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14020135

Quantum many-body problems are notorious hard. This is partly because the Hilbert space becomes exponentially big with the particle number `N`. While exact solutions are often considered intractable, numerous approaches have been proposed using approximations. A common trait of these approaches is to use an ansatz such that the number of parameters either does not depend on `N` or is proportional to `N`, e.g., the matrix-product state for spin lattices, the BCS wave function for superconductivity, the Laughlin wave function for fractional quantum Hall effects, and the Gross-Pitaecskii theory for BECs. Among them the product ansatz for BECs has precisely predicted many useful properties of Bose gases at ultra-low temperature. As particle-particle correlation becomes important, however, it begins to fail. To capture the quantum correlations, we propose a new

set of states, which constitute a natural generalization of the product-state ansatz. Our state of `N`=`d`& times;`n` identical particles is derived by symmetrizing the `n`-fold product of a `d`-particle quantum state. For fixed `d`, the parameter space of our state does not grow with `N`. Numerically, we show that our ansatz gives the right description for the ground state and time evolution of the two-site Bose-Hubbard model.

©2012 Perimeter Institute for Theoretical Physics