Universal information of critical quantum spin chains from wavefunction overlap

Given a critical quantum spin chain, we show how universal information about its quantum critical point can be extracted from wavefunction overlaps. More specifically, we consider overlap between low-energy eigenstates of the spin chain Hamiltonian with different boundary conditions, namely periodic boundary conditions and open boundary conditions. We show that such overlaps decay polynomially with the system size, where the exponent only depends on the central charge. Furthermore, the bulk-to-boundary operator product expansion (OPE) coefficients can be extracted from the overlaps involving excited states. We illustrate the proposal with the Ising model and the three-state Potts model.

Automated summary

This study demonstrates how universal information about the quantum critical point of a critical quantum spin chain can be extracted from wavefunction overlaps. Specifically, the overlap between low-energy eigenstates of the spin chain Hamiltonian with different boundary conditions is considered. It is found that such overlaps decay polynomially with the system size, with the exponent solely dependent on the central charge. Additionally, the bulk-to-boundary operator product expansion (OPE) coefficients can be obtained from the overlaps involving excited states.