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The problem of finding the minimum-energy configuration of particles on a lattice, subject to a generic short-ranged repulsive interaction, is studied analytically. The study is relevant to charge ordered states of interacting fermions, as described by the spinless Falicov-Kimball model. For a range of particle density including the half-filled case, it is shown that the minimum-energy states coincide with the large-U neutral ground state ionic configurations of the Falicov-Kimball model, thus providing a characterization of the latter as ``most homogeneous ionic arrangements. These obey hierarchical rules, leading to a sequence of phases described by the Farey tree. For lower densities, a new family of minimum-energy configurations is found, having the novel property that they are aperiodic even when the particle density is a rational number. In some cases there occurs local phase separation, resulting in an inherent sensitivity of the ground state to the detailed form of the interaction potential.
Microfabricated ion traps are a major advancement towards scalable quantum computing with trapped ions. The development of more versatile ion-trap designs, in which tailored arrays of ions are positioned in two dimensions above a microfabricated surf
Motivated by recent experimental development, we investigate spin-orbit coupled repulsive Fermi atoms in a one-dimensional optical lattice. Using the density-matrix renormalization group method, we calculate momentum distribution function, gap, and s
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We study the real time evolution of the correlation functions in a globally quenched interacting one dimensional lattice system by means of time adaptive density matrix renormalization group. We find a clear light-cone behavior quenching the repulsiv
Previous theoretical and experimental research has shown that current NISQ devices constitute powerful platforms for analogue quantum simulation. With the exquisite level of control offered by state-of-the-art quantum computers, we show that one can