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We determine the superfluid transition temperatures $T_c$ and the ground states of the attractive Hubbard model and find new insulating phases associated with non-integer filling at sufficiently strong pairing attraction $|U|$. These…
We investigate the mapping between magnetic susceptibility and entanglement in the metallic, insulating, conventional and exotic polarized superfluid phases of one-dimensional fermionic lattice systems as described by the Hubbard model.…
We investigate the half-filled Hubbard model with spatially alternating interactions by means of the two-site dynamical mean-field theory. It is found that a single Mott transition occurs when two kinds of interactions are increased. This…
Motivated by the possibility to load multi-color fermionic atoms in optical lattices, we study the entropy dependence of the properties of the one-dimensional antiferromagnetic SU(N) Heisenberg model, the effective model of the SU(N)…
We present a {\it numerically exact} study of the Hubbard model with spin-dependent anisotropic hopping on the square lattice using auxiliary-field quantum Monte Carlo method. At half filling, the system undergoes Ising phase transitions…
We consider a cloud of fermionic atoms in an optical lattice described by a Hubbard model with an additional linear potential. While homogeneous interacting systems mainly show damped Bloch oscillations and heating, a finite cloud behaves…
We explore the rich nature of correlations in the ground state of ultracold atoms trapped in state-dependent optical lattices. In particular, we consider interacting fermionic ytterbium or strontium atoms, realizing a two-orbital Hubbard…
We discuss the known construction of two interacting superconducting circuits, based on Josephson junctions, that can be precisely engineered and easily controlled. In particular, we use the parametric excitation of two circuits, realized…
We report on the site-resolved observation of characteristic states of the two-dimensional repulsive Fermi-Hubbard model, using ultracold $^{40}$K atoms in an optical lattice. By varying the tunneling, interaction strength, and external…
For a simple-cubic optical lattice with lattice spacing d, occupied by two species of fermionic atoms of mass m that interact repulsively, we ask what conditions maximize the Neel temperature in the Mott insulating phase at density one atom…
We derive effective lattice models for ultracold bosonic or fermionic nonreactive molecules (NRMs) in an optical lattice, analogous to the Hubbard model that describes ultracold atoms in a lattice. In stark contrast to the Hubbard model,…
We investigate the interplay of temperature and trap effects in cold particle systems at their quantum critical regime, such as cold bosonic atoms in optical lattices at the transitions between Mott-insulator and superfluid phases. The…
These lecture notes review recent progress in studying the Fermi-Hubbard model using ultracold gases in optical lattices. We focus on results from quantum gas microscope experiments that have allowed site-resolved measurements of charge and…
The experimental investigation of quantum phases in optical lattice systems provides major challenges. Recently, dynamical generation of double occupancy via modulation of the hopping amplitude t has been used to characterize the strongly…
The physics of the triangular lattice Hubbard model exhibits a rich phenomenology, ranging from a metal-insulator transition, intriguing thermodynamic behavior, and a putative spin liquid phase at intermediate coupling, ultimately becoming…
We study the two-dimensional square lattice Hubbard model for small to moderate interaction strengths $1\leq U/t\leq 4$ by means of the ladder dual fermion approach. The non-local correlations beyond dynamical mean-field theory lower the…
We determine antiferromagnetic (AF) signatures in the half-filled Hubbard model at strong coupling on a cubic lattice and in lower dimensions. Upon cooling, the transition from the charge-excitation regime to the AF Heisenberg regime is…
We investigate two-site electronic correlations within generalized Hubbard model, which incorporates the conventional Hubbard model (parameters: $t$ (hopping between nearest neighbours), $U$ (Coulomb repulsion (attraction)) supplemented by…
We investigate the dynamics of Rydberg electrons excited from the ground state of ultracold atoms trapped in an optical lattice. We first consider a lattice comprising an array of double-well potentials, where each double well is occupied…
We investigate one-dimensional harmonically trapped two-component systems for repulsive interaction strengths ranging from the non-interacting to the strongly interacting regime for Fermi-Fermi mixtures. A new and powerful mapping between…