Basis-update and Galerkin time integration in canonical matrix-product-state form

Abstract:Matrix product state algorithms must enlarge their bond spaces as entanglement grows and compress them to control cost. We formulate basis-update and Galerkin (BUG) time integration as a sequence of canonical MPS sweeps for Hamiltonians represented as matrix product operators. We show when two natural basis updates produce the same trial space and when transporting coefficients between successive bases preserves the represented state. Under these conditions, the existing first-order error bound for uncompressed tree-tensor-network BUG also applies to the alternating-endpoint MPS schedule. We verify the uncompressed implementation against an independent six-site calculation. We then compare BUG with two-site TDVP for 16-site transverse-field Ising and Haldane-Shastry dynamics. At matched timestep and truncation settings, BUG performs fewer local exponential actions and has lower runtime. These settings do not produce equal accuracy. The runtime versus accuracy curves cross for the Ising model and are close for the Haldane-Shastry model. The comparison therefore identifies model-dependent trade-offs rather than a general advantage for either method.

Quantum Physics (quant-ph); Other Condensed Matter (cond-mat.other)

arXiv:2608.16994 [quant-ph]

(or arXiv:2608.16994v1 [quant-ph] for this version)

https://doi.org/10.48550/arXiv.2608.16994 Focus to learn more arXiv-issued DOI via DataCite

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.