Spontaneous Currents in Spinless Fermion Lattice Models at the Strong-Coupling Limit

TL;DR

This paper investigates conditions under which lattice Hamiltonians with interacting spinless fermions exhibit spontaneous orbital currents, deriving effective models and analyzing long-range order in various geometries.

Contribution

It introduces an effective pseudospin Hamiltonian for spinless fermions on lattice arrays, identifying conditions for spontaneous orbital current order and extending to spinfull variants.

Findings

Derived effective Hamiltonian with pseudospins representing currents

Identified conditions for long-range orbital current order

Connected spinless models to spinfull variants in literature

Abstract

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 x 2L ladder, a 2 x 2 x 2L "tube", or a 2L x 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.