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Bulletin of the American Physical Society

Finite entanglement scaling at novel phase transitions in the Bose-Hubbard model with pairing terms

Michael P. Zaletel, Roger S. K. Mong, Joel E. Moore

Published Feb 29, 2012• 0 citations
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We analyze the quantum phase transition in the Bose-Hubbard model borrowing two tools from quantum-information theory, i.e., the ground-state fidelity and entanglement measures. We consider systems at unitary filling comprising up to 50 sites and show for the first time that a finite-size scaling analysis of these quantities provides excellent estimates for the quantum critical point. We conclude that fidelity is particularly suited for revealing a quantum phase transition and pinning down the critical point thereof, while the success of entanglement measures depends on the mechanisms governing the transition.
We propose a Hamiltonian of ultracold spinless atom in optical lattices including the two-body interaction of nearest neighbors, which reduces to the Bose-Hubbard model in weak-interaction limit. An atom-pair hopping term appearing in the Hamiltonian explains naturally the recent experimental observation of correlated tunneling in a double-well trap with strong atom-atom interactions and moreover leads to a dynamic process of atom-pair tunneling where strongly interacting atoms can tunnel back and forth as a fragmented pair. Finally a dynamics of oscillations induced by the atom-pair tunneling is found in the strong interaction regime, where the Bose-Hubbard model gives rise to the insulator state with fixed time-averaged value of atom-occupation number only. Quantum phase transitions between two quantum phases characterized by degenerate and nondegenerate ground states are shown to be coinciding with the Landau second-order phase-transition theory. In the system of finite atom number the degeneracy of ground states can be removed by quantum tunneling for the even number of atoms but not for the odd number.