to be published in Physical Review
Electron Spin Resonance of SrCu2(BO3)2 at High Magnetic Field
We calculate the electron spin resonance (ESR) spectra of the
quasi-two-dimensional dimer spin liquid SrCu2(BO3)2 as a function of magnetic
field B. Using the standard Lanczos method, we solve a Shastry-Sutherland
Hamiltonian with additional Dzyaloshinsky-Moriya (DM) terms which are crucial
to explain different qualitative aspects of the ESR spectra. In particular, a
nearest-neighbor DM interaction with a non-zero D_z component is required to
explain the low frequency ESR lines for B || c. This suggests that crystal
symmetry is lowered at low temperatures due to a structural phase transition.Comment: 4 pages, 4 b&w figure
Distribution functions in percolation problems
Percolation clusters are random fractals whose geometrical and transport
properties can be characterized with the help of probability distribution
functions. Using renormalized field theory, we determine the asymptotic form of
various of such distribution functions in the limits where certain scaling
variables become small or large. Our study includes the pair-connection
probability, the distributions of the fractal masses of the backbone, the red
bonds and the shortest, the longest and the average self-avoiding walk between
any two points on a cluster, as well as the distribution of the total
resistance in the random resistor network. Our analysis draws solely on
general, structural features of the underlying diagrammatic perturbation
theory, and hence our main results are valid to arbitrary loop order.Comment: 15 pages, 1 figur
Detecting Hidden Differences via Permutation Symmetries
We present a method for describing and characterizing the state of N
particles that may be distinguishable in principle but not in practice due to
experimental limitations. The technique relies upon a careful treatment of the
exchange symmetry of the state among experimentally accessible and
experimentally inaccessible degrees of freedom. The approach we present allows
a new formalisation of the notion of indistinguishability and can be
implemented easily using currently available experimental techniques. Our work
is of direct relevance to current experiments in quantum optics, for which we
provide a specific implementation.Comment: 8 pages, 1 figur
Controlling Physical Systems with Symmetries
Symmetry properties of the evolution equation and the state to be controlled
are shown to determine the basic features of the linear control of unstable
orbits. In particular, the selection of control parameters and their minimal
number are determined by the irreducible representations of the symmetry group
of the linearization about the orbit to be controlled. We use the general
results to demonstrate the effect of symmetry on the control of two sample
physical systems: a coupled map lattice and a particle in a symmetric
potential.Comment: 6 page
Symmetry Decomposition of Potentials with Channels
We discuss the symmetry decomposition of the average density of states for
the two dimensional potential and its three dimensional
generalisation . In both problems, the energetically
accessible phase space is non-compact due to the existence of infinite channels
along the axes. It is known that in two dimensions the phase space volume is
infinite in these channels thus yielding non-standard forms for the average
density of states. Here we show that the channels also result in the symmetry
decomposition having a much stronger effect than in potentials without
channels, leading to terms which are essentially leading order. We verify these
results numerically and also observe a peculiar numerical effect which we
associate with the channels. In three dimensions, the volume of phase space is
finite and the symmetry decomposition follows more closely that for generic
potentials --- however there are still non-generic effects related to some of
the group elements
Invariant structure of the hierarchy theory of fractional quantum Hall states with spin
We describe the invariant structure common to abelian fractional quantum Hall
systems with spin. It appears in a generalization of the lattice description of
the polarized hierarchy that encompasses both partially polarized and
unpolarized ground state systems. We formulate, using the spin-charge
decomposition, conditions that should be satisfied so that the description is
SU(2) invariant. In the case of the spin- singlet hierarchy construction, we
find that there are as many SU(2) symmetries as there are levels in the
construction. We show the existence of a spin and charge lattice for the
systems with spin. The ``gluing'' of the charge and spin degrees of freedom in
their bulk is described by the gluing theory of lattices.Comment: 21 pages, LaTex, Submitted to Phys. Rev.
Thermodynamics of Coupled Identical Oscillators within the Path Integral Formalism
A generalization of symmetrized density matrices in combination with the
technique of generating functions allows to calculate the partition function of
identical particles in a parabolic confining well. Harmonic two-body
interactions (repulsive or attractive) are taken into account. Also the
influence of a homogeneous magnetic field, introducing anisotropy in the model,
is examined. Although the theory is developed for fermions and bosons, special
attention is payed to the thermodynamic properties of bosons and their
condensation.Comment: 13 REVTEX pages + 9 postscript figure
Multi-Particle Pseudopotentials for Multi-Component Quantum Hall Systems
The Haldane pseudopotential construction has been an extremely powerful
concept in quantum Hall physics --- it not only gives a minimal description of
the space of Hamiltonians but also suggests special model Hamiltonians (those
where certain pseudopotential are set to zero) that may have exactly solvable
ground states with interesting properties. The purpose of this paper is to
generalize the pseudopotential construction to situations where interactions
are N-body and where the particles may have internal degrees of freedom such as
spin or valley index. Assuming a rotationally invariant Hamiltonian, the
essence of the problem is to obtain a full basis of wavefunctions for N
particles with fixed relative angular momentum L. This basis decomposes into
representations of SU(n) with n the number of internal degrees of freedom. We
give special attention to the case where the internal degree of freedom has n=2
states, which encompasses the important cases of spin-1/2 particles and quantum
Hall bilayers. We also discuss in some detail the cases of spin-1 particles
(n=3) and graphene (n=4, including two spin and two valley degrees of freedom).Comment: 46 pages ; 9 tables ; no figures. (The revision fixes a number of
typos and updates the formatting
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