Matrix Product State applications for the ALPS project

TL;DR

This paper introduces new applications within the ALPS software package that utilize matrix product states to efficiently simulate low-dimensional quantum systems, including ground states, excitations, and time evolution.

Contribution

It presents a flexible, efficient implementation of MPS-based algorithms for various quantum models, incorporating symmetry conservation for improved performance.

Findings

Achieved performance comparable to leading codes in the community.

Successfully simulated itinerant fermions in 1D.

Demonstrated quantum magnetism model results.

Abstract

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.