Related papers: The bosonic Hubbard model on a three dimensional f…
We review the properties of reduced density matrices for free fermionic or bosonic many-particle systems in their ground state. Their basic feature is that they have a thermal form and thus lead to a quasi-thermodynamic problem with a…
Strongly-interacting ultra-cold atoms in tight-binding optical lattice potentials provide an ideal platform to realize the fundamental Hubbard model. Here, after outlining the elementary single particle solution, we review and expand our…
To explore superfluidity in flat-band systems, we consider a Bose-Hubbard model on a cross-linked ladder with $\pi$ flux, which has a flat band with a gap between the other band for noninteracting particles, where we study the effect of the…
We study ground-state properties in a hard-core Bose-Hubbard model on a layered triangular lattice. Combining cluster mean-field theory with the density matrix renormalization group method, we discuss the effect of the interlayer coupling…
Using a generalised version of Gershgorin's circle theorem, rigorous boundaries on the energies of the lowest states of a broad class of line graphs above a critical filling are derived for hardcore bosonic systems. Also a lower boundary on…
Phase transitions in systems described by Bose-Fermi-Hubbard model on a lattice with two nonequivalent sublattices are investigated in this work. The case of hard-core bosons is considered and pseudospin formalism is used. Phase diagrams…
We construct generalized Hofstadter models that possess "color-entangled" flat bands and study interacting many-body states in such bands. For a system with periodic boundary conditions and appropriate interactions, there exist gapped…
We analyse the ground-state quantum phase diagram of hardcore Bosons interacting with repulsive dipolar potentials. The bosons dynamics is described by the extended-Bose-Hubbard Hamiltonian on a two-dimensional lattice. The ground state…
We present exact explicit analytical results describing the exact ground state of four electrons in a two dimensional square Hubbard cluster containing 16 sites taken with periodic boundary conditions. The presented procedure, which works…
We propose a general approach to analyse diagonal ordering patterns in bosonic lattice models with algebraically decaying density-density interactions on arbitrary lattices. The key idea is a systematic search for the energetically best…
We present rigorous results for the SU($n$) Fermi-Hubbard models with finite-range hopping in $d$ ($\ge 2$) dimensions. The models are defined on a class of decorated lattices. We first study the models with flat bands at the bottom of the…
The Hubbard model is a paradigmatic model of strongly correlated quantum matter, thus making it desirable to investigate with quantum simulators such as ultracold atomic gases. Here, we consider the problem of two atoms interacting in a…
In a flat band superconductor, bosonic excitations can disperse while unpaired electrons are immobile. To study this strongly interacting system, we construct a family of multi-band Hubbard models with exact eta-pairing ground states in all…
A numerical bootstrap method is proposed to provide rigorous and nontrivial bounds in general quantum many-body systems with locality. In particular, lower bounds on ground state energies of local lattice systems are obtained by imposing…
Flat band physics is a central theme in modern condensed matter physics. By constructing a tight--binding single particle system that has vanishing momentum dispersion in one or more bands, and subsequently including more particles and…
We propose a powerful and convenient method to systematically design flat-band lattice models, which overcomes the difficulties underlying the previous method. Especially, our method requires no elaborate calculations, applies to arbitrary…
Being dispersionless, flat bands on periodic lattices are solely characterized by their macroscopically degenerate eigenstates: compact localized states (CLSs) in real space and Bloch states in reciprocal space. Based on this property, this…
The physics of strongly correlated quantum particles within a flat band was originally explored as a route to itinerant ferromagnetism and, indeed, a celebrated theorem by Lieb rigorously establishes that the ground state of the repulsive…
A general class of hopping models on a finite bipartite lattice is considered, including the Hubbard model and the Falicov-Kimball model. For the half-filled band, the single-particle density matrix $\uprho (x,y)$ in the ground state and in…
We derive an upper bound on the ground state energy of the three-dimensional (3D) repulsive Hubbard model on the cubic lattice agreeing in the low density limit with the known asymptotic expression of the ground state energy of the dilute…