2,749 research outputs found
Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain
Corrections to the asymptotic correlation function in a Heisenberg spin-1/2
antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a
function of the distance r or the chain size L. This leads to significant
differences with numerical results. We calculate the sub-leading logarithmic
corrections to the finite-size correlation function, using renormalization
group improved perturbation theory, and compare the result with numerical data.Comment: 7 pages Revtex, 3 figure
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
Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain
The exact amplitude for the asymptotic correlation function in the S=1/2
Heisenberg antiferromagnetic chain is determined: goes to (-1)^r
delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation
functions for small xxz anisotropy and the form of finite-size corrections to
the correlation function are also analysed.Comment: 8 pages, 3 figures, added reference and discussio
Impurities in S=1/2 Heisenberg Antiferromagnetic Chains: Consequences for Neutron Scattering and Knight Shift
Non-magnetic impurities in an S=1/2 Heisenberg antiferromagnetic chain are
studied using boundary conformal field theory techniques and finite-temperature
quantum Monte Carlo simulations. We calculate the static structure function,
S_imp(k), measured in neutron scattering and the local susceptibility, chi_i
measured in Knight shift experiments. S_imp(k) becomes quite large near the
antiferromagnetic wave-vector, and exhibits much stronger temperature
dependence than the bulk structure function. \chi_i has a large component which
alternates and increases as a function of distance from the impurity.Comment: 8 pages (revtex) + one postscript file with 6 figures. A complete
postscript file with all figures + text (10pages) is available from
http://fy.chalmers.se/~eggert/struct.ps or by request from
[email protected] Submitted to Phys. Rev. Let
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
Abelian bosonization approach to quantum impurity problems
Using Abelian Bosonization, we develop a simple and powerful method to
calculate the correlation functions of the two channel Kondo model and its
variants. The method can also be used to identify all the possible boundary
fixed points and their maximum symmetry, to calculate straightforwardly the
finite size spectra, to demonstrate the physical picture at the boundary
explicitly. Comparisons with Non-Abelian Bosonization method are made. Some
fixed points corresponding to 4 pieces of bulk fermions coupled to s=1/2
impurity are listed.Comment: 12 pages, REVTEX, 1 Table, no figures. To appear in Phys. Rev. Letts.
July 21, 199
Non-Fermi liquid behavior in Kondo models
Despite the fact that the low energy behavior of the basic Kondo model cannot
be studied perturbatively it was eventually shown by Wilson, Anderson, Nozieres
and others to have a simple "local Fermi liquid theory" description. That is,
electronic degrees of freedom become effectively non-interacting in the zero
energy limit. However, generalized versions of the Kondo model involving more
than one channel or impurity may exhibit low energy behavior of a less trivial
sort which can, nonetheless, be solved exactly using either Bethe ansatz or
conformal field theory and bosonization techniques. Now the low energy limit
exhibits interacting many body behavior. For example, processes in which a
single electron scatters off the impurity into a multi electron-hole state have
a non-vanishing (and sometimes large) amplitude at zero energy. This
corresponds to a rare solveable example of non-Fermi liquid behavior. Essential
features of these phenomena are reviewed.Comment: A brief review submitted to the special issue of J. Phys. Soc. of
Japan, "Kondo effect -- 40 years after the discovery
Logarithmic corrections to finite size spectrum of SU(N) symmetric quantum chains
We consider SU(N) symmetric one dimensional quantum chains at finite
temperature. For such systems the correlation lengths, ground state energy, and
excited state energies are investigated in the framework of conformal field
theory. The possibility of different types of excited states are discussed.
Logarithmic corrections to the ground state energy and different types of
excited states in the presence of a marginal opeartor, are calculated. Known
results for SU(2) and SU(4) symmetric systems follow from our general formula.Comment: 5 pages, 1 figure; Typos corrected and minor changes made for clarit
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
- …