2,275 research outputs found
On a Renormalization Group Approach to Dimensional Crossover
A recently proposed renormalization group approach to dimensional crossover
in quasi-one-dimensional quantum antiferromagnets is improved and then shown to
give identical results, in some cases, to those obtained earlier.Comment: 8 pages, Rev Tex, no figure
Critical phenomena and quantum phase transition in long range Heisenberg antiferromagnetic chains
Antiferromagnetic Hamiltonians with short-range, non-frustrating interactions
are well-known to exhibit long range magnetic order in dimensions,
but exhibit only quasi long range order, with power law decay of correlations,
in d=1 (for half-integer spin). On the other hand, non-frustrating long range
interactions can induce long range order in d=1. We study Hamiltonians in which
the long range interactions have an adjustable amplitude lambda, as well as an
adjustable power-law , using a combination of quantum Monte Carlo
and analytic methods: spin-wave, large-N non-linear sigma model, and
renormalization group methods. We map out the phase diagram in the lambda-alpha
plane and study the nature of the critical line separating the phases with long
range and quasi long range order. We find that this corresponds to a novel line
of critical points with continuously varying critical exponents and a dynamical
exponent, z<1.Comment: 27 pages, 12 figures. RG flow added. Final version to appear in JSTA
S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment
The structure function, S(k), for the s=1, Haldane gap antiferromagnetic
chain, is measured accurately using the recent density matrix renormalization
group method, with chain-length 100. Excellent agreement with the nonlinear
model prediction is obtained, both at where a single
magnon process dominates and at where a two magnon process
dominates. We repeat our calculation with crystal field anisotropy chosen to
model NENP, obtaining good agreement with both field theory predictions and
recent experiments. Correlation lengths, gaps and velocities are determined for
both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02
Response of finite spin-S Heisenberg chains to local perturbations
We consider the properties of finite isotropic antiferromagnetic Heisenberg
chains with S=1/2, 1, 3/2 spins when a weak magnetic field is applied on a few
sites, using White's density matrix renormalization group (DMRG) method. For
the S=1 chain there exists only one length scale in the system which determines
the behavior of the one- and two-point correlation functions both around the
local perturbation and near the free boundary. For the critical,
half-odd-integer spin cases the exponent of the spin-spin correlation function
was found to be , and the exponent of the decay of the site
magnetization around the perturbed site is . Close to a free
boundary, however, the behavior is completely different for S=1/2 and .Comment: 13 pages, 7 figure
Phase diagram of a 1 dimensional spin-orbital model
We study a 1 dimensional spin-orbital model using both analytical and
numerical methods. Renormalization group calculations are performed in the
vicinity of a special integrable point in the phase diagram with SU(4)
symmetry. These indicate the existence of a gapless phase in an extended region
of the phase diagram, missed in previous studies. This phase is SU(4) invariant
at low energies apart from the presence of different velocities for spin and
orbital degrees of freedom. The phase transition into a gapped dimerized phase
is in a generalized Kosterlitz-Thouless universality class. The phase diagram
of this model is sketched using the density matrix renormalization group
technique.Comment: 11 pages, 5 figures, new references adde
Impurities in Heisenberg Antiferromagnets
The Heisenberg Antiferromagnet is studied in the presence of two kinds
of local impurities. First, a perturbed antiferromagnetic bond with
at the center of an even-length open chain is considered. Using the density
matrix renormalization group method we find that, for sufficiently strong or
weak , a bound state is localized at the impurity site, giving rise to an
energy level in the Haldane gap. The energy of the bound state is in agreement
with perturbative results, based on chain-end excitations, both in the
weak and strong coupling limit. In a region around the uniform limit, ,
no states are found with energy below the Haldane gap. Secondly, a
impurity at the center of an otherwise even-length open chain is considered.
The coupling to the impurity is varied. Bound states in the Haldane gap
are found {\it only} for sufficiently weak (antiferromagnetic) coupling. For a
impurity coupled with a strong (antiferromagnetic) bond, {\it no}
states are found in the Haldane. Our results are in good qualitative agreement
with recent experiments on doped NENP and YBaNiO.Comment: 29 pages, RevTeX 3.0, 12 uuencoded postscript figures include
Numerical Study of the Antiferrromagnetic Spin Chain with Bond Alternation
We study the quantum spin chain with bond alternation {\cal H}=\sum _i
(1-(-1)^i\delta)\vect{S}_i\cdot \vect{S}_{i+1} by the density matrix
renormalization group method recently proposed by Steven R. White
(\PRL{69}{3844}{1993}). We find a massless point at .
We also find the edge states in the region under the open
boundary condition, which disappear in the region . At the
massless point, the spin wave velocity is and the central
charge is . Our results indicate that a continuous phase
transition occurs at the massless point accompanying
breaking of the hidden symmetry.Comment: 9 pages and 1 PostScript figure, Revtex 3.0 (Minor corrections in
TEX-file format to remove possible compilatory troubles.
Optical conductivity of unconventional charge density wave systems: Role of vertex corrections
The optical conductivity of a d-CDW conductor is calculated for electrons on
a square lattice and a nearest-neighbor charge-charge interaction using the
lowest-order conserving approximation. The spectral properties of the
Drude-like peak at low frequencies and the broad hump due to transitions across
the gap at large frequencies are discussed, also as a function of temperature
and of the second-nearest neighbor hopping term t'. We find that vertex
corrections enhance the d.c. conductivity, make the Drude peak narrower and
provide a smooth transition from a renormalized regime at low to the bare
theory at high frequencies. It is also shown that vertex corrections enhance
the temperature dependence of the restricted optical sum leading to a
non-negligible violation of the sum rule in the d-CDW state.Comment: 10 pages, 6 figure
Correlation amplitude for S=1/2 XXZ spin chain in the critical region
The density-matrix renormalization-group technique is used to calculate the
spin correlation functions and of the one-dimensional
S=1/2 XXZ model in the gapless regime. The numerical results for open chains of
200 spins are analyzed by comparing them with correlation functions calculated
from a low-energy field theory. This gives precise estimates of the amplitudes
of the correlation functions in the thermodynamic limit. The exact amplitude
recently conjectured by Lukyanov and Zamolodchikov and the logarithmic
correction in the Heisenberg model are confirmed numerically.Comment: 4 pages, 3 figures, final versio
Critical Nature of Non-Fermi Liquid in Spin 3/2 Multipolar Kondo Model
A multipolar Kondo model of an impurity spin S_I=3/2 interacting with
conduction electrons with spin s_c=3/2 is investigated using boundary conformal
field theory. A two-channel Kondo (2CK) -like non-Fermi liquid (NFL) under the
particle-hole symmetry is derived explicitly using a ``superspin absorption''
in the sector of a hidden symmetry, SO(5). We discuss the difference between
the usual spin-1/2 2CK NFL fixed point and the present one. In particular, we
find that, unlike the usual 2CK model, the low temperature impurity specific
heat is proportional to temperature.Comment: 4 pages, 2 figure
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