11,091 research outputs found
Matrix Product State applications for the ALPS project
The density-matrix renormalization group method has become a standard
computational approach to the low-energy physics as well as dynamics of
low-dimensional quantum systems. In this paper, we present a new set of
applications, available as part of the ALPS package, that provide an efficient
and flexible implementation of these methods based on a matrix-product state
(MPS) representation. Our applications implement, within the same framework,
algorithms to variationally find the ground state and low-lying excited states
as well as simulate the time evolution of arbitrary one-dimensional and
two-dimensional models. Implementing the conservation of quantum numbers for
generic Abelian symmetries, we achieve performance competitive with the best
codes in the community. Example results are provided for (i) a model of
itinerant fermions in one dimension and (ii) a model of quantum magnetism.Comment: 11+5 pages, 8 figures, 2 example
TRIQS: A Toolbox for Research on Interacting Quantum Systems
We present the TRIQS library, a Toolbox for Research on Interacting Quantum
Systems. It is an open-source, computational physics library providing a
framework for the quick development of applications in the field of many-body
quantum physics, and in particular, strongly-correlated electronic systems. It
supplies components to develop codes in a modern, concise and efficient way:
e.g. Green's function containers, a generic Monte Carlo class, and simple
interfaces to HDF5. TRIQS is a C++/Python library that can be used from either
language. It is distributed under the GNU General Public License (GPLv3).
State-of-the-art applications based on the library, such as modern quantum
many-body solvers and interfaces between density-functional-theory codes and
dynamical mean-field theory (DMFT) codes are distributed along with it.Comment: 27 page
Matrix Recipes for Hard Thresholding Methods
In this paper, we present and analyze a new set of low-rank recovery
algorithms for linear inverse problems within the class of hard thresholding
methods. We provide strategies on how to set up these algorithms via basic
ingredients for different configurations to achieve complexity vs. accuracy
tradeoffs. Moreover, we study acceleration schemes via memory-based techniques
and randomized, -approximate matrix projections to decrease the
computational costs in the recovery process. For most of the configurations, we
present theoretical analysis that guarantees convergence under mild problem
conditions. Simulation results demonstrate notable performance improvements as
compared to state-of-the-art algorithms both in terms of reconstruction
accuracy and computational complexity.Comment: 26 page
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