by Giacomo Giudice
This has been tested using MATLAB R2016a down to R2014a. Given Mathwork's history of releasing non-backwards-compatible updates, things will probably break in future versions.
A (very) small library for to simulate many-body quantum systems with Matrix Product States (MPS). It is designed to be scalable and performant at the same time staying flexible enough to be hackable. It is mostly focused on time evolution of finite MPS, both through Time-Evolving Block Decimation (TEBD) using the Trotter-Suzuki decomposition, as well as the Time-Dependent Variational Principle (TDVP). It also features single-site Iterative Variational Optimization to find ground states of Hamiltonian systems.
- Scalable All routines are written with performance in mind, all underlying contractions are optimal for large bond dimension D. The complexity should never be more than O(D3).
- Efficient The underlying and most time-consuming operations, such as SVD decomposition and tensor contraction reduce to built-in MATLAB operations, which are very fast.
- Hackable The different matrix-product objects are not hidden under many layers of abstraction, but are simple cell arrays. Objects can then be easily inspected, and the code is meant to be played around with.
Add a addpath('<path>/mps') and you are good to go.
A good place to start is the examples folder. There are currently some MWEs of different methods for time-evolution in examples/spinwave and some examples of ground state estimation routines in examples/ground_states.
Additionally, the test folder demonstrates the use of the elementary functions.
CUDA support has been discontinued. Copying matrix product elements to GPU is possible with gpuArray(complex(<tensor>)), but correct memory management is critical.
- U. Schollwöck, The density-matrix renormalization group in the age of matrix product states, Annals of Physics (2011).
- F. Verstraete, V. Murg, and J.I. Cirac, Matrix product states, projected entangled pair states, and variational renormalization group methods for quantum spin systems, Advances in Physics (2008).
- J. Haegeman, C. Lubich, I. Oseledets, B. Vandereycken, F. Verstraete, Unifying time evolution and optimization with matrix product states, Physical Review B (2016).