Hidden rotational symmetry in a generalized Ising model with rectangular symmetry

Abstract

Novel quantum phases are of interest both fundamentally and practically. In this paper, a toy lattice model with exact four-fold rotational symmetry (C4), which can be taken as a straightforward generalization of the usual Ising model, is studied. The phase diagram in the t–T plane is plotted, where t is the energy controlling quantum fluctuations and T is the temperature. The diagram features an exotic phase (termed the S-phase), which meets the conventional ordered and disordered phases at a tri-critical point. The S-phase distinguishes itself from the conventional ordered phase by its symmetry properties. In fact, it is shown to arise from the spontaneous breaking of the continuous rotational symmetry rather than the C4 symmetry. This is manifested in the long-wavelength fluctuations, which are shown to be the gapless Nambu–Goldstone modes following a quadratic dispersion relation, similar to that of the XY model. Further, discontinuous quantum phase transitions are found and they are argued to occur subsequent to the S-phase.