Emergence of Gaussianity in the thermodynamic limit of interacting fermions

Abstract

Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-$\frac{1}{2}$ chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.

8 pages, 4 figures

References in corpus (8)

• Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
• Spin transport in a tunable Heisenberg model realized with ultracold atoms
• Entanglement Hamiltonian Tomography in Quantum Simulation
• Detection of Kardar-Parisi-Zhang hydrodynamics in a quantum Heisenberg spin-$1/2$ chain
• The quantum sine-Gordon model with quantum circuits
• Quantum state discrimination: a geometric approach
• Essential singularity in the Renyi entanglement entropy of the one-dimensional XYZ spin-1/2 chain
• Decay and recurrence of non-Gaussian correlations in a quantum many-body system