Fig. 4: Global phase diagrams of the generic toric code (TC) and double semion (DS) wavefunctions.
From: Non-Hermitian effects of the intrinsic signs in topologically ordered wavefunctions
a The phase diagram of the generic TC wavefunction with two tuning parameters hx and hz. The Higgs phase and confining phase correspond to charge and magnetic anyon condensed phases, respectively. Capital letters (black dots) indicate critical/transition points, where point J is a tricritical point, and others are the phase transition points. The phase transition lines JH and JKF belong to the two-dimensional Ising universality class, and the line IJ is characterized by the Kosterlitz–Thouless transition. b The phase diagram of the generic DS wavefunction with two tuning parameters hx and hz. Adjacent to the DS phase, there exist a gapped dilute loop phase, a gapless dense loop phase, and a spontaneously party-time-symmetry breaking (PTSB) phase. The diagram is characterized by different critical points in the hx−hz plane, where the point E is the fixed point of the dense loop phase, the points B and C are two tricritical points, and others are phase transition points. The phase transition line BH is described by the two-dimensional Ising universality class. The phase transition lines AB, BC, and CF are described by non-unitary conformal field theories, while the line CL is a discontinuous phase transition.
