The one-dimensional Long-Range Falikov-Kimball Model: Thermal Phase Transition and Disorder-Free Localisation

Abstract

Disorder or interactions can turn metals into insulators. One of the simplest settings to study this physics is given by the Falikov-Kimball model, which describes itinerant fermions interacting with a classical Ising background field. Despite the translational invariance of the model, inhomogenous configurations of the background field give rise to effective disorder physics which lead to a rich phase diagram in two (or more) dimensions with finite temperature charge density wave (CDW) transitions and interaction-tuned Anderson versus Mott localized phases. Here, we propose a generalised Falikov-Kimball model in one dimension with long-range interactions which shows a similarly rich phase diagram. We use an exact Markov Chain Monte Carlo method to map the phase diagram and compute the energy resolved localisation properties of the fermions. We compare the behaviour of this transitionally invariant model to an Anderson model of uncorrelated binary disorder about a background CDW field which confirms that the fermionic sector only fully localizes for very large system sizes.

arXiv comment7 pages, 4 figures

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Cited by in corpus (6)

• Spectral response of disorder-free localized lattice gauge theories
• Violation of Luttinger's theorem in the simplest doped Mott insulator: Falicov-Kimball model in strong correlation limit
• The competition between antiferromagnetism and superconductivity in a doped Hubbard model with anisotropic interaction
• Anomalous Quantum Relaxation in the Infinite Temperature Hubbard Chain
• Effects of critical correlations on quantum percolation in two dimensions
• Disorder-free localization transition in a two-dimensional lattice gauge theory