Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver

• URL: http://arxiv.org/abs/2212.13267v1
• Date: Mon, 26 Dec 2022 19:00:01 GMT
• Title: Matrix Product Renormalization Group: Potential Universal Quantum Many-Body Solver
• Authors: Masahiko G. Yamada, Takumi Sanno, Masahiro O. Takahashi, Yutaka Akagi, Hidemaro Suwa, Satoshi Fujimoto, Masafumi Udagawa
• Abstract summary: We propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG) MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems.
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• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The density matrix renormalization group (DMRG) is a celebrated tensor network algorithm, which computes the ground states of one-dimensional quantum many-body systems very efficiently. Here we propose an improved formulation of continuous tensor network algorithms, which we name a matrix product renormalization group (MPRG). MPRG is a universal quantum many-body solver, which potentially works at both zero and finite temperatures, in two and higher dimensions, and is even applicable to open quantum systems. Furthermore, MPRG does not rely on any variational principles and thus supports any kind of non-Hermitian systems in any dimension. As a demonstration, we present critical properties of the Yang-Lee edge singularity in one dimension as a representative non-Hermitian system.

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