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Revista de la Academia Colombiana de Ciencias Exactas Físicas y Naturales

Magnetic transition of ytterbium atoms confined in optical superlattice with local ferromagnetic interaction

Diego-F Ramírez, R. Franco, Jereson Silva-Valencia

Published Apr 18, 2024• 0 citations
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Abstract

We used the density matrix renormalization group to study the ground state of ytterbium atoms (171Yb) for the Hund lattice model, where the delocalized atoms are confined in a onc-dimensional optical superlattice and his number is one third of the lattice sites. We found a paramagnetic-ferromagnetic quantum phase transition for any value of the potential strength. The local critical ferromagnetic coupling decreases as the superlattice potential increases.

DOI
10.18257/raccefyn.2583

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We used the density matrix renormalization group to study the ground state of ytterbium atoms (171Yb) for the Hund lattice model, where the delocalized atoms are confined in a onc-dimensional optical superlattice and his number is one third of the lattice sites. We found a paramagnetic-ferromagnetic quantum phase transition for any value of the potential strength. The local critical ferromagnetic coupling decreases as the superlattice potential increases.
Using the density matrix renormalization group method, we study a system of 171 Yb atoms confined in a one-dimensional optical lattice. The atoms in the 1 So state undergo a double-well potential, whereas the atoms in the 3 P 0 state are localized. This system is modelled by the Kondo lattice model plus a double-well potential for the free carries. We obtain phase diagrams composed of ferromagnetic and spiral phases, where the critical points always increase with the interwell tunneling parameter. We conclude that this quantum phase transition can be tuned by the double-well potential parameters as well as by the common parameters: local coupling and density.
We investigate the ground-state of a new Kondo lattice model, where the free carriers interact repulsively between them and undergo an external superlattice potential. This model can be simulated with 171 Yb atoms confined in optical lattices. We use the density matrix renormalization group method to evaluate the charge and spin gaps, and the structure factors. We found that the ground-state evolves from a Kondo spin liquid state to a charge-gapped antiferromagnetic state with zero spin gap, when the antiferromagnetic exchange increases. Also, we verify that the quantum critical point varies linearly with the repulsion and the exchange.
We study the ground-state properties of spin-1/2 fermionic atoms confined in a one-dimensional optical superlattice with harmonic confinement by using the density-matrix renormalization group method. For this purpose, we consider an ionic Hubbard model that has superlattice potentials with two-site periodicity. We find that several different types of insulating regimes coexist even if the number of atoms at each site is not an integer, but its average within the unit cell is an integer or half integer. This is contrasted to the coexisting phase of the metallic and Mott-insulating regimes known for the ordinary Hubbard model in an optical lattice. The phase characteristics are elucidated by investigating the profiles of the atom density, the local density (spin) fluctuations, the double occupation probability, and the spin correlations in detail.
We describe the ground state of a gas of bosonic atoms with two coherently coupled internal levels in a deep optical lattice in a one-dimensional geometry. In the single-band approximation this system is described by a Bose-Hubbard Hamiltonian. The system has a superfluid and a Mott insulating phase that can be either paramagnetic or ferromagnetic. We characterize the quantum phase transitions at unit filling by means of a density-matrix renormalization-group technique and compare the results with a mean-field approach and an effective spin Hamiltonian. The presence of the ferromagnetic Ising-like transition modifies the Mott lobes. In the Mott insulating region the system maps to the ferromagnetic spin-1/2 XXZXXZXXZ model in a transverse field and the numerical results compare very well with the analytical results obtained from the spin model. In the superfluid regime quantum fluctuations strongly modify the phase transition with respect to the well-established mean-field three-dimensional classical bifurcation.