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

TL;DR

This paper demonstrates that sine-square deformation in one-dimensional quantum critical systems can effectively connect the system's ends, transforming open-edge systems into ones with periodic topology, thus offering a new way to control quantum state topology.

Contribution

It introduces a novel application of sine-square deformation to alter the topology of quantum states in critical spin systems, linking open edges to create a periodic ground state.

Findings

Sine-square deformation links system ends, changing topology.

Ground state becomes effectively periodic despite open edges.

Deformation controls quantum state topology via energy-scale modification.

Abstract

We study the one-dimensional quantum critical spin systems with the sine-square deformation, in which the energy scale in the Hamiltonian at the position $x$ is modified by the function $f_x = \sin^2\left[{\pi}{L}(x-1/2)]$, 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 wave function. Our results propose a new method to control the topology of quantum states by energy-scale deformation.