Topological Order: From Long-Range Entangled Quantum Matter to a Unified Origin of Light and Electrons

Figure 2

(a) Disordered states that do not break the symmetry. (b) Ordered states that spontaneously break the symmetry. The energy function 𝜀_𝑔(𝜙) has a symmetry 𝜙→−𝜙∶𝜀_𝑔(𝜙)=𝜀_𝑔(−𝜙). However, as we change the parameter 𝑔, the minimal energy state (the ground state) may respect the symmetry (a), or may not respect the symmetry (b). This is the essence of spontaneous symmetry breaking.