Universal information of critical quantum spin chains from wavefunction overlap
Yijian Zou
Abstract
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.
Topics & Concepts
Hamiltonian (control theory)Wave functionIsing modelPhysicsBoundary value problemQuantum mechanicsQuantumEigenvalues and eigenvectorsCritical point (mathematics)Excited stateCritical exponentBoundary (topology)Matrix product stateCentral chargeQuantum entanglementMathematicsPhase transitionMathematical analysisMathematical optimizationConformal mapQuantum many-body systemsQuantum and electron transport phenomenaPhysics of Superconductivity and Magnetism