arXiv:1902.01114 · Scientific Reports

Entanglement structure of the two-component Bose-Hubbard model as a quantum simulator of a Heisenberg chain

Ivan Morera, A. Polls, Bruno Juliá-Díaz

Published Jul 1, 2019• 8 citations

Abstract

We consider a quantum simulator of the Heisenberg chain with ferromagnetic interactions based on the two-component 1D Bose-Hubbard model at filling equal to two in the strong coupling regime. The entanglement properties of the ground state of the two-component Bose-Hubbard model are compared to those of the effective spin model as the interspecies interaction approaches the intraspecies one. A numerical study of the entanglement properties of the two-component Bose-Hubbard model is supplemented with analytical expressions derived from the effective spin Hamiltonian. When the pure ferromagnetic Heisenberg chain is considered, the entanglement properties of the effective Hamiltonian are not properly predicted by the quantum simulator.

DOI: 10.1038/s41598-019-45737-4

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arXiv:1902.01114 · Scientific Reports

Entanglement structure of the two-component Bose-Hubbard model as a quantum simulator of a Heisenberg chain

Ivan Morera, A. Polls, Bruno Juliá-Díaz

Published Jul 1, 2019• 8 citations

arXiv HTML PDF

Abstract

DOI: 10.1038/s41598-019-45737-4

Related papers

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Using a similarity Hamiltonian renormalization procedure, we determine an effective spin-

\frac{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-

\frac{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 $L\ensuremath{\sim}30$. 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.

{Z}_{2}

symmetry, when the spin-orbit coupling term becomes comparable to the hopping kinetic energy and the intercomponent interaction is smaller than the intracomponent one as well. This effect is expected to be detectable with the present realization of the synthetic spin-orbit coupling in experiments.

Strongly interacting one-dimensional (1D) Bose--Fermi mixtures form a tunable

XXZ

spin chain. Within the spin-chain model developed here, all properties of these systems can be calculated from states representing the ordering of the bosons and fermions within the atom chain and from the ground-state wave function of spinless noninteracting fermions. We validate the model by means of an exact diagonalization of the full few-body Hamiltonian in the strongly interacting regime. Using the model, we explore the phase diagram of the atom chain as a function of the boson-boson (BB) and boson-fermion (BF) interaction strengths and calculate the densities, momentum distributions, and trap-level occupancies for up to 17 particles. In particular, we find antiferromagnetic (AFM) and ferromagnetic (FM) order and a demixing of the bosons and fermions in certain interaction regimes. We find, however, no demixing for equally strong BB and BF interactions, in agreement with earlier calculations that combined the Bethe ansatz with a local-density approximation.