Computing excited states with isometric tensor networks in two-dimensions

Fuente: arXiv
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Main Authors: Dektor, Alec, Chi, Runze, Van Beeumen, Roel, Yang, Chao
Format: Preprint
Published: 2025
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author Dektor, Alec
Chi, Runze
Van Beeumen, Roel
Yang, Chao
author_facet Dektor, Alec
Chi, Runze
Van Beeumen, Roel
Yang, Chao
contents We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new block isometric projected entangled pair state (block-isoPEPS) ansatz that generalizes the block matrix product state (MPS) framework, widely used for Hamiltonians defined on one-dimensional chains, to two-dimensions. The proposed block-isoPEPS ansatz offers several attractive features for PEPS-based algorithms, including exact block orthogonalization, controlled local truncation via singular value decompositions, and efficient evaluation of observables. We demonstrate the proposed inexact subspace iteration for block-isoPEPS by computing excitations of the two-dimensional transverse-field Ising and Heisenberg models and compare our results with existing PEPS methods. Our results demonstrate that block isometric tensor networks provide a scalable framework for studying excitations in quantum many-body systems beyond one dimension.
format Preprint
id arxiv_https___arxiv_org_abs_2510_20063
institution arXiv
publishDate 2025
record_format arxiv
spellingShingle Computing excited states with isometric tensor networks in two-dimensions
Dektor, Alec
Chi, Runze
Van Beeumen, Roel
Yang, Chao
Numerical Analysis
65F15, 15A69
We present a new subspace iteration method for computing low-lying eigenpairs (excited states) of high-dimensional quantum many-body Hamiltonians with nearest neighbor interactions on two-dimensional lattices. The method is based on a new block isometric projected entangled pair state (block-isoPEPS) ansatz that generalizes the block matrix product state (MPS) framework, widely used for Hamiltonians defined on one-dimensional chains, to two-dimensions. The proposed block-isoPEPS ansatz offers several attractive features for PEPS-based algorithms, including exact block orthogonalization, controlled local truncation via singular value decompositions, and efficient evaluation of observables. We demonstrate the proposed inexact subspace iteration for block-isoPEPS by computing excitations of the two-dimensional transverse-field Ising and Heisenberg models and compare our results with existing PEPS methods. Our results demonstrate that block isometric tensor networks provide a scalable framework for studying excitations in quantum many-body systems beyond one dimension.
title Computing excited states with isometric tensor networks in two-dimensions
topic Numerical Analysis
65F15, 15A69
url https://arxiv.org/abs/2510.20063