1,518 research outputs found
Quasiperiodic Hubbard chains
Low energy properties of half-filled Fibonacci Hubbard models are studied by
weak coupling renormalization group and density matrix renormalization group
method. In the case of diagonal modulation, weak Coulomb repulsion is
irrelevant and the system behaves as a free Fibonacci chain, while for strong
Coulomb repulsion, the charge sector is a Mott insulator and the spin sector
behaves as a uniform Heisenberg antiferromagnetic chain. The off-diagonal
modulation always drives the charge sector to a Mott insulator and the spin
sector to a Fibonacci antiferromagnetic Heisenberg chain.Comment: 4 pages, 4 figures; Final version to appear in Phys. Rev. Let
Critical Properties of the transition between the Haldane phase and the large-D phase of the spin-1/2 ferromagnetic-antiferromagnetic Heisenberg chain with on-site anisotropy"
We analytically study the ground-state quantum phase transition between the
Haldane phase and the large- (LD) phase of the
ferromagnetic-antiferromagnetic alternating Heisenberg chain with on-site
anisotropy. We transform this model into a generalized version of the
alternating antiferromagnetic Heisenberg model with anisotropy. In the
transformed model, the competition between the transverse and longitudinal bond
alternations yields the Haldane-LD transition. Using the bosonization method,
we show that the critical exponents vary continuously on the Haldane-LD
boundary. Our scaling relations between critical exponents very well explains
the numerical results by Hida.Comment: text 12 pages (Plain TeX), LaTeX sourse files of a table and a figure
on reques
Computing automorphic forms on Shimura curves over fields with arbitrary class number
We extend methods of Greenberg and the author to compute in the cohomology of
a Shimura curve defined over a totally real field with arbitrary class number.
Via the Jacquet-Langlands correspondence, we thereby compute systems of Hecke
eigenvalues associated to Hilbert modular forms of arbitrary level over a
totally real field of odd degree. We conclude with two examples which
illustrate the effectiveness of our algorithms.Comment: 15 pages; final submission to ANTS I
Divergence-free Nonrenormalizable Models
A natural procedure is introduced to replace the traditional, perturbatively
generated counter terms to yield a formulation of covariant, self-interacting,
nonrenormalizable scalar quantum field theories that has the added virtue of
exhibiting a divergence-free perturbation analysis. To achieve this desirable
goal it is necessary to reexamine the meaning of the free theory about which
such a perturbation takes place.Comment: 22 pages. Version accepted for publication; involves modest addition
to the end of Sec.
Effects of Single-site Anisotropy on Mixed Diamond Chains with Spins 1 and 1/2
Effects of single-site anisotropy on mixed diamond chains with spins 1 and
1/2 are investigated in the ground states and at finite temperatures. There are
phases where the ground state is a spin cluster solid, i.e., an array of
uncorrelated spin-1 clusters separated by singlet dimers. The ground state is
nonmagnetic for the easy-plane anisotropy, while it is paramagnetic for the
easy-axis anisotropy. Also, there are the N\'eel, Haldane, and large-
phases, where the ground state is a single spin cluster of infinite size and
the system is equivalent to the spin-1 Heisenberg chain with alternating
anisotropy. The longitudinal and transverse susceptibilities and entropy are
calculated at finite temperatures in the spin-cluster-solid phases. Their
low-temperature behaviors are sensitive to anisotropy.Comment: 8 pages, 4 figure
Interacting Boson Theory of the Magnetization Process of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain
The low temperature magnetization process of the
ferromagnetic-antiferromagnetic Heisenberg chain is studied using the
interacting boson approximation. In the low field regime and near the
saturation field, the spin wave excitations are approximated by the
function boson gas for which the Bethe ansatz solution is available. The finite
temperature properties are calculated by solving the integral equation
numerically. The comparison is made with Monte Carlo calculation and the limit
of the applicability of the present approximation is discussed.Comment: 4 pages, 7 figure
Excitation Spectrum of the Spin-1/2 Ferromagnetic-Antiferromagnetic Alternating Heisenberg Chain:
The natural explanation of the excitation spectrum of the spin-1
antiferromagnetic Heisenberg chain is given from the viewpoint of the spin-1/2
ferromagnetic-antiferromagnetic alternating Heisenberg chain. The energy
spectrum of the latter is calculated with fixed momentum by numerical
diagonalization of finite size systems. It consists of a branch of propagating
triplet pair (triplet wave) and the continuum of multiple triplet waves for
weak ferromagnetic coupling. As the ferromagnetic coupling increases, the
triplet wave branch is absorbed in the continuum for small , reproducing the
characteristics of the spin-1 antiferromagnetic Heisenberg chain.Comment: 12 Pages REVTEX, Postscript file for the figures included.
SKPH-94-C00
Spectral stochastic processes arising in quantum mechanical models with a non-L2 ground state
A functional integral representation is given for a large class of quantum
mechanical models with a non--L2 ground state. As a prototype the particle in a
periodic potential is discussed: a unique ground state is shown to exist as a
state on the Weyl algebra, and a functional measure (spectral stochastic
process) is constructed on trajectories taking values in the spectrum of the
maximal abelian subalgebra of the Weyl algebra isomorphic to the algebra of
almost periodic functions. The thermodynamical limit of the finite volume
functional integrals for such models is discussed, and the superselection
sectors associated to an observable subalgebra of the Weyl algebra are
described in terms of boundary conditions and/or topological terms in the
finite volume measures.Comment: 15 pages, Plain Te
Field Induced Multiple Reentrant Quantum Phase Transitions in Randomly Dimerized Antiferromagnetic S=1/2 Heisenberg Chains
The multiple reentrant quantum phase transitions in the
antiferromagnetic Heisenberg chains with random bond alternation in the
magnetic field are investigated by the density matrix renormalization group
method combined with the interchain mean field approximation. It is assumed
that the odd-th bond is antiferromagnetic with strength and even-th bond
can take the values {\JS} and {\JW} ({\JS} > J > {\JW} > 0) randomly
with probability and , respectively. The pure version ( and
) of this model has a spin gap but exhibits a field induced
antiferromagnetism in the presence of interchain coupling if Zeeman energy due
to the magnetic field exceeds the spin gap. For , the
antiferromagnetism is induced by randomness at small field region where the
ground state is disordered due to the spin gap in the pure case. At the same
time, this model exhibits randomness induced plateaus at several values of
magnetization. The antiferromagnetism is destroyed on the plateaus. As a
consequence, we find a series of reentrant quantum phase transitions between
the transverse antiferromagnetic phases and disordered plateau phases with the
increase of the magnetic field for moderate strength of interchain coupling.
Above the main plateaus, the magnetization curve consists of a series of small
plateaus and the jumps between them, It is also found that the
antiferromagnetism is induced by infinitesimal interchain coupling at the jumps
between the small plateaus. We conclude that this antiferromagnetism is
supported by the mixing of low lying excited states by the staggered interchain
mean field even though the spin correlation function is short ranged in the
ground state of each chain.Comment: 5 pages, 8 figure
Quantum Spins and Quasiperiodicity: a real space renormalization group approach
We study the antiferromagnetic spin-1/2 Heisenberg model on a two-dimensional
bipartite quasiperiodic structure, the octagonal tiling -- the aperiodic
equivalent of the square lattice for periodic systems.
An approximate block spin renormalization scheme is described for this
problem. The ground state energy and local staggered magnetizations for this
system are calculated, and compared with the results of a recent Quantum Monte
Carlo calculation for the tiling. It is conjectured that the ground state
energy is exactly equal to that of the quantum antiferromagnet on the square
lattice.Comment: To appear in Physical Review Letter
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