This present theoretical study investigates the geometric control of quantum conformal field theories through radius compression-induced quantum critical phenomena. It reveals an intrinsic relationship between the Berry connection and variations in both the radial component, δR, and spin components, Sa, within the quantum conformal subspace. Radius compression in such systems can generate a Berry curvature analogous to magnetic fields, which releases topological waves via quantum tunneling mechanisms. External electric fields offer effective control over spin S, while laser techniques enable precise modulation of the radial variation δR. Within the context of conformal space compression, tunneling effects may couple with Berry magnetic fields that possess topological protection. These findings demonstrate that geometric quantum bits (such as arbitrary control of anyons in topological quantum computing) and directional transport designs for novel transistors can be realized through radius-compression-induced Berry fields. For a quantum anomalous Hall insulator to maintain its Chern number (C = 1) and chiral edge state conduction within the topologically protected regime, the compression of its radius may lead to the observation of Berry-curvature-induced magnetic fields by strong external electric field.
Wenzhong Liu (Tue,) studied this question.