123 research outputs found
Constraint-based sequence mining using constraint programming
The goal of constraint-based sequence mining is to find sequences of symbols
that are included in a large number of input sequences and that satisfy some
constraints specified by the user. Many constraints have been proposed in the
literature, but a general framework is still missing. We investigate the use of
constraint programming as general framework for this task. We first identify
four categories of constraints that are applicable to sequence mining. We then
propose two constraint programming formulations. The first formulation
introduces a new global constraint called exists-embedding. This formulation is
the most efficient but does not support one type of constraint. To support such
constraints, we develop a second formulation that is more general but incurs
more overhead. Both formulations can use the projected database technique used
in specialised algorithms. Experiments demonstrate the flexibility towards
constraint-based settings and compare the approach to existing methods.Comment: In Integration of AI and OR Techniques in Constraint Programming
(CPAIOR), 201
A Density Matrix Algorithm for 3D Classical Models
We generalize the corner transfer matrix renormalization group, which
consists of White's density matrix algorithm and Baxter's method of the corner
transfer matrix, to three dimensional (3D) classical models. The
renormalization group transformation is obtained through the diagonalization of
density matrices for a cubic cluster. A trial application for 3D Ising model
with m=2 is shown as the simplest case.Comment: 15 pages, Latex(JPSJ style files are included), 8 ps figures,
submitted to J. Phys. Soc. Jpn., some references are correcte
Snapshot Observation for 2D Classical Lattice Models by Corner Transfer Matrix Renormalization Group
We report a way of obtaining a spin configuration snapshot, which is one of
the representative spin configurations in canonical ensemble, in a finite area
of infinite size two-dimensional (2D) classical lattice models. The corner
transfer matrix renormalization group (CTMRG), a variant of the density matrix
renormalization group (DMRG), is used for the numerical calculation. The matrix
product structure of the variational state in CTMRG makes it possible to
stochastically fix spins each by each according to the conditional probability
with respect to its environment.Comment: 4 pages, 8figure
Symmetric States of Composite Systems
Størmer proved a theorem on the integral decomposition of symmetric states on a C*-algebra ⊗B. Motivated by problems in statistical mechanics, we define symmetric states on a composite algebra A⊗(⊗B) and extend Størmer’s theorem to this situation. Applications to spin-boson models are sketched
Density Matrix Renormalization Group of Gapless Systems
We investigate convergence of the density matrix renormalization group (DMRG)
in the thermodynamic limit for gapless systems. Although the DMRG correlations
always decay exponentially in the thermodynamic limit, the correlation length
at the DMRG fixed-point scales as , where is the number
of kept states, indicating the existence of algebraic order for the exact
system. The single-particle excitation spectrum is calculated, using a
Bloch-wave ansatz, and we prove that the Bloch-wave ansatz leads to the
symmetry for translationally invariant half-integer
spin-systems with local interactions. Finally, we provide a method to compute
overlaps between ground states obtained from different DMRG calculations.Comment: 11 pages, RevTex, 5 figure
Energy Versus Magnetic-Field Diagram of the Spin-1 Haldane System with an Impurity
Energy versus magnetic-field diagram of the spin- Haldane system with an
impurity bond is studied in terms of spin-1/2 degree of freedom at the sites
neighboring the impurity bond by means of analytical method. We examine the
equivalence between the realistic Hamiltonian and the phenomenological
Hamiltonian which is composed two spin-1/2 spins representing the spin-1/2
degree of freedom. It is proved that when the strength of the impurity bond is
sufficiently weak, the two Hamiltonians are equivalent to each other, as far as
the energies of the low-lying states are concerned. We determine the
correspondence between the interaction constants in the phenomenological
Hamiltonian and those in the realistic Hamiltonian.Comment: 10 pages, plain TeX (Postscript figures are included), KU-CCS-93-00
Effect of a Spin-1/2 Impurity on the Spin-1 Antiferromagnetic Heisenberg Chain
Low-lying excited states as well as the ground state of the spin-1 antiferro-
magnetic Heisenberg chain with a spin-1/2 impurity are investigated by means of
a variational method and a method of numerical diagonalization. It is shown
that 1) the impurity spin brings about massive modes in the Haldane gap, 2)
when the the impurity-host coupling is sufficiently weak, the phenomenological
Hamiltonian used by Hagiwara {\it et al.} in the analysis of ESR experimental
results for NENP containing a small amount of spin-1/2 Cu impurities is
equivalent to a more realistic Hamiltonian, as far as the energies of the
low-lying states are concerned, 3) the results obtained by the variational
method are in semi-quantitatively good agreement with those obtained by the
numerical diagonalization.Comment: 11 pages, plain TeX (Postscript figures are included), KU-CCS-93-00
Connectivity transition in the frustrated S=1 chain revisited
The phase transition in the antiferromagnetic isotropic Heisenberg S=1 chain
with frustrating next-nearest neighbor coupling alpha is reconsidered. We
identify the order parameter of the large-alpha phase as describing two
intertwined strings, each possessing a usual string order. The transition has a
topological nature determined by the change in the string connectivity.
Numerical evidence from the DMRG results is supported by the effective theory
based on soliton states.Comment: 4 pages, 2 figures, Revtex 4, submitted to PR
One-site density matrix renormalization group and alternating minimum energy algorithm
Given in the title are two algorithms to compute the extreme eigenstate of a
high-dimensional Hermitian matrix using the tensor train (TT) / matrix product
states (MPS) representation. Both methods empower the traditional alternating
direction scheme with the auxiliary (e.g. gradient) information, which
substantially improves the convergence in many difficult cases. Being
conceptually close, these methods have different derivation, implementation,
theoretical and practical properties. We emphasize the differences, and
reproduce the numerical example to compare the performance of two algorithms.Comment: Submitted to the proceedings of ENUMATH 201
The spectral gap for some spin chains with discrete symmetry breaking
We prove that for any finite set of generalized valence bond solid (GVBS)
states of a quantum spin chain there exists a translation invariant
finite-range Hamiltonian for which this set is the set of ground states. This
result implies that there are GVBS models with arbitrary broken discrete
symmetries that are described as combinations of lattice translations, lattice
reflections, and local unitary or anti-unitary transformations. We also show
that all GVBS models that satisfy some natural conditions have a spectral gap.
The existence of a spectral gap is obtained by applying a simple and quite
general strategy for proving lower bounds on the spectral gap of the generator
of a classical or quantum spin dynamics. This general scheme is interesting in
its own right and therefore, although the basic idea is not new, we present it
in a system-independent setting. The results are illustrated with an number of
examples.Comment: 48 pages, Plain TeX, BN26/Oct/9
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