We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the $p$ -band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which ${p}_{z}$ and ${p}_{x}+i{p}_{y}$ (or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the $p$-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which ${p}_{z}$ and ${p}_{x}+i{p}_{y}$ (or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.

arXiv:1103.5964Physical Review ANov 21, 201113 citations

Spontaneous currents in spinless fermion lattice models at the strong-coupling limit

Sumiran Pujari, Christopher L. Henley

What kind of lattice Hamiltonian manifestly has an ordered state with spontaneous orbital currents? We consider interacting spinless fermions on an array of square plaquettes, connected by weak hopping; the array geometry may be a $2\ifmmode\times\else\texttimes\fi{}2L$ ladder, a $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2L$ ``tube,'' or a $2L\ifmmode\times\else\texttimes\fi{}2L$ square grid. At half filling, we derive an effective Hamiltonian in terms of pseudospins, of which one component represents orbital currents, and find the conditions sufficient for orbital current long-range order. We consider spinfull variants of the aforesaid spinless models and make contact with other spinfull models in the literature purported to possess spontaneous currents.What kind of lattice Hamiltonian manifestly has an ordered state with spontaneous orbital currents? We consider interacting spinless fermions on an array of square plaquettes, connected by weak hopping; the array geometry may be a $2\ifmmode\times\else\texttimes\fi{}2L$ ladder, a $2\ifmmode\times\else\texttimes\fi{}2\ifmmode\times\else\texttimes\fi{}2L$ ``tube,'' or a $2L\ifmmode\times\else\texttimes\fi{}2L$ square grid. At half filling, we derive an effective Hamiltonian in terms of pseudospins, of which one component represents orbital currents, and find the conditions sufficient for orbital current long-range order. We consider spinfull variants of the aforesaid spinless models and make contact with other spinfull models in the literature purported to possess spontaneous currents.

arXiv:0811.0590Physical Review BAug 25, 20090 citations

Cluster approach to the spinless fermion model

Dieter Ihle

physica status solidi (b)Oct 1, 19831 citation

Topological phases of spinless p -orbital fermions in zigzag optical lattices

Gaoyong Sun, Wen‐Long You, Tao Zhou

Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless $p$ -orbital fermions with local interorbital hoppings and repulsive interactions between ${p}_{x}$ and ${p}_{y}$ bands in zigzag optical lattices. We show that spinless $p$ -band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless $p$-orbital fermions with local interorbital hoppings and repulsive interactions between ${p}_{x}$ and ${p}_{y}$ bands in zigzag optical lattices. We show that spinless $p$-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.

arXiv:2007.16057Physical Review ADec 1, 20203 citations

We study the quantum phases of a three-color Hubbard model that arises in the dynamics of the

p

-band orbitals of spinless fermions in an optical lattice. Strong, color-dependent interactions are induced by an optical Feshbach resonance. Starting from the microscopic scattering properties of ultracold atoms, we derive the orbital exchange constants at 1/3 filling on the cubic optical lattice. Using this, we compute the phase diagram in a Gutzwiller ansatz. We find phases with ``axial orbital order'' in which

{p}_{z}

and

{p}_{x}+i{p}_{y}

(or ${p}_{x}\ensuremath{-}i{p}_{y}$) orbitals alternate.

Motivated by the experiment [St-Jean et al., Nat. Photonics 11, 651 (2017)] on topological phases with collective photon modes in a zigzag chain of polariton micropillars, we study spinless

p

-orbital fermions with local interorbital hoppings and repulsive interactions between

{p}_{x}

and

{p}_{y}

bands in zigzag optical lattices. We show that spinless

p

-band fermions in zigzag optical lattices can mimic the interacting Su-Schrieffer-Heeger model and the effective transverse field Ising model in the presence of local hoppings. We analytically and numerically discuss the ground-state phases and quantum phase transitions of the model. This work provides a simple scheme to simulate topological phases and the quench dynamics of many-body systems in optical lattices.