232 research outputs found
Corner Transfer Matrix Renormalization Group Method Applied to the Ising Model on the Hyperbolic Plane
Critical behavior of the Ising model is investigated at the center of large
scale finite size systems, where the lattice is represented as the tiling of
pentagons. The system is on the hyperbolic plane, and the recursive structure
of the lattice makes it possible to apply the corner transfer matrix
renormalization group method. From the calculated nearest neighbor spin
correlation function and the spontaneous magnetization, it is concluded that
the phase transition of this model is mean-field like. One parameter
deformation of the corner Hamiltonian on the hyperbolic plane is discussed.Comment: 4 pages, 5 figure
On calculation of vector spin chirality for zigzag spin chains
We calculate the vector spin chirality for zigzag spin chains having
U(1) symmetry, using the density matrix renormalization group combined with
unitary transformation. We then demonstrate the occurrence of the chiral order
for the zigzag XY chain and discuss the associated phase transition. The
results are consistent with the analysis based on the bosonization and the long
distance behaviour of the chirality correlation function. For the
zigzag Heisenberg chain in a magnetic field, we also verify the chiral order
that is predicted by the effective field theory and the chirality correlation
function, and then determine its magnetic phase diagram.Comment: 7 pages, 9 figures, accepted for publication in J. Phys. Soc. Jp
Wilson-like real-space renormalization group and low-energy effective spectrum of the XXZ chain in the critical regime
We present a novel real-space renormalization group(RG) for the
one-dimensional XXZ model in the critical regime, reconsidering the role of the
cut-off parameter in Wilson's RG for the Kondo impurity problem. We then
demonstrate the RG calculation for the XXZ chain with the free boundary.
Comparing the hierarchical structure of the obtained low-energy spectrum with
the Bethe ansatz result, we find that the proper scaling dimension is
reproduced as a fixed point of the RG transformation.Comment: 4 pages, 6 figures, typos corrected, final versio
Fractional S^z excitation and its bound state around the 1/3 plateau of the S=1/2 Ising-like zigzag XXZ chain
We present the microscopic view for the excitations around the 1/3 plateau
state of the Ising-like zigzag XXZ chain. We analyze the low-energy excitations
around the plateau with the degenerating perturbation theory from the Ising
limit, combined with the Bethe-form wave function. We then find that the
domain-wall particles carrying and its bound state of describe well the low-energy excitations around the 1/3 plateau state. The
formation of the bound state of the domain-walls clearly provides the
microscopic mechanism of the cusp singularities and the even-odd behavior in
the magnetization curve.Comment: 13 pages, 15 figure
Hyperbolic Deformation Applied to S = 1 Spin Chains - Scaling Relation in Excitation Energy -
We investigate excitation energies of hyperbolically deformed S = 1 spin
chains, which are specified by the local energy scale f_j^{~} = \cosh j
\lambda, where j is the lattice index and \lambda is the deformation parameter.
The elementary excitation is well described by a quasiparticle hopping model,
which is also expressed in the form of hyperbolic deformation. It is possible
to estimate the excitation gap \Delta in the uniform limit \lambda \rightarrow
0, by means of a finite size scaling with respect to the system size N and the
deformation parameter \lambda.Comment: 5 pages, 4 figure
Bond Operator Mean Field Approach to the Magnetization Plateaux in Quantum Antiferromagnets -- Application to the S=1/2 Coupled Dimerized Zigzag Heisenberg Chains
The magnetization plateaux in two dimensionally coupled S=1/2 dimerized
zigzag Heisenberg chains are investigated by means of the bond operator mean
field approximation. In the absence of the interchain coupling, this model is
known to have a plateau at half of the saturation magnetization accompanied by
the spontanuous translational symmetry breakdown. The parameter regime in which
the plateau appears is reproduced well within the present approximation. In the
presence of the interchain coupling, this plateau is shown to be suppressed.
This result is also supported by the numerical diagonalization calculation.Comment: 7 pages, 8 figure
Magnetic phase diagram of the S=1/2 antiferromagnetic zigzag spin chain in the strongly frustrated region: cusp and plateau
We determine the magnetic phase diagram of the antiferromagnetic(AF) zigzag
spin chain in the strongly frustrated region, using the density matrix
renormalization group method. We find the magnetization plateau at 1/3 of the
full moment accompanying the spontaneous symmetry breaking of the translation,
the cusp singularities above and/or below the plateau, and the even-odd effect
in the magnetization curve. We also discuss the formation mechanisms of the
plateau and cusps briefly.Comment: 4 pages, 8 figures, revised version, to appear in J.Phys.Soc.Jp
Hyperbolic Deformation on Quantum Lattice Hamiltonians
A group of non-uniform quantum lattice Hamiltonians in one dimension is
introduced, which is related to the hyperbolic -dimensional space. The
Hamiltonians contain only nearest neighbor interactions whose strength is
proportional to , where is the lattice index and where
is a deformation parameter. In the limit the
Hamiltonians become uniform. Spacial translation of the deformed Hamiltonians
is induced by the corner Hamiltonians. As a simple example, we investigate the
ground state of the deformed Heisenberg spin chain by use of the
density matrix renormalization group (DMRG) method. It is shown that the ground
state is dimerized when is finite. Spin correlation function show
exponential decay, and the boundary effect decreases with increasing .Comment: 5 pages, 4 figure
Antiferromagnetic Zigzag Spin Chain in Magnetic Fields at Finite Temperatures
We study thermodynamic behaviors of the antiferromagnetic zigzag spin chain
in magnetic fields, using the density-matrix renormalization group method for
the quantum transfer matrix. We focus on the thermodynamics of the system near
the critical fields in the ground-state magnetization process(- curve):
the saturation field, the lower critical field associated with excitation gap,
and the field at the middle-field cusp singularity. We calculate magnetization,
susceptibility and specific heat of the zigzag chain in magnetic fields at
finite temperatures, and then discuss how the calculated quantities reflect the
low-lying excitations of the system related with the critical behaviors in the
- curve.Comment: accepted for publication in Physical Review
Comparison between disordered quantum spin 1/2 chains
We study the magnetic properties of two types of one dimensional XX spin 1/2
chains. The first type has only nearest neighbor interactions which can be
either antiferromagnetic or ferromagnetic and the second type which has both
nearest neighbor and next nearest neighbor interactions, but only
antiferromagnetic in character. We study these systems in the presence of low
transverse magnetic fields both analytically and numerically. Comparison of
results show a close relation between the two systems, which is in agreement
with results previously found in Heisenberg chains by means of a numerical real
space renormalization group procedure.Comment: 7 page
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