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Springer eBooks

On the Gibbs States for One-Dimensional Lattice Boson Systems with a Long-Range Interaction

Enzo Olivieri, Pierre Picco, Yurii M. Suhov

Published Jan 1, 1993• 1 citation
Publisher
DOI
10.1007/978-94-011-1691-6_43

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We simulate a one-dimensional system of a few ultracold bosons trapped in an optical lattice with long-range interactions from an ab initio perspective using the MCTDH-B method. We emphasise the distinct influence of the long-range interactions and the effects not observed by systems with contact interactions. We consider both the nearest-neighbour and the next-nearest neighbour interactions in addition to the usual contact interactions. We observe and analyse the ground state that arises due to the intricate interplay between the interaction potentials and the non-trivial influence of the particle number. By systematically tuning the coupling between different interaction types and varying particle numbers across different regimes, we uncover a diverse set of novel ground-state configurations whose emergence is governed by the delicate interplay of competing energetic factors.
The quantum walk of two hard-core bosons in one-dimensional lattice under the effect of long-range inter-particle interaction is studied in detail. We also simulate the influence of an isolated defect that may exist in the lattice on the quantum walk of two particles by adding an additional potential energy to a certain lattice site. Using exact diagonalization method, the continuous-time quantum walk is directly simulated. The numerical simulations show that the range of interaction (long-range or short-range), the strength of the inter-particle interaction, the initial state of the two particles and the presence of the isolated defect have great influences on the quantum walk. Under the effect of strong long-range interaction, the particles initially located on the non-adjacent lattice sites have a co-walking behavior, while under the short-range interactions (nearest-neighbor interactions) only two particles initially located on the neighboring lattice sites can exhibit co-walking. After introducing the isolated defect into the system with strong interaction, two particles residing on the same side of the isolated defect keep co-walking, while two particles located on either sides of the isolated defect or one particle located on the isolated defect and the other particle staying on the side of the isolated defect, the two particles keep stationary or co-walking near the defect, displaying the characteristics of localization. By using the second-order perturbation theory of degenerate quantum system, a comprehensive theoretical analysis of the above numerical results is given. The theoretical analysis reveals the underlying physical law of quantum walks of two particles in one-dimensional lattice under the effects of strong long-range interaction and isolated defect in the lattice.