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

I Morera,Bruno Juliá-Díaz,Artur Polls

doi:10.1038/s41598-019-45737-4

I Morera, Bruno Juliá-Díaz + Show 1 more

Open Access

https://doi.org/10.1038/s41598-019-45737-4

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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.

Highlights

The Bose-Hubbard model is almost ubiquitous nowadays in the interpretation of ultracold atomic gases experiments with optical lattices[1]
The extent to which a quantum simulator of a well-known spin system captures the entanglement properties of the ground state of the effective Hamiltonian has been scrutinized
We have considered the entanglement properties of the ground state of the two-component 1D Bose-Hubbard model in the strong-coupling regime for total filling νA = νB = 1

Summary

Heisenberg chain

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. We will study the entanglement properties of the system as the interspecies interaction is increased towards the point where all interactions are equal In this way, the effective spin model goes from an anisotropic Heisenberg model into the isotropic Heisenberg one. Analytical results using perturbation theory will be complemented with numerical calculations using DMRG (density matrix renormalization group) In this way we can compare the entanglement present in the TCBH with that of the spin model, paying particular attention to the critical phases which appear in the latter.

Results

2SL M

Conclusions

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