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

Orbital Order in Mott Insulators of Spinless p -Band Fermions

Erhai Zhao, W. Vincent Liu

A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.A gas of strongly interacting single-species (spinless) p-orbital fermionic atoms in 2D optical lattices is proposed and studied. Several interesting new features are found. In the Mott limit on a square lattice, the gas is found to be described effectively by an orbital exchange Hamiltonian equivalent to a pseudospin-1/2 XXZ model. For a triangular, honeycomb, or kagome lattice, the orbital exchange is geometrically frustrated and described by a new quantum 120 degrees model. We determine the orbital ordering on the kagome lattice, and show how orbital wave fluctuations select ground states via the order by disorder mechanism for the honeycomb lattice. We discuss experimental signatures of various orbital ordering.

arXiv:0801.0589Physical Review LettersApr 22, 200893 citations

Fermionic duality approach to strongly-interacting lattice models

Joe Mitchell, Tigran Sedrakyan, Victor M. Galitski

Bulletin of the American Physical SocietyMar 24, 20110 citations

Supersymmetry breaking and Nambu-Goldstone fermions with cubic dispersion

Noriaki Sannomiya, Hosho Katsura, Yu Nakayama

We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and ${Q}^{\ifmmode\dagger\else\textdagger\fi{}}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$ . The system is strongly interacting for small $g$ , and in the extreme limit $g=0$ , the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large- $g$ limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of $g$ and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.We introduce a lattice fermion model in one spatial dimension with supersymmetry (SUSY) but without particle number conservation. The Hamiltonian is defined as the anticommutator of two nilpotent supercharges $Q$ and ${Q}^{\ifmmode\dagger\else\textdagger\fi{}}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter $g$. The system is strongly interacting for small $g$, and in the extreme limit $g=0$, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-$g$ limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of $g$ and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.

arXiv:1612.02285Physical review. D/Physical review. D.Mar 2, 201733 citations

Q

and ${Q}^{\ifmmode\dagger\else\textdagger\fi{}}$. Each supercharge is built solely from spinless fermion operators and depends on a parameter

g

. The system is strongly interacting for small

g

, and in the extreme limit

g=0

, the number of zero-energy ground states grows exponentially with the system size. By contrast, in the large-

g

limit, the system is noninteracting and SUSY is broken spontaneously. We study the model for modest values of

g

and show that under certain conditions spontaneous SUSY breaking occurs in both finite and infinite chains. We analyze the low-energy excitations both analytically and numerically. Our analysis suggests that the Nambu-Goldstone fermions accompanying the spontaneous SUSY breaking have cubic dispersion at low energies.