94 research outputs found
Integrability-based analysis of the hyperfine-interaction -nduced decoherence in quantum dots
Using the Algebraic Bethe Ansatz in conjunction with a simple Monte Carlo
sampling technique, we study the problem of the decoherence of a central spin
coupled to a nuclear spin bath. We describe in detail the full crossover from
strong to weak external magnetic field field, a limit where a large
non-decaying coherence factor is found. This feature is explained by
Bose-Einstein-condensate-like physics which also allows us to argue that the
corresponding zero frequency peak would not be broadened by statistical or
ensemble averaging.Comment: 5 pages, 4 figures, published versio
Spin decoherence due to a randomly fluctuating spin bath
We study the decoherence of a spin in a quantum dot due to its hyperfine
coupling to a randomly fluctuating bath of nuclear spins. The system is
modelled by the central spin model with the spin bath initially being at
infinite temperature. We calculate the spectrum and time evolution of the
coherence factor using a Monte Carlo sampling of the exact eigenstates obtained
via the algebraic Bethe ansatz. The exactness of the obtained eigenstates
allows us to study the non-perturbative regime of weak magnetic fields in a
full quantum mechanical treatment. In particular, we find a large non-decaying
fraction in the zero-field limit. The crossover from strong to weak fields is
similar to the decoherence starting from a pure initial bath state treated
previously. We compare our results to a simple semiclassical picture [Merkulov
et al., Phys. Rev. B 65, 205309 (2002)] and find surprisingly good agreement.
Finally, we discuss the effect of weakly coupled spins and show that they will
eventually lead to complete decoherence
Integrability of an extended d+id-wave pairing Hamiltonian
We introduce an integrable Hamiltonian which is an extended d+id-wave pairing
model. The integrability is deduced from a duality relation with the
Richardson-Gaudin (s-wave) pairing model, and associated to this there exists
an exact Bethe ansatz solution. We study this system using the continuum limit
approach and solve the corresponding singular integral equation obtained from
the Bethe ansatz solution. We also conduct a mean-field analysis and show that
results from these two approaches coincide for the ground state in the
continuum limit. We identify instances of the integrable system where the
excitation spectrum is gapless, and discuss connections to non-integrable
models with d+id-wave pairing interactions through the mean-field analysis.Comment: 7 pages, 1 figur
Determinant representation of the domain-wall boundary condition partition function of a Richardson-Gaudin model containing one arbitrary spin
In this work we present a determinant expression for the domain-wall boundary
condition partition function of rational (XXX) Richardson-Gaudin models which,
in addition to spins , contains one arbitrarily large spin
.
The proposed determinant representation is written in terms of a set of
variables which, from previous work, are known to define eigenstates of the
quantum integrable models belonging to this class as solutions to quadratic
Bethe equations. Such a determinant can be useful numerically since systems of
quadratic equations are much simpler to solve than the usual highly non-linear
Bethe equations. It can therefore offer significant gains in stability and
computation speed.Comment: 17 pages, 0 figure
Non-equilibrum dynamics in the strongly excited inhomogeneous Dicke model
Using the exact eigenstates of the inhomogeneous Dicke model obtained by
numerically solving the Bethe equations, we study the decay of bosonic
excitations due to the coupling of the mode to an ensemble of two-level (spin
1/2) systems. We compare the quantum time-evolution of the bosonic mode
population with the mean field description which, for a few bosons agree up to
a relatively long Ehrenfest time. We demonstrate that additional excitations
lead to a dramatic shortening of the period of validity of the mean field
analysis. However, even in the limit where the number of bosons equal the
number of spins, the initial instability remains adequately described by the
mean-field approach leading to a finite, albeit short, Ehrenfest time. Through
finite size analysis, we also present indications that the mean field approach
could still provide an adequate description for thermodynamically large systems
even at long times. However, for mesoscopic systems one cannot expect it to
capture the behavior beyond the initial decay stage in the limit of an
extremely large number of excitations.Comment: 9 pages, 7 figures, Phys. Rev. B in pres
Quadratic operator relations and Bethe equations for spin-1/2 Richardson-Gaudin models
In this work we demonstrate how one can, in a generic approach, derive a set
of simple quadratic Bethe equations for integrable Richardson-Gaudin (RG)
models built out of spins-1/2. These equations depend only on the
eigenvalues of the various conserved charges so that any solution of these
equations defines, indirectly through the corresponding set of eigenvalues, one
particular eigenstate.
The proposed construction covers the full class of integrable RG models of
the XYZ (including the subclasses of XXZ and XXX models) type realised in terms
of spins-1/2, coupled with one another through ,
, terms, including, as well,
magnetic field-like terms linear in the Pauli matrices.
The approach exclusively requires integrability, defined here only by the
requirement that conserved charges (with ) such that
exist . The result is therefore
valid, and equally simple, for models with or without symmetry, with or
without a properly defined pseudo-vacuum as well as for models with non-skew
symmetric couplings.Comment: 13 page
Exact mesoscopic correlation functions of the pairing model
We study the static correlation functions of the Richardson pairing model
(also known as the reduced or discrete-state BCS model) in the canonical
ensemble. Making use of the Algebraic Bethe Ansatz formalism, we obtain exact
expressions which are easily evaluated numerically for any value of the pairing
strength up to large numbers of particles. We provide explicit results at
half-filling and extensively discuss their finite-size scaling behavior.Comment: 15 Pages, 12 figure
Chiral SU(2)_k currents as local operators in vertex models and spin chains
The six-vertex model and its spin- descendants obtained from the fusion
procedure are well-known lattice discretizations of the SU WZW models,
with . It is shown that, in these models, it is possible to exhibit a
local observable on the lattice that behaves as the chiral current in
the continuum limit. The observable is built out of generators of the su
Lie algebra acting on a small (finite) number of lattice sites. The
construction works also for the multi-critical quantum spin chains related to
the vertex models, and is verified numerically for and using
Bethe Ansatz and form factors techniques.Comment: 31 pages, 7 figures; published versio
Replica study of pinned bubble crystals
In higher Landau levels (), the ground state of the two-dimensional
electron gas in a strong perpendicular magnetic field evolves from a Wigner
crystal for small filling of the partially filled Landau level, into a
succession of bubble states with increasing number of guiding centers per
bubble as increases, to a modulated stripe state near . In
this work, we compute the frequency-dependent longitudinal conductivity of the Wigner and bubble crystal states in the presence
of disorder. We apply an elastic theory to the crystal states which is
characterized by a shear and a bulk modulus. We obtain both moduli from the
microscopic time-dependent Hartree-Fock approximation. We then use the replica
and Gaussian variational methods to handle the effects of disorder. Within the
semiclassical approximation we get the dynamical conductivity as well as the
pinning frequency as functions of the Landau level filling factor and compare
our results with recent microwave experiments.Comment: 19 pages and 6 eps figure
- …