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arXiv:1102.4797

The ground state of the bose-hubbard model is a supersolid

Philip Warren Anderson

Published Feb 23, 2011• 2 citations
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Abstract

The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator solid and that it has a low-energy spectrum of vortex-like phase fluctuations. Whether the ground state is necessarily commensurate remains an open question.

DOI
10.48550/arxiv.1102.4797

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The Bose-Hubbard model is well-defined description of a Bose solid which may be realistic for cold atoms in a periodic optical lattice. We show that contrary to accepted theories it can never have as a ground state a perfect Mott insulator solid and that it has a low-energy spectrum of vortex-like phase fluctuations. Whether the ground state is necessarily commensurate remains an open question.
Motivated by experiments on Josephson junction arrays, and cold atoms in an optical lattice in a synthetic magnetic field, we study the ``fully frustrated'' Bose-Hubbard model with half a magnetic flux quantum per plaquette. We obtain the phase diagram of this model on a two-leg ladder at integer filling via the density matrix renormalization group approach, complemented by Monte Carlo simulations on an effective classical XYXYXY model. The ground state at intermediate correlations is consistently shown to be a chiral Mott insulator (CMI) with a gap to all excitations and staggered loop currents which spontaneously break time-reversal symmetry. We characterize the CMI state as a vortex supersolid or an indirect exciton condensate, and discuss various experimental implications.
We discuss the superfluid (SF) to Mott-insulator transition of cold atoms in optical lattices recently observed by Greiner et al (2002 Nature 415 39). The fundamental properties of both phases and their experimental signatures are discussed carefully, including the limitations of the standard Gutzwiller approximation. It is shown that in a one-dimensional dilute Bose-gas with a strong transverse confinement (Tonks-gas), even an arbitrary weak optical lattice is able to induce a Mott-like state with crystalline order, provided the dimensionless interaction parameter is larger than a critical value of order one. The SF–insulator transition of the Bose–Hubbard model in this case continuously evolves into a transition of the commensurate–incommensurate type with decreasing strength of the external optical lattice.
We use the Gutzwiller ansatz and analyze the phase diagram of the extended Bose-Hubbard Hamiltonian with on-site (UUU) and nearest-neighbor (VVV) repulsions. For ddd-dimensional hypercubic lattices, when 2dV<U2\mathit{dV}<U2dV<U, it is well known that the ground state alternates between the charge-density-wave (CDW) and Mott insulators, and the supersolid (SS) phase occupies small regions around the CDW insulators. However, when 2dV>U2\mathit{dV}>U2dV>U, in this Rapid Communication, we show that the ground state has only CDW insulators, and more importantly, the SS phase occupies a much larger region in the phase diagram, existing up to very large hopping values which could be orders of magnitude higher than that of the well-known case. In particular, the SS-superfluid phase boundary increases linearly as a function of hopping when $2\mathit{dV}\ensuremath{\gtrsim}1.5U$, for which the prospects of observing the SS phase with dipolar Bose gases loaded into optical lattices is much higher.
We study the soft-core extended Bose-Hubbard model in a two-dimensional triangular lattice by using the quantum Monte Carlo methods. The ground-state phase diagram of the system exhibits a very fruitful structure and is much intriguing. Aside from the Mott insulating state, four kinds of solid states with respect to the commensurate filling factors $\ensuremath{\rho}=1∕3,2∕3$ and $\ensuremath{\rho}=1$ are identified. In incommensurate fillings, superfluid, supersolid, as well as phase-separation states are detected. As in the case of the hard-core bosons, a supersolid phase exists in $1∕3<\ensuremath{\rho}<2∕3$ while it is unstable toward the phase separation in $\ensuremath{\rho}<1∕3$. However, this instability is refrained in $2∕3<\ensuremath{\rho}<1$ due to the softening of the bosons, and then a supersolid phase survives.
We report our findings on the quantum phase transitions in cold bosonic atoms in a one-dimensional optical lattice using the finite-size density-matrix renormalization-group method in the framework of the extended Bose-Hubbard model. We consider wide ranges of values for the filling factors and the nearest-neighbor interactions. At commensurate fillings, we obtain two different types of charge-density wave phases and a Mott insulator phase. However, departure from commensurate fillings yields the exotic supersolid phase where both the crystalline and the superfluid orders coexist. In addition, we obtain the signatures for the solitary waves and the superfluid phase.