Quantifying the effect of interactions in quantum many-body systems

Abstract

Free fermion systems enjoy a privileged place in physics. With their simple structure they can explain a variety of effects, ranging from insulating and metallic behaviours to superconductivity and the integer quantum Hall effect. Interactions, e.g. in the form of Coulomb repulsion, can dramatically alter this picture by giving rise to emerging physics that may not resemble free fermions. Examples of such phenomena include high-temperature superconductivity, fractional quantum Hall effect, Kondo effect and quantum spin liquids. The non-perturbative behaviour of such systems remains a major obstacle to their theoretical understanding that could unlock further technological applications. Here, we present a pedagogical review of "interaction distance" [Nat. Commun. 8, 14926 (2017)] -- a systematic method that quantifies the effect interactions can have on the energy spectrum and on the quantum correlations of generic many-body systems. In particular, the interaction distance is a diagnostic tool that identifies the emergent physics of interacting systems. We illustrate this method on the simple example of a one-dimensional Fermi-Hubbard dimer.

27 pages, 8 figures; submission to SciPost

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Cited by in corpus (10)

• Product Spectrum Ansatz and the Simplicity of Thermal States
• Quantifying the efficiency of state preparation via quantum variational eigensolvers
• An exact one-particle theory of bosonic excitations: From a generalized Hohenberg-Kohn theorem to convexified N-representability
• Interaction distance in the extended XXZ model
• Quantifying fermionic interactions from the violation of Wick's theorem
• Energy spectrum of interacting gas: cluster expansion method
• Persistent non-Gaussian correlations in out-of-equilibrium Rydberg atom arrays
• Hamiltonian Forging of a Thermofield Double
• Efficiency of free auxiliary models in describing interacting fermions: from the Kohn-Sham model to the optimal entanglement model
• Emergence of Gaussianity in the thermodynamic limit of interacting fermions