Connecting distant ends of one-dimensional critical systems by a sine-square deformation

We study one-dimensional quantum critical spin systems with sine-square deformation, in which the energy scale in the Hamiltonian at position x is modified by the function fₓ=sin²[πL(x-1/2)], where L is the length of the system. By investigating the entanglement entropy, spin correlation functions, and wave-function overlap, we show that the sine-square deformation changes the topology of the geometrical connection of the ground state drastically: Although the system apparently has open edges, the sine-square deformation links those ends and realizes the periodic ground state at the level of the wave function. Our results propose a method to control the topology of quantum states by energy-scale deformation.