1,402 research outputs found
Non-Hermitian Luttinger Liquids and Vortex Physics
As a model of two thermally excited flux liquids connected by a weak link, we
study the effect of a single line defect on vortex filaments oriented parallel
to the surface of a thin planar superconductor. When the applied field is
tilted relative to the line defect, the physics is described by a nonhermitian
Luttinger liquid of interacting quantum bosons in one spatial dimension with a
point defect. We analyze this problem using a combination of analytic and
numerical density matrix renormalization group methods, uncovering a delicate
interplay between enhancement of pinning due to Luttinger liquid effects and
depinning due to the tilted magnetic field. Interactions dramatically improve
the ability of a single columnar pin to suppress vortex tilt when the Luttinger
liquid parameter g is less than or equal to one.Comment: 4 pages, 5 eps figures, minor changes made, one reference adde
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
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
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
Power law violation of the area law in quantum spin chains
The sub-volume scaling of the entanglement entropy with the system's size,
, has been a subject of vigorous study in the last decade [1]. The area law
provably holds for gapped one dimensional systems [2] and it was believed to be
violated by at most a factor of in physically reasonable
models such as critical systems.
In this paper, we generalize the spin model of Bravyi et al [3] to all
integer spin- chains, whereby we introduce a class of exactly solvable
models that are physical and exhibit signatures of criticality, yet violate the
area law by a power law. The proposed Hamiltonian is local and translationally
invariant in the bulk. We prove that it is frustration free and has a unique
ground state. Moreover, we prove that the energy gap scales as , where
using the theory of Brownian excursions, we prove . This rules out the
possibility of these models being described by a conformal field theory. We
analytically show that the Schmidt rank grows exponentially with and that
the half-chain entanglement entropy to the leading order scales as
(Eq. 16). Geometrically, the ground state is seen as a uniform superposition of
all colored Motzkin walks. Lastly, we introduce an external field which
allows us to remove the boundary terms yet retain the desired properties of the
model. Our techniques for obtaining the asymptotic form of the entanglement
entropy, the gap upper bound and the self-contained expositions of the
combinatorial techniques, more akin to lattice paths, may be of independent
interest.Comment: v3: 10+33 pages. In the PNAS publication, the abstract was rewritten
and title changed to "Supercritical entanglement in local systems:
Counterexample to the area law for quantum matter". The content is same
otherwise. v2: a section was added with an external field to include a model
with no boundary terms (open and closed chain). Asymptotic technique is
improved. v1:37 pages, 10 figures. Proc. Natl. Acad. Sci. USA, (Nov. 2016
Exact finite-size spectrum for the multi-channel Kondo model and Kac-Moody fusion rules
The finite-size spectrum for the multi-channel Kondo model is derived
analytically from the exact solution, by mapping the nontrivial Z part of
the Kondo scattering into that for the RSOS model coupled with the impurity.
The analysis is performed for the case of , where is the number of
channel and is the impurity spin. The result obtained is in accordance with
the Kac-Moody fusion hypothesis proposed by Affleck and Ludwig.Comment: RevTex, 4 page
Solution of two channel spin-flavor Kondo model
We investigate a model where an impurity couples to both the spin and the
flavor currents of the two channel conduction electrons. This model can be used
as a prototype model of a magnetic impurity tunneling between two sites in a
metal and of some heavy fermion systems where the ground state of the impurity
has a fourfold degeneracy. The system is shown to flow to a doubly degenerate
non fermi-liquid(NFL) fixed point; the thermodynamic quantities show NFL
behaviors, but the transport quantities show fermi liquid (FL) behaviors . A
spin-flavor coupling double tensor term is shown to drive the system to one of
the two singlet FL fixed points. The relation with SU(4) Coqblin-Schrieffer
model is studied. The implications on the possible experiments are given.Comment: 11 pages, REVTEX, no figures. To appear in Phys. Rev. B (Rapid Comm.)
July 1, 199
Phase diagram of an impurity in the spin-1/2 chain: two channel Kondo effect versus Curie law
We consider a magnetic s=1/2 impurity in the antiferromagnetic spin chain as
a function of two coupling parameters: the symmetric coupling of the impurity
to two sites in the chain and the coupling between the two sites .
By using field theory arguments and numerical calculations we can identify all
possible fixed points and classify the renormalization flow between them, which
leads to a non-trivial phase diagram. Depending on the detailed choice of the
two (frustrating) coupling strengths, the stable phases correspond either to a
decoupled spin with Curie law behavior or to a non-Fermi liquid fixed point
with a logarithmically diverging impurity susceptibility as in the two channel
Kondo effect. Our results resolve a controversy about the renormalization flow.Comment: 5 pages in revtex format including 4 embedded figures (using epsf).
The latest version in PDF format is available from
http://fy.chalmers.se/~eggert/papers/phase-diagram.pd
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
Exact Critical Properties of the Multi-Component Interacting Fermion Model with Boundaries
Exact critical properties of the one-dimensional SU() interacting fermion
model with open boundaries are studied by using the Bethe ansatz method. We
derive the surface critical exponents of various correlation functions using
boundary conformal field theory. They are classified into two types, i.e. the
exponents for the chiral SU() Tomonaga-Luttinger liquid and those related to
the orthogonality catastrophe. We discuss a possible application of the results
to the photoemission (absorption) in the edge state of the fractional quantum
Hall effect.Comment: 17 pages, RevTe
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