We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative $d$ -wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative $d$ -wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a $d$ -wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to ``quantum simulate'' the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.We study the conditions under which, using a canonical transformation, the phases sought after for the repulsive Hubbard model, namely, a Mott insulator in the paramagnetic and antiferromagnetic phases, and a putative $d$-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative $d$-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a $d$-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to ``quantum simulate'' the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.

arXiv:0812.4422Physical Review AMar 19, 200978 citations

Antiferromagnetic state in the three-band Hubbard model

Tetsuro Asahata, Akira Oguri, Sadamichi Maekawa

Physica C SuperconductivityDec 1, 19941 citation

Antiferromagnetic Order in the Hubbard Model: Spin-Charge Rotating Reference Frame Approach

T. A. Zaleski, T. K. Kopeć

We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice.We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem.As our theory describes the evolution from a Slater (U t) to a Mott-Heisenberg (U t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.We study the antiferromagnetic phase of three-dimensional Hubbard model with nearest neighbors hopping on a bipartite cubic lattice.We use the quantum SU(2)×U(1) rotor approach that yields a fully self-consistent treatment of the antiferromagnetic state that respects the symmetry properties of the model and satisfies the Mermin-Wagner theorem.As our theory describes the evolution from a Slater (U t) to a Mott-Heisenberg (U t) antiferromagnet, we present the phase diagram of the antiferromagnetic Hubbard model as a function of the crossover parameter U/t.

Acta Physica Polonica AJul 1, 20081 citation

d

-wave superfluid can be deduced from observations in an optical lattice loaded with a spin-imbalanced ultracold Fermi gas with attractive interactions, thus realizing the attractive Hubbard model. We argue that the Mott insulator and antiferromagnetic phase of the repulsive Hubbard model are easier to observe in the attractive Hubbard mode as a band insulator of Cooper pairs and superfluid phase, respectively. The putative

d

-wave superfluid phase of the repulsive Hubbard model doped away from half filling is related to a

d

-wave antiferromagnetic phase for the attractive Hubbard model. We discuss the advantages of this approach to ``quantum simulate'' the Hubbard model in an optical lattice over the simulation of the doped Hubbard model in the repulsive regime. We also point out a number of technical difficulties of the proposed approach and, in some cases, suggest possible solutions.