Long-range order in a simple model of interacting fermions

Alan Coleman

Yukimi Goto, Tohru Koma

We study a lattice fermion model with antiferromagnetic interactions on the three-dimensional cubic lattice. The hopping term of the Hamiltonian has a Weyl-type dispersion. We prove that the model has reflection positivity. Moreover, by relying on the property, we prove the existence of the antiferromagnetic long-range order at low temperatures in a strong coupling regime.

Alan Coleman, Vyacheslav I. Yukalov

Silvia Neri, François Damanet, Andrew J. Daley +2 more

We investigate the possibility of engineering dissipatively long-range order that is robust against heating in strongly interacting fermionic systems, relevant for atoms in cavity QED. It was previously shown [Tindall ] that it is possible to stabilize long-range order in a Hubbard model by exploiting a dissipative mechanism in the Lindblad limit, this latter being valid for spectrally unstructured baths. Here, we first show that this mechanism still holds when including additional spin-exchange interactions in the model, that is, for the tUJ model. Moreover, by means of a Redfield approach that goes beyond the Lindblad case, we show how the stability of the engineered state depends crucially on properties of the bath spectral density and discuss the feasibility of those properties in an experiment.

Marcin Szyniszewski

Tatsuya Kishi, Kenn Kubo

The existence of long range order (LRO) is examined in the antiferromagnetic Heisenberg model on the square or the simple cubic lattice with the next nearest neighbor interactions which are taken to be λ times the nearest neighbor ones (λ≧0). It is rigorously shown that Néel LRO exists at a low temperature on the simple cubic lattice and in the ground state on the square lattice for λ smaller than a critical value λ c . On the square lattice λ c increases with S starting from 0.072 for S =1 and approaches 0.5 in the limit S →∞. On the simple cubic lattice λ c =0.002 for S =1/2 and approaches 0.25 in the limit S →∞.