273 research outputs found
Spectral properties of the 2D Holstein t-J model
Employing the Lanczos algorithm in combination with a kernel polynomial
moment expansion (KPM) and the maximum entropy method (MEM), we show a way of
calculating charge and spin excitations in the Holstein t-J model, including
the full quantum nature of phonons. To analyze polaron band formation we
evaluate the hole spectral function for a wide range of electron-phonon
coupling strengths. For the first time, we present results for the optical
conductivity of the 2D Holstein t-J model.Comment: 2 pages, Latex. Submitted to Physica C, Proc. Int. Conf. on M2HTSC
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Hard core perturbation theory
A novel perturbative expansion of the dynamic susceptibility about the ground state wave function is proposed. The method uses Liouville perturbation expansions, the Hubbard-Stratonovich transformation of the Hamiltonian with fictitious bosons, projection super-operators and super-duper-operators. The method is especially applicable to the dynamical susceptibility of strongly-interacting systems, where ground state correlation functions and density matrices are available from calculations or experiments. To illustrate the method, the final state corrections to the impulse approximation are derived for high momentum transfer neutron scattering. 18 refs., 3 figs
Optimal query complexity for estimating the trace of a matrix
Given an implicit matrix with oracle access for any
, we study the query complexity of randomized algorithms for
estimating the trace of the matrix. This problem has many applications in
quantum physics, machine learning, and pattern matching. Two metrics are
commonly used for evaluating the estimators: i) variance; ii) a high
probability multiplicative-approximation guarantee. Almost all the known
estimators are of the form for being i.i.d. for some special distribution.
Our main results are summarized as follows. We give an exact characterization
of the minimum variance unbiased estimator in the broad class of linear
nonadaptive estimators (which subsumes all the existing known estimators). We
also consider the query complexity lower bounds for any (possibly nonlinear and
adaptive) estimators: (1) We show that any estimator requires
queries to have a guarantee of variance at most
. (2) We show that any estimator requires
queries to achieve a
-multiplicative approximation guarantee with probability at
least . Both above lower bounds are asymptotically tight.
As a corollary, we also resolve a conjecture in the seminal work of Avron and
Toledo (Journal of the ACM 2011) regarding the sample complexity of the
Gaussian Estimator.Comment: full version of the paper in ICALP 201
Final state effects on superfluid He in the deep inelastic regime
A study of Final State Effects (FSE) on the dynamic structure function of
superfluid He in the Gersch--Rodriguez formalism is presented. The main
ingredients needed in the calculation are the momentum distribution and the
semidiagonal two--body density matrix. The influence of these ground state
quantities on the FSE is analyzed. A variational form of is used, even
though simpler forms turn out to give accurate results if properly chosen.
Comparison to the experimental response at high momentum transfer is performed.
The predicted response is quite sensitive to slight variations on the value of
the condensate fraction, the best agreement with experiment being obtained with
. Sum rules of the FSE broadening function are also derived and
commented. Finally, it is shown that Gersch--Rodriguez theory produces results
as accurate as those coming from other more recent FSE theories.Comment: 20 pages, RevTex 3.0, 11 figures available upon request, to be appear
in Phys. Rev.
Considerations on the quantum double-exchange Hamiltonian
Schwinger bosons allow for an advantageous representation of quantum
double-exchange. We review this subject, comment on previous results, and
address the transition to the semiclassical limit. We derive an effective
fermionic Hamiltonian for the spin-dependent hopping of holes interacting with
a background of local spins, which is used in a related publication within a
two-phase description of colossal magnetoresistant manganites.Comment: 7 pages, 3 figure
Beyond the binary collision approximation for the large- response of liquid He
We discuss corrections to the linear response of a many-body system beyond
the binary collision approximation. We first derive for smooth pair
interactions an exact expression of the response , considerably
simplifying existing forms and present also the generalization for interactions
with a strong, short-range repulsion. We then apply the latter to the case of
liquid He. We display the numerical influence of the correction
around the quasi-elastic peak and in the low-intensity wings of the response,
far from that peak. Finally we resolve an apparent contradiction in previous
discussions around the fourth order cumulant expansion coefficient. Our results
prove that the large- response of liquid He can be accurately understood
on the basis of a dynamical theory.Comment: 19 p. Figs. available on reques
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Spectral properties of the 2D Holstein t-J model
Employing the Lanczos algorithm in combination with a kernel polynomial moment expansion (KPM) and the maximum entropy method (MEM), we show a way of calculating charge and spin excitations in the Holstein t-J model, including the full quantum nature of phonons. To analyze polaron band formation we evaluate the hole spectral function for a wide range of electron-phonon coupling strengths. For the first time, we present results for the optical conductivity of the 2D Holstein t-J model
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The Kernel Polynomial Method for non-orthogonal electronic structure calculations
The Kernel Polynomial Method (KPM) has been successfully applied to tight-binding electronic structure calculations as an O(N) method. Here we extend this method to nonorthogonal basis sets with a sparse overlap matrix S and a sparse Hamiltonian H. Since the KPM method utilizes matrix vector multiplications it is necessary to apply S{sup -1} H onto a vector. The multiplication of S{sup -1} is performed using a preconditioned conjugate gradient method and does not involve the explicit inversion of S. Hence the method scales the same way as the original KPM method, i.e. O(N), although there is an overhead due to the additional conjugate gradient part. We show an application of this method to defects in a titanate/platinum interface and to a large scale electronic structure calculation of amorphous diamond
Magnon-magnon interactions in the Spin-Peierls compound CuGeO_3
In a magnetic substance the gap in the Raman spectrum, Delta_R, is
approximatively twice the value of the neutron scattering gap, Delta_S, if the
the magnetic excitations (magnons) are only weakly interacting.
But for CuGeO_3 the experimentally observed ratio Delta_R/Delta_S is
approximatively 1.49-1.78, indicating attractive magnon-magnon interactions in
the quasi-1D Spin-Peierls compound CuGe_3.
We present numerical estimates for Delta_R/Delta_S from exact diagonalization
studies for finite chains and find agreement with experiment for intermediate
values of the frustration parameter alpha.
An analysis of the numerical Raman intensity leads us to postulate a
continuum of two-magnon bound states in the Spin-Peierls phase. We discuss in
detail the numerical method used, the dependence of the results on the model
parameters and a novel matrix-element effect due to the dimerization of the
Raman-operator in the Spin-Peierls phase.Comment: submitted to PRB, Phys. Rev. B, in pres
Condensate fraction in liquid 4He at zero temperature
We present results of the one-body density matrix (OBDM) and the condensate
fraction n_0 of liquid 4He calculated at zero temperature by means of the Path
Integral Ground State Monte Carlo method. This technique allows to generate a
highly accurate approximation for the ground state wave function Psi_0 in a
totally model-independent way, that depends only on the Hamiltonian of the
system and on the symmetry properties of Psi_0. With this unbiased estimation
of the OBDM, we obtain precise results for the condensate fraction n_0 and the
kinetic energy K of the system. The dependence of n_0 with the pressure shows
an excellent agreement of our results with recent experimental measurements.
Above the melting pressure, overpressurized liquid 4He shows a small condensate
fraction that has dropped to 0.8% at the highest pressure of p = 87 bar.Comment: 12 pages. 4 figures. Accepted for publication on "Journal of Low
Temperature Physics
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