552 research outputs found
On the nonlinearity interpretation of q- and f-deformation and some applications
q-oscillators are associated to the simplest non-commutative example of Hopf
algebra and may be considered to be the basic building blocks for the symmetry
algebras of completely integrable theories. They may also be interpreted as a
special type of spectral nonlinearity, which may be generalized to a wider
class of f-oscillator algebras. In the framework of this nonlinear
interpretation, we discuss the structure of the stochastic process associated
to q-deformation, the role of the q-oscillator as a spectrum-generating algebra
for fast growing point spectrum, the deformation of fermion operators in
solid-state models and the charge-dependent mass of excitations in f-deformed
relativistic quantum fields.Comment: 11 pages Late
Phase diagram and hidden order for generalized spin ladders
We investigate the phase diagram of antiferromagnetic spin ladders with
additional exchange interactions on diagonal bonds by variational and numerical
methods. These generalized spin ladders interpolate smoothly between the
chain with competing nn and nnn interactions, the chain with
alternating exchange and the antiferromagnetic chain. The Majumdar-Ghosh
ground states are formulated as matrix product states and are shown to exhibit
the same type of hidden order as the af chain. Generalized matrix product
states are used for a variational calculation of the ground state energy and
the spin and string correlation functions. Numerical (Lanczos) calculations of
the energies of the ground state and of the low-lying excited states are
performed, and compare reasonably with the variational approach. Our results
support the hypothesis that the dimer and Majumdar-Ghosh points are in the same
phase as the af chain.Comment: 23 pages, REVTEX, 7 figure
Variable range hopping and quantum creep in one dimension
We study the quantum non linear response to an applied electric field of
a one dimensional pinned charge density wave or Luttinger liquid in presence of
disorder. From an explicit construction of low lying metastable states and of
bounce instanton solutions between them, we demonstrate quantum creep as well as a sharp crossover at towards a linear response
form consistent with variable range hopping arguments, but dependent only on
electronic degrees of freedom
Ground State Phase Diagram of S=1 XXZ Chains with Uniaxial Single-Ion-Type Anisotropy
One dimensional S=1 XXZ chains with uniaxial single-ion-type anisotropy are
studied by numerical exact diagonalization of finite size systems. The
numerical data are analyzed using conformal field theory, the level
spectroscopy, phenomenological renormalization group and finite size scaling
method. We thus present the first quantitatively reliable ground state phase
diagram of this model. The ground states of this model contain the Haldane
phase, large-D phase, N\'{e}el phase, two XY phases and the ferromagnetic
phase. There are four different types of transitions between these phases: the
Brezinskii-Kosterlitz-Thouless type transitions, the Gaussian type transitions,
the Ising type transitions and the first order transitions. The location of
these critical lines are accurately determined.Comment: 8 pages, 19 figure
Magnetic Properties of J-J-J' Quantum Heisenberg Chains with Spin S=1/2, 1, 3/2 and 2 in a Magnetic Field
By means of the density matrix renormalization group (DMRG) method, the
magnetic properties of the J-J-J quantum Heisenberg chains with spin
, 1, 3/2 and 2 in the ground states are investigated in the presence of
a magnetic field. Two different cases are considered: (a) when is
antiferromagnetic and is ferromagnetic (i.e. the AF-AF-F chain),
the system is a ferrimagnet. The plateaus of the magnetization are observed. It
is found that the width of the plateaus decreases with increasing the
ferromagnetic coupling, and disappears when passes over a
critical value. The saturated field is observed to be independent of the
ferromagnetic coupling; (b) when is ferromagnetic and is
antiferromagnetic (i.e. the F-F-AF chain), the system becomes an
antiferromagnet. The plateaus of the magnetization are also seen. The width of
the plateaus decreases with decreasing the antiferromagnetic coupling, and
disappears when passes over a critical value. Though the ground
state properties are quite different, the magnetization plateaus in both cases
tend to disappear when the ferromagnetic coupling becomes more dominant.
