Matrix-product-state GPLHR for non-Hermitian many-body eigenproblems
Abstract
Computing multiple eigenstates of non-Hermitian many-body operators plays an important role in investigating excitation spectra, spectral properties, and relaxation dynamics in interacting and open quantum systems. However, this task is challenging because the eigenvectors are generally nonorthogonal and the Hilbert space dimension grows exponentially with system size. Here, we formulate the generalized preconditioned locally harmonic residual (GPLHR) method in a matrix product state (MPS) framework to efficiently compute multiple targeted right eigenstates whose eigenvalues lie near a specified shift in the complex plane. Successive randomized compression (SRC) is employed to accelerate operator applications. We test the method on transcorrelated and complex Hubbard chains, an interacting non-Hermitian Su-Schrieffer-Heeger (SSH) chain, and a Liouvillian model. The results demonstrate that GPLHR combined with MPS provides an efficient and accurate approach for computing multiple eigenstates of non-Hermitian many-body operators.
Related
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BibTeX
@misc{wu2026matrixproductstate,
title = {{Matrix-product-state GPLHR for non-Hermitian many-body eigenproblems}},
author = {Xingyao Wu and Zhangyu Yang and Yanbin Chen and Yu Wang and Feng Chen},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15387},
eprint = {2610.15387},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15387},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Matrix-product-state GPLHR for non-Hermitian many-body eigenproblems
AU - Xingyao Wu
AU - Zhangyu Yang
AU - Yanbin Chen
AU - Yu Wang
AU - Feng Chen
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15387
UR - https://arxiv.org/abs/2610.15387
AB - Computing multiple eigenstates of non-Hermitian many-body operators plays an important role in investigating excitation spectra, spectral properties, and relaxation dynamics in interacting and open quantum systems. However, this task is challenging because the eigenvectors are generally nonorthogonal and the Hilbert space dimension grows exponentially with system size. Here, we formulate the generalized preconditioned locally harmonic residual (GPLHR) method in a matrix product state (MPS) framework to efficiently compute multiple targeted right eigenstates whose eigenvalues lie near a specified shift in the complex plane. Successive randomized compression (SRC) is employed to accelerate operator applications. We test the method on transcorrelated and complex Hubbard chains, an interacting non-Hermitian Su-Schrieffer-Heeger (SSH) chain, and a Liouvillian model. The results demonstrate that GPLHR combined with MPS provides an efficient and accurate approach for computing multiple eigenstates of non-Hermitian many-body operators.
ER -