XXZ spin-1/2 representation of a finite-U Bose-Hubbard chain at half-integer filling

Abstract

Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-1/2 representation of the Bose-Hubbard model at half-integer filling and at a finite on-site interaction energy U. By means of bosonization, we are able to recast the effective Hamiltonian as that of a spin-1/2 XXZ magnetic chain with pertinently renormalized coupling and anisotropy parameters. We use this mapping to provide analytical estimates of the correlation functions of the Bose-Hubbard model. We then compare such results with those based on DMRG numerical simulations of the Bose-Hubbard model for various values of U and for a number L of lattice sites as low as L ~ 30. We find an excellent agreement up to 10% between the output of analytical and numerical computations, even for relatively small values of U. Our analysis implies that, also at finite U, the 1D Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.

17 pages, 12 .eps figures

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Cited by in corpus (8)

• Purification and many-body localization in cold atomic gases
• Modulational instabilities in lattices with power-law hoppings and interactions
• Factorization and criticality in finite XXZ systems of arbitrary spin
• Quantum simulator of link models using spinor dipolar ultracold atoms
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• Real fermion modes, impurity entropy, and nontrivial fixed points in the phase diagram of junctions of interacting quantum wires and topological superconductors
• Strongly Interacting Two-component Coupled Bose Gas in Optical Lattices