Quantum critical point of the Ising chain from boundary effects

We propose two easy-to-study observables in the quantum Ising chain with open boundary conditions. They measure the length at which boundaries affect the longitudinal or transverse magnetization. We show that their finite-size scaling behaviour encodes the position of the quantum critical point and the universal scaling exponent $\nu$. The applicability of proposed observables in small systems is also discussed. We expect that our results will be useful in quantum simulation of spin systems.