Simple Fermionic Model of Deconfined Phases and Phase Transitions

Using quantum Monte Carlo simulations, we study a series of models of fermions coupled to quantum Ising spins on a square lattice with N flavors of fermions per site for N = 1, 2, and 3. The models have an extensive number of conserved quantities but are not integrable, and they have rather rich phase diagrams consisting of several exotic phases and phase transitions that lie beyond the Landau-Ginzburg paradigm. In particular, one of the prominent phases forN > 1 corresponds to 2N gapless Dirac fermions coupled to an emergent Z(2) gauge field in its deconfined phase. However, unlike a conventional Z(2) gauge theory, we do not impose Gauss's Law by hand; instead, it emerges because of spontaneous symmetry breaking. Correspondingly, unlike a conventional Z(2) gauge theory in two spatial dimensions, our models have a finite-temperature phase transition associated with the melting of the order parameter that dynamically imposes the Gauss's law constraint at zero temperature. By tuning a parameter, the deconfined phase undergoes a transition into a short-range entangled phase, which corresponds to Neel antiferromagnet or superconductor for N = 2 and a valence-bond solid for N = 3. Furthermore, for N = 3, the valence-bond solid further undergoes a transition to a Neel phase consistent with the deconfined quantum critical phenomenon studied earlier in the context of quantum magnets.