Optimal free descriptions of many-body theories

Abstract

Interacting bosons or fermions give rise to some of the most fascinating phases of matter, including high-temperature superconductivity, the fractional quantum Hall effect, quantum spin liquids and Mott insulators. While these systems are promising for technological applications, they also present conceptual challenges as they require approaches beyond mean-field and perturbation theory. Here we develop a general framework for identifying the free theory that is closest to a given interacting model in terms of their ground state correlations. Moreover, we quantify the distance between them using the entanglement spectrum. When this interaction distance is small, the optimal free theory provides an effective description of the low energy physics of the interacting model. Our construction of the optimal free model is non-perturbative in nature, thus it offers a new theoretical framework for investigating strongly correlated systems.

7+2 pages, 4+1 figures

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• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Free-fermion descriptions of parafermion chains and string-net models
• Physical Entanglement Between Localized Orbitals
• Quantifying the effect of interactions in quantum many-body systems
• Topological contextuality and anyonic statistics of photonic-encoded parafermions
• Fermionic Magic Resources of Quantum Many-Body Systems
• Fermionic correlations as metric distances: a useful tool for materials science
• Interaction distance in the extended XXZ model
• Quantifying fermionic interactions from the violation of Wick's theorem
• Persistent non-Gaussian correlations in out-of-equilibrium Rydberg atom arrays
• Weak ergodicity breaking transition in randomly constrained model
• Measures of distance in quantum mechanics
• Machine Learning Entanglement Freedom Or: How I Learned to Stop Worrying and Love Linear Regression
• Emergence of Gaussianity in the thermodynamic limit of interacting fermions
• Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model
• Free fermion representation of the topological surface code