Diagonal Isometric Form for Tensor Product States in Two Dimensions

Fuente: arXiv
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Autori principali: Sappler, Benjamin, Kawano, Masataka, Zaletel, Michael P, Pollmann, Frank
Natura: Preprint
Pubblicazione: 2025
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author Sappler, Benjamin
Kawano, Masataka
Zaletel, Michael P
Pollmann, Frank
author_facet Sappler, Benjamin
Kawano, Masataka
Zaletel, Michael P
Pollmann, Frank
contents Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.
format Preprint
id arxiv_https___arxiv_org_abs_2507_08080
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Diagonal Isometric Form for Tensor Product States in Two Dimensions
Sappler, Benjamin
Kawano, Masataka
Zaletel, Michael P
Pollmann, Frank
Strongly Correlated Electrons
Quantum Physics
Isometric tensor product states (isoTPS) generalize the isometric form of the one-dimensional matrix product states (MPS) to tensor networks in two and higher dimensions. Here, we introduce an alternative isometric form for isoTPS by incorporating auxiliary tensors to represent the orthogonality hypersurface. We implement the time evolving block decimation (TEBD) algorithm on this new isometric form and benchmark the method by computing ground states and the real time evolution of the transverse field Ising model in two dimensions on large square lattices of up to 1250 sites. Our results demonstrate that isoTPS can efficiently capture the entanglement structure of two-dimensional area law states. The short-time dynamics is also accurately reproduced even at the critical point. Our isoTPS formulation further allows for a natural extension to different lattice geometries, such as the honeycomb or kagome latice.
title Diagonal Isometric Form for Tensor Product States in Two Dimensions
topic Strongly Correlated Electrons
Quantum Physics
url https://arxiv.org/abs/2507.08080