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 onsite 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 density matrix renormalization group numerical simulations of the Bose-Hubbard model for various values of U and for a number L of lattice sites as low as L similar to 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 one-dimensional Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.

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

ROSSINI, DAVIDE;
2013

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 onsite 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 density matrix renormalization group numerical simulations of the Bose-Hubbard model for various values of U and for a number L of lattice sites as low as L similar to 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 one-dimensional Bose-Hubbard model with suitably chosen parameters may be seen as a quantum simulator of the XXZ chain.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11384/10721
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