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. PROGRAM SUMMARY Program title: ALPS MPS Catalogue identifier: AEUL_v1_0 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEUL_v1_0.html Program obtainable from: CPC Program Library, Queen’s University, Belfast, N. Ireland Licensing provisions: Use of ‘mps optim’, ‘mps tevol’, ‘mps meas’ or ‘mps overlap’ requires citation of this paper. Use of any ALPS program requires citation of the ALPS [1] paper. No. of lines in distributed program, including test data, etc.: 373799 No. of bytes in distributed program, including test data, etc.: 2019043 Distribution format: tar.gz Programming language: C++, OpenMP for parallelization. Computer: PC, HPC cluster. Operating system: Any, tested on Linux, Mac OS X and Windows. Has the code been vectorized or parallelized?: Parallelized using OpenMP 1 to 24 processors used. RAM: 100 MB–100 GB. Classification: 7.7. External routines: ALPS [1, 2], BLAS/LAPACK, HDF5. Nature of problem: Solution of quantum many-body systems is generally a hard problem. The many-body Hilbert space grows exponentially with the system size which limits exact diagonalization results to only 20–40 spins, and the fermionic negative sign problem limits the Quantum Monte Carlo methods to a few special cases. Solution method: The matrix product states ansatz provides a controllable truncation of the Hilbert space which makes it currently the method of choice to investigate low-dimensional systems in condensed matter physics. Our implementation allows simulation of arbitrary one-dimensional and two-dimensional models and achieves performance competitive with the best codes in the community. We implement conservation of quantum numbers for generic Abelian symmetries. Running time: 10 s–8h per sweep. References: [1] B. Bauer, et al. (ALPS Collaboration), The ALPS project release 2.0: open source software for strongly correlated systems, J. Stat. Mech. 2011 (05) (2011) P05001. http://dx.doi.org/10.1088/1742-5468/2011/05/P05001. [2] http://alps.comp-phys.org.

Subject headings

NATURVETENSKAP  -- Fysik -- Annan fysik (hsv//swe)

NATURAL SCIENCES  -- Physical Sciences -- Other Physics Topics (hsv//eng)

Keyword

DMRG

Ground state

MPS

Time evolution

Publication and Content Type

ref (subject category)

art (subject category)