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

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

Correlated Fermion Systems on a Lattice: Hubbard Model

WORLD SCIENTIFIC eBooksMar 5, 20170 citations

Phases of correlated spinless fermions on the honeycomb lattice

Martin Hohenadler, Maria Daghofer

Bulletin of the American Physical SocietyMar 4, 20140 citations

Lattice fermion models with spontaneous orbital currents in strong-interaction limit

Christopher L. Henley

Bulletin of the American Physical SocietyMar 13, 20060 citations

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.