28 citations · 81 across the 19 of their papers we have counts for
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Ground state energy of the dilute Bose-Hubbard gas on Bravais lattices
Norbert Mokrzański, Marcin Napiórkowski, Jacek Wojtkiewicz
We study interacting bosons on a three-dimensional Bravais lattice with positive hopping amplitudes and on-site repulsive interactions. We prove that, in the dilute limit ,…
Ground state energies of the Hubbard models and the Hartree Fock approximation
Jacek Wojtkiewicz, Piotr H. Chankowski
According to the `folk knowledge', the Hartree-Fock (H-F) approximation applied to the Hubbard model becomes exact in the limit of small coupling (the smaller , the better…
Non-existence of Bose-Einstein condensation in Bose-Hubbard model in dimensions 1 and 2
Piotr Stachura, Wiesław Pusz, Jacek Wojtkiewicz
We apply the Bogoliubov inequality to the Bose-Hubbard model to rule out the possibility of Bose-Einstein condensation. The result holds in one and two dimensions, for any filling…
Operator reflection positivity inequalities and their applications to interacting quantum rotors
Jacek Wojtkiewicz, Wiesław Pusz, Piotr Stachura
In the Reflection Positivity theory and its application to statistical mechanical systems, certain matrix inequalities play a central role. The Dyson-Lieb-Simon and Kennedy-Lieb-Sh…
On the phase diagram of the anisotropic XY chain in transverse magnetic field
Tomasz Maciążek, Jacek Wojtkiewicz
We investigate an explicite formula for ground state energy of the anisotropic XY chain in transverse magnetic field. In particular, we examine the smoothness properties of the exp…