Quantum spin liquids in a square lattice subject to an Abelian flux

Abstract: We report that a possible Z2 quantum spin liquid (QSL) can be observed in a new class of frustrated system: spinor bosons subject to a pi flux in a square lattice. We construct a new class of Ginsburg-Landau (GL) type of effective action to classify possible quantum or topological phases at any coupling strengths. It can be used to reproduce the frustrated SF with the 4 sublattice $ 90^{\circ} $ coplanar spin structure plus its excitations in the weak coupling limit and the FM Mott plus its excitations in the strong coupling limit achieved in our previous work. It also establishes deep and intrinsic connections between the GL effective action and the order from quantum disorder (OFQD) phenomena in the weak coupling limit. Most importantly, it predicts two possible new phases at intermediate couplings: a FM SF phase or a frustrated magnetic Mott phase. We argue that the latter one is more likely and melts into a $ Z_2 $ quantum spin liquid (QSL) phase. If the heating issue can be under a reasonable control at intermediate couplings $ U/t \sim 1 $, the topological order of the $ Z_2 $ QSL maybe uniquely probed by the current cold atom or photonic experimental techniques.