Unveiling Order from Chaos by approximate 2-localization of random matrices

• URL: http://arxiv.org/abs/2303.02782v1
• Date: Sun, 5 Mar 2023 21:44:02 GMT
• Title: Unveiling Order from Chaos by approximate 2-localization of random matrices
• Abstract summary: We show that an arbitrary Hamiltonian can be written as a linear combination of two-body interactions terms with high precision. Our results suggest a possible mechanism for the emergence of locality from chaos.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Quantum many-body systems are typically endowed with a tensor product structure. This structure is inherited from probability theory, where the probability of two independent events is the product of the probabilities. The tensor product structure of a Hamiltonian thus gives a natural decomposition of the system into independent smaller subsystems. Considering a particular Hamiltonian and a particular tensor product structure, one can ask: is there a basis in which this Hamiltonian has this desired tensor product structure? In particular, we ask: is there a basis in which an arbitrary Hamiltonian has a 2-local form, i.e. it contains only pairwise interactions? Here we show, using numerical and analytical arguments, that generic Hamiltonian (e.g. a large random matrix) can approximately be written as a linear combination of two-body interactions terms with high precision; that is the Hamiltonian is 2-local in a carefully chosen basis. We show that these Hamiltonians are robust to perturbations. Taken together, our results suggest a possible mechanism for the emergence of locality from chaos.

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