This paper reviews recent experimental and theoretical progress concerning many-body
phenomena in dilute, ultracold gases. It focuses on effects beyond standard weak-coupling …

We review recent developments in the physics of ultracold atomic and molecular gases in
optical lattices. Such systems are nearly perfect realisations of various kinds of Hubbard …

Basic properties of cold Bose atoms in optical lattices are reviewed. The main principles of
correct self-consistent description of arbitrary systems with Bose-Einstein condensate are …

The mathematical study of the Bose gas goes back to the? rst quarter of the twentieth
century, with the invention of quantum mechanics. The name refers to the Indian physicist …

We have studied the system of hard-core bosons on a two-dimensional optical lattice using
a variational algorithm based on projected entangled-pair states. We have investigated the …

We study the ground-state properties and nonequilibrium dynamics of hard-core bosons
confined in one-dimensional lattices in the presence of an additional periodic potential …

Gaussian boson sampling, a computational model that is widely believed to admit quantum
supremacy, has already been experimentally demonstrated and is claimed to surpass the …

How and why could an interacting system of many particles be described as if all particles
were independent and identically distributed? This question is at least as old as statistical …

We discuss recently introduced numerical linked-cluster (NLC) algorithms that allow one to
obtain temperature-dependent properties of quantum lattice models, in the thermodynamic …

We investigate the dynamics of a boson gas with three-body interactions in dimensions d= 1,
2. We prove that in the limit of infinite particle number, the BBGKY hierarchy of k-particle …