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Quantum phase transitions in a novel Fermi-Bose Hubbard model

Lincoln D. Carr, Daniel E. Sheehy, Murray Holland

Bulletin of the American Physical SocietyMar 23, 20050 citations

Quantum phase transitions in the Bose Hubbard model with pairing potential

Myung-Hoon Chung

Journal of the Korean Physical SocietyApr 1, 20220 citations

Mott phases and quantum phase transitions of extended Bose–Hubbard models in 2+1 dimensions

K. Sengupta

arXiv:cond-mat/0703506Physica A Statistical Mechanics and its ApplicationsMay 9, 20070 citations

Spectral analysis of two-dimensional Bose-Hubbard models

David Fischer, Darius Hoffmann, Sandro Wimberger

One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.One-dimensional Bose-Hubbard models are well known to obey a transition from regular to quantum-chaotic spectral statistics. We are extending this concept to relatively simple two-dimensional many-body models. Also in two dimensions a transition from regular to chaotic spectral statistics is found and discussed. In particular, we analyze the dependence of the spectral properties on the bond number of the two-dimensional lattices and the applied boundary conditions. For maximal connectivity, the systems behave most regularly in agreement with the applicability of mean-field approaches in the limit of many nearest-neighbor couplings at each site.

arXiv:1604.05664Physical Review AApr 22, 201616 citations

Spectral statistics of driven Bose-Hubbard models

Jesús Mateos, Fernando Sols, C. E. Creffield

Abstract We study the spectral statistics of a one-dimensional Bose–Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system’s spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose–Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.Abstract We study the spectral statistics of a one-dimensional Bose–Hubbard model subjected to kinetic driving; a form of Floquet engineering where the kinetic energy is periodically driven in time with a zero time-average. As the amplitude of the driving is increased, the ground state of the resulting flat-band system passes from the Mott insulator regime to an exotic superfluid. We show that this transition is accompanied by a change in the system’s spectral statistics from Poisson to GOE-type. Remarkably, and unlike in the conventional Bose–Hubbard model which we use as a benchmark, the details of the GOE statistics are sensitive to the parity of both the particle number and the lattice sites. We show how this effect arises from a hidden symmetry of the Hamiltonian produced by this form of Floquet driving.

arXiv:2306.09785Journal of Statistical Mechanics Theory and ExperimentJun 12, 20243 citations

Rigorous results of phase transition theory in lattice boson models

Дмитрий Петрович Санкович

Quantum systems of particles obeying Bose statistics and moving in d -dimensional lattices are studied. The original Bose–Hubbard Hamiltonian is considered, together with model systems related to this Hamiltonian: the Bose–Hubbard model with exchange interaction of infinite radius and the Bose–Hubbard model with infinite interaction potential. Rigorous results concerning the proof of the existence of Bose condensation and a phase transition to the Mott insulator state in these systems are presented.Quantum systems of particles obeying Bose statistics and moving in d -dimensional lattices are studied. The original Bose–Hubbard Hamiltonian is considered, together with model systems related to this Hamiltonian: the Bose–Hubbard model with exchange interaction of infinite radius and the Bose–Hubbard model with infinite interaction potential. Rigorous results concerning the proof of the existence of Bose condensation and a phase transition to the Mott insulator state in these systems are presented.

Proceedings of the Steklov Institute of MathematicsAug 1, 20151 citation

Quantum phase transition and spectral statistics in Bose–Hubbard model

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