2,043 research outputs found
Krylov-space approach to the equilibrium and the nonequilibrium single-particle Green's function
The zero-temperature single-particle Green's function of correlated fermion
models with moderately large Hilbert-space dimensions can be calculated by
means of Krylov-space techniques. The conventional Lanczos approach consists of
finding the ground state in a first step, followed by an approximation for the
resolvent of the Hamiltonian in a second step. We analyze the character of this
approximation and discuss a numerically exact variant of the Lanczos method
which is formulated in the time domain. This method is extended to get the
nonequilibrium single-particle Green's function defined on the
Keldysh-Matsubara contour in the complex time plane. The proposed method will
be important as an exact-diagonalization solver in the context of
self-consistent or variational cluster-embedding schemes. For the recently
developed nonequilibrium cluster-perturbation theory, we discuss the efficient
implementation and demonstrate the feasibility of the Krylov-based solver. The
dissipation of a strong local magnetic excitation into a non-interacting bath
is considered as an example for applications.Comment: 20 pages, 5 figures, v2 with minor corrections, JPCM in pres
Quantum Simulation of Interacting Fermion Lattice Models in Trapped Ions
We propose a method of simulating efficiently many-body interacting fermion
lattice models in trapped ions, including highly nonlinear interactions in
arbitrary spatial dimensions and for arbitrarily distant couplings. We map
products of fermionic operators onto nonlocal spin operators and decompose the
resulting dynamics in efficient steps with Trotter methods, yielding an overall
protocol that employs only polynomial resources. The proposed scheme can be
relevant in a variety of fields as condensed-matter or high-energy physics,
where quantum simulations may solve problems intractable for classical
computers.Comment: 5 pages, 2 figures + Supplementary Materia
A continuous-time solver for quantum impurity models
We present a new continuous time solver for quantum impurity models such as
those relevant to dynamical mean field theory. It is based on a stochastic
sampling of a perturbation expansion in the impurity-bath hybridization
parameter. Comparisons to quantum Monte Carlo and exact diagonalization
calculations confirm the accuracy of the new approach, which allows very
efficient simulations even at low temperatures and for strong interactions. As
examples of the power of the method we present results for the temperature
dependence of the kinetic energy and the free energy, enabling an accurate
location of the temperature-driven metal-insulator transition.Comment: Published versio
Exact numerical methods for a many-body Wannier Stark system
We present exact methods for the numerical integration of the Wannier-Stark
system in a many-body scenario including two Bloch bands. Our ab initio
approaches allow for the treatment of a few-body problem with bosonic
statistics and strong interparticle interaction. The numerical implementation
is based on the Lanczos algorithm for the diagonalization of large, but sparse
symmetric Floquet matrices. We analyze the scheme efficiency in terms of the
computational time, which is shown to scale polynomially with the size of the
system. The numerically computed eigensystem is applied to the analysis of the
Floquet Hamiltonian describing our problem. We show that this allows, for
instance, for the efficient detection and characterization of avoided crossings
and their statistical analysis. We finally compare the efficiency of our
Lanczos diagonalization for computing the temporal evolution of our many-body
system with an explicit fourth order Runge-Kutta integration. Both
implementations heavily exploit efficient matrix-vector multiplication schemes.
Our results should permit an extrapolation of the applicability of exact
methods to increasing sizes of generic many-body quantum problems with bosonic
statistics
Adaptively truncated Hilbert space based impurity solver for dynamical mean-field theory
We present an impurity solver based on adaptively truncated Hilbert spaces.
The solver is particularly suitable for dynamical mean-field theory in
circumstances where quantum Monte Carlo approaches are ineffective. It exploits
the sparsity structure of quantum impurity models, in which the interactions
couple only a small subset of the degrees of freedom. We further introduce an
adaptive truncation of the particle or hole excited spaces, which enables
computations of Green functions with an accuracy needed to avoid unphysical
(sign change of imaginary part) self-energies. The method is benchmarked on the
one-dimensional Hubbard model.Comment: 10 pages, 7 figure
- …