Besides, no fundamental difference between the systems with spin half-integer
and integer has been found.Comment: 8 pages, 9 figures, to be published in J. Phys.: Condens. Matte
Magnetization Process of the S=1 and 1/2 Uniform and Distorted Kagome Heisenberg Antiferromagnets
The magnetization process of the S=1 and 1/2 kagome Heisenberg
antiferromagnet is studied by means of the numerical exact diagonalization
method. It is found that the magnetization curve at zero temperature has a
plateau at 1/3 of the full magnetization. In the presence of lattice distortion, this plateau is enhanced and eventually the
ferrimagnetic state is realized. There also appear the minor plateaux above the
main plateau. The physical origin of these phenomena is discussed.Comment: 5 pages, 10 figures included, to be published in J. Phys. Soc. Jp
Density-Matrix Renormalization-Group Analysis of Quantum Critical Points: I. Quantum Spin Chains
We present a simple method, combining the density-matrix
renormalization-group (DMRG) algorithm with finite-size scaling, which permits
the study of critical behavior in quantum spin chains. Spin moments and
dimerization are induced by boundary conditions at the chain ends and these
exhibit power-law decay at critical points. Results are presented for the
spin-1/2 Heisenberg antiferromagnet; an analytic calculation shows that
logarithmic corrections to scaling can sometimes be avoided. We also examine
the spin-1 chain at the critical point separating the Haldane gap and dimerized
phases. Exponents for the dimer-dimer and the spin-spin correlation functions
are consistent with results obtained from bosonization.Comment: 21 pages, 12 figures, new results and added references, to appear in
PR
Behavior of a frustrated quantum spin chain with bond dimerization
We clarified behavior of the excitation gap in a frustrated S=1/2 quantum
spin chain with bond dimerization by using the numerical diagonalization of
finite systems and a variational approach. The model interpolates between the
independent dimer model and the S=1 spin chain by changing a strength of the
dimerization. The energy gap is minimum at the fully-frustrated point, where a
localized kink and a freely mobile anti-kink govern the low-lying excitations.
Away from the point, a kink and an antikink form a bound state by an effective
triangular potential between them. The consequential gap enhancement and the
localization length of the bound state is obtained exactly in the continuous
limit. The gap enhancement obeys a power law with exponent 2/3. The method and
the obtained results are common to other frustrated double spin-chain systems,
such as the one-dimensional J_1 - J_2 model, or the frustrated ladder model.Comment: 11 pages, REVTeX, 8 figures in eps-fil
Antiferromagnetic spin ladders: crossover between spin S = 1/2 and S = 1 chains
We study a model of two weakly coupled isotropic spin-1/2 Heisenberg chains
with an antiferromagnetic coupling along the chains. It is shown that the
system always has a spectral gap. For the case of identical chains the model in
the continuous limit is equivalent to 4 decoupled noncritical Ising models. For
this case we obtain the exact expressions for the asymptotics of spin-spin
correlation functions. When the chains have different exchange integrals the
spectrum at low energies is well described by the O(3) nonlinear sigma model.
We discuss the topological order parameter related to the gap formation and
give a detailed description of the dynamical magnetic susceptibility.Comment: 27 pages, latex, no figure
Critical properties of S=1/2 Heisenberg ladders in magnetic fields
The critical properties of the Heisenberg two-leg ladders are
investigated in a magnetic field. Combining the exact diagonalization method
and the finite-size-scaling analysis based on conformal field theory, we
calculate the critical exponents of spin correlation functions numerically. For
a strong interchain coupling, magnetization dependence of the critical
exponents shows characteristic behavior depending on the sign of the interchain
coupling. We also calculate the critical exponents for the Heisenberg
two-leg ladder with a diagonal interaction, which is thought as a model
Hamiltonian of the organic spin ladder compound
. Numerical results are compared with
experimental results of temperature dependence of the NMR relaxation rate
.Comment: REVTeX, 10 pages, 8 figures, accepted for Phys. Rev.
- …