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arXiv · 2402.05198

Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors

Alberto Giuseppe Catalano
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Abstract

Matrix product states (MPSs) and matrix product operators (MPOs) are fundamental tools in the study of quantum many-body systems, particularly in the context of tensor network methods such as Time-Evolving Block Decimation (TEBD). However, constructing compact MPO representations for Hamiltonians with interactions beyond nearest-neighbors, such as those arising in atomic, molecular, and optical (AMO) systems or in systems with ring geometry, remains a challenge. In this paper, we propose a novel approach for the direct construction of compact MPOs tailored specifically for the exponential of spin Hamiltonians. This approach allows for a more efficient time evolution, using TEBD, of spin systems with interactions beyond nearest-neighbors, such as long-range spin-chains, periodic systems and more complex cluster model, with interactions involving more than two spins.

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Alberto Giuseppe Catalano. 2024-02-07. Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors. https://doi.org/10.1103/jpt3-xjjf

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