Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors

• URL: http://arxiv.org/abs/2402.05198v1
• Date: Wed, 7 Feb 2024 19:08:01 GMT
• Title: Numerically efficient unitary evolution for Hamiltonians beyond nearest-neighbors
• Authors: Alberto Giuseppe Catalano
• Abstract summary: Matrix product states (MPSs) and matrix product operators (MPOs) are fundamental tools in the study of quantum many-body systems. We propose a novel approach for the direct construction of compact MPOs tailored specifically for the exponential of spin Hamiltonians.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 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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