Seminarium Fizyki Materii Skondensowanej

The 2d Z2 gauge theory coupled to matter describes fermions on a square lattice interacting with a dynamical Z2 valued gauge field. Depending on the parameters, the model is expected to realize several interesting phases of matter. I will present a result that shows that, at half-filling and for large enough fermionic hopping, the ground state of the gauge theory coincides with the π-flux phase, characterized by magnetic flux equal to π in every elementary lattice plaquette. This proves in particular the semimetallic behavior of the ground state of the model. Furthermore, we compute the magnetic susceptibility of the gauge theory, and we prove that it is given by the one of massless 2d Dirac fermions, as observed in recent numerical simulations. The proof is based on reflection positivity and on the chessboard estimate. In the last part of the talk, I will discuss recent progress in understanding the stability of the π-flux phase in presence of Hubbard-type interactions, via the combination of reflection positivity methods, rigorous renormalization group techniques, and Ward identities. Joint work with Leonardo Goller (SISSA).