Site basis excitation Ansatz for matrix product states, by Steven R. White

SciPost Physics Core Home Authoring Refereeing Submit a manuscript About Site basis excitation Ansatz for matrix product states Steven R. White SciPost Phys. Core 9, 020 (2026) · published 8 April 2026 Part of the In Memoriam: Ian Affleck Collection in the In Memoriam Series. doi: 10.21468/SciPostPhysCore.9.2.020 pdf BiBTeX RIS Submissions/Reports Abstract We introduce a simple and efficient variation of the tangent-space excitation Ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matrix, akin to a non-orthogonal band-theory diagonalization. The approach is based on an infinite MPS description of the ground state, and we introduce an extremely simple alternative to variational uniform matrix product states (VUMPS) based on finite system DMRG. For the $S=1$ Heisenberg chain, our method—site basis excitation Ansatz (SBEA)—efficiently produces the one-magnon dispersion with high accuracy. We also examine the role of MPS gauge choices, finding that not imposing a gauge condition—leaving the basis nonorthogonal—is crucial for the approach, whereas imposing a left-orthonormal gauge (as in prior work) severely hampers convergence. We also show how one can construct Wannier excitations, analogous to the Wannier functions of band theory, where one Wannier excitation, translated to all sites, can reconstruct the single magnon modes exactly for all momenta. × TY - JOURPB - SciPost FoundationDO - 10.21468/SciPostPhysCore.9.2.020TI - Site basis excitation Ansatz for matrix product statesPY - 2026/04/08UR - https://scipost.org/SciPostPhysCore.9.2.020JF - SciPost Physics CoreJA - SciPost Phys. CoreVL - 9IS - 2SP - 020A1 - White, StevenAB - We introduce a simple and efficient variation of the tangent-space excitation Ansatz used to compute elementary excitation spectra of one-dimensional quantum lattice systems using matrix product states (MPS). A small basis for the excitation tensors is formed based on a single diagonalization analogous to a single site DMRG step but for multiple states. Once overlap and Hamiltonian matrix elements are found, obtaining the excitation for any momentum only requires diagonalization of a tiny matrix, akin to a non-orthogonal band-theory diagonalization. The approach is based on an infinite MPS description of the ground state, and we introduce an extremely simple alternative to variational uniform matrix product states (VUMPS) based on finite system DMRG. For the $S=1$ Heisenberg chain, our method—site basis excitation Ansatz (SBEA)—efficiently produces the one-magnon dispersion with high accuracy. We also examine the role of MPS gauge choices, finding that not imposing a gauge condition—leaving the basis nonorthogonal—is crucial for the approach, whereas imposing a left-orthonormal gauge (as in prior work) severely hampers convergence. We also show how one can construct Wannier excitations, analogous to the Wannier functions of band theory, where one Wannier excitation, translated to all sites, can reconstruct the single magnon modes exactly for all momenta.ER - × @Article{10.21468/SciPostPhysCore.9.2.020, title={{Site basis excitation Ansatz for matrix product states}}, author={Steven R. White}, journal={SciPost Phys. Core}, volume={9}, pages={020}, year={2026}, publisher={SciPost}, doi={10.21468/SciPostPhysCore.9.2.020}, url={https://scipost.org/10.21468/SciPostPhysCore.9.2.020},} Disclosure of Generative AI use The author(s) disclose that the following generative AI tools have been used in the preparation of this publication I explored using Chatgpt model o3 in a several ways to speed up and perhaps improve the paper writing, after the work was done. It was very useful in looking up background work and in helping me make the inline tensor network diagram figures. I experimented with using o3 and several other models to make several independent rough drafts of the paper based on my notes. This was fascinating, and useful to get the writing started, but I found the writing quality below my standards and rewrote every paragraph and sentence. Ontology / Topics See full Ontology or Topics database. Density matrix renormalization group (DMRG) Tensor networks Author / Affiliation: mappings to Contributors and Organizations See all Organizations. 1 Steven White 1 University of California, Irvine [UCI] Funder for the research work leading to this publication National Science Foundation [NSF]