2,222 research outputs found
Edge Critical Behaviour of the 2-Dimensional Tri-critical Ising Model
Using previous results from boundary conformal field theory and
integrability, a phase diagram is derived for the 2 dimensional Ising model at
its bulk tri-critical point as a function of boundary magnetic field and
boundary spin-coupling constant. A boundary tri-critical point separates phases
where the spins on the boundary are ordered or disordered. In the latter range
of coupling constant, there is a non-zero critical field where the
magnetization is singular. In the former range, as the temperature is lowered,
the boundary undergoes a first order transition while the bulk simultaneously
undergoes a second order transition.Comment: 6 pages, RevTex, 3 postscript figure
Neel order in doped quasi one-dimensional antiferromagnets
We study the Neel temperature of quasi one-dimensional S=1/2 antiferromagnets
containing non-magnetic impurities. We first consider the temperature
dependence of the staggered susceptibility of finite chains with open boundary
conditions, which shows an interesting difference for even and odd length
chains. We then use a mean field theory treatment to incorporate the three
dimensional inter-chain couplings. The resulting Neel temperature shows a
pronounced drop as a function of doping by up to a factor of 5.Comment: 4 pages in revtex4 format including 2 epsf-embedded figures. The
latest version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/staggered.pd
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
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
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
Crossover in the two-impurity Kondo model induced by direct charge tunneling
Quantum critical behavior in the two-impurity Kondo model requires the
distinct separation of two scales, T_K >> T*, where T_K is the Kondo
temperature and T* is the scale at which the system renormalizes away from the
quantum critical point to a stable Fermi liquid fixed point. We provide a
derivation of T* based on the renormalization group to lowest order. This
result is confirmed by a numerical renormalization group (NRG) analysis which
supplements the analytic derivation with additional quantitative precision. The
form of the low-energy Fermi liquid fixed point is derived and subsequently
confirmed by the NRG. We discuss implications for series double quantum dot
systems.Comment: 10 pages, 6 figures; resubmitted Oct. 31, 2011 to include corrections
discovered after original submissio
The Haldane Energy Gap of A Doped Linear-Chain Heisenberg Antiferromagnet
Using the valence-bond-solid (VBS) approach and the Schwinger boson mean
field approximation, we study the dependence of the Haldane gap of a spin-1
linear chain Heisenberg antiferromagnet on impurity doping with different
spins. The impurity spins affect the singlet pairing order parameter
and the constraint factor . As a result, the Haldane gap is reduced by
a factor , with as the impurity concentration, and
eventually collapses at with as the VBS correlation
length. This theoretical prediction can be verified by neutron scattering
experiments.Comment: REVTEX, 12 pages, no figure
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
Corrections to scaling in entanglement entropy from boundary perturbations
We investigate the corrections to scaling of the Renyi entropies of a region
of size l at the end of a semi-infinite one-dimensional system described by a
conformal field theory when the corrections come from irrelevant boundary
operators. The corrections from irrelevant bulk operators with scaling
dimension x have been studied by Cardy and Calabrese (2010), and they found not
only the expected corrections of the form l^(4-2x) but also unusual corrections
that could not have been anticipated by finite-size scaling arguments alone.
However, for the case of perturbations from irrelevant boundary operators we
find that the only corrections that can occur to leading order are of the form
l^(2-2x_b) for boundary operators with scaling dimension x_b < 3/2, and l^(-1)
when x_b > 3/2. When x_b=3/2 they are of the form l^(-1)log(l). A marginally
irrelevant boundary perturbation will give leading corrections going as
log(l)^(-3). No unusual corrections occur when perturbing with a boundary
operator.Comment: 8 pages. Minor improvements and updated references. Published versio
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
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