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Random phase approximation (RPA) was proposed by Bohm and Pines in four seminal papers during 1951-1953 to describe the correlation of fermions, namely the correction to the Hartree-Fock theory. While...
In this talk we introduce some recent developments of Heisenberg-Pauli-Weyl uncertainty principle in the different settings.
The state-of-the-art error correcting codes are based on large random constructions (random graphs, random permutations, . . . ) and are decoded by linear-time iterative algorithms. Because of these f...
In a recent Letter [1] (see also [2]) the authors presented numerical evidence supporting an idea of a direct transition between the superfluid (SF) and Mott insulating (MI) phases in the disordered B...
Two sorts of bosons in an optical lattice at commensurate filling factors can form five stable superfluid and insulating ground states with rich and nontrivial phase diagram. The structure of the grou...
We study superfluid-solid zero-temperature transitions in two-dimensional lattice boson-spin models using worm-algorithm Monte Carlo simulations. We observe that such transitions are typically first o...
Depending on the Hamiltonian parameters, two-component bosons in an optical lattice can form at least three different superfluid phases in which both components participate in the superflow: a (strong...
We study properties of the supersolid phase observed for hard-core bosons on the triangular lattice near half-integer filling factor, and the phase diagram of the system at finite temperature. We find...
We consider the interference of two overlapping ideal Bose-Einstein condensates. The usual description of this phenomenon involves the introduction of a condensate wave function with a definite phase....
We study different solid phases of 4He, by means of path integral Monte Carlo simulations based on a recently developed worm algorithm. Our study includes simulations that start off from a high-T gas ...
We report results of quantum Monte Carlo simulations of the Bose-Hubbard model in three dimensions. Critical parameters for the superfluid-to-Mott-insulator transition are determined with significantl...
We have studied by quantum Monte Carlo simulations the low temperature phase diagram of a mixture of isotopic, hard core bosons, described by the t-Jz-J⊥ model, with J⊥=αJz. The coexistence of superfl...
We establish the phase diagram of the disordered three-dimensional Bose-Hubbard model at unity filling which has been controversial for many years. The theorem of inclusions, proven by Pollet et al. [...
We construct a mapping between the two-dimensional toric code model in external magnetic fields, hz and hx, and the three-dimensional classical Ising system with plaquette interactions, which is equiv...
Phase transitions waves in atomic chains with double-well potential play a fundamental role in materials science, but very little is known about their mathematical properties. In particular, the only ...

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