Detecting the footprint of central charge using IBM quantum simulator
Phase transitions are ubiquitous phenomena in physics. Physical systems close to phase transition are known to become scale-invariant and manifest universality. In two dimensions, there is an infinite-dimensional algebra of local conformal transformations which can be solved exactly and the corresponding field theory description is known as conformal field theory (CFT). While the central charge is one of the characterizations of the underlying symmetry of the corresponding CFT's, they have not been experimentally detected. In this work, we measure the central charge associated with CFT corresponding to various spin chains such as the transverse-field Ising model and XXZ chain by preparing the IBM quantum system. We show that at and close to the critical point, Shannon entropy of measurable quantities such as formation probabilities manifest a footprint of central charge allowing us to extract the central charge. Leveraging on the power of variational algorithms such as Variational Quantum Eigensolver (VQE) and Adiabatically-Assisted Variational Quantum Eigensolver (AAVQE), we prepare the ground state of the transverse-field Ising model with periodic and open boundary conditions, at and near the critical point and perform our measurement for various system sizes.