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

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.

References in corpus (20)

• Decoherence, einselection, and the quantum origins of the classical
• From Quantum Chaos and Eigenstate Thermalization to Statistical Mechanics and Thermodynamics
• Random Matrix Theories in Quantum Physics: Common Concepts
• Comments on the Sachdev-Ye-Kitaev model
• Decoherence, the measurement problem, and interpretations of quantum mechanics
• The distribution of the ratio of consecutive level spacings in random matrix ensembles
• Black Holes and Random Matrices
• Matrix Models for Beta Ensembles
• Quantum chaos challenges many-body localization
• Quantum tensor product structures are observable-induced
• Parameter Space Compression Underlies Emergent Theories and Predictive Models
• Space from Hilbert Space: Recovering Geometry from Bulk Entanglement
• Quantum Mereology: Factorizing Hilbert Space into Subsystems with Quasi-Classical Dynamics
• Universal spectral form factor for many-body localization
• Locality from the Spectrum
• The Universe from a Single Particle
• Mad-Dog Everettianism: Quantum Mechanics at Its Most Minimal
• The Universe from a Single Particle II
• The Universe from a Single Particle III
• Reality as a Vector in Hilbert Space

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