Sine-square deformation of free fermion systems in one and higher dimensions

TL;DR

This paper investigates the sine-square deformation (SSD) in free fermion systems across one and higher dimensions, showing it preserves translational invariance and suppresses boundary effects, with exact ground states in certain cases.

Contribution

It provides a simple theory explaining how SSD maintains translational invariance and demonstrates its effectiveness in higher dimensions for boundary suppression.

Findings

SSD reproduces the ground state of uniform periodic systems in 1D.

In 2D, SSD effectively suppresses boundary modulations.

Exact Fermi sea ground state for certain 1D systems with SSD.

Abstract

We study free fermion systems with the sine-square deformation (SSD), in which the energy scale of local Hamiltonians is modified according to the scaling function f(x)=sin^2[\pi(x-1/2)/L], where x is the position of the local Hamiltonian and L is the length of the system in the x direction. It has been revealed that when applied to one-dimensional critical systems the SSD realizes the translationally-invariant ground state which is the same as that of the uniform periodic system. In this paper, we propose a simple theory to explain how the SSD maintains the translational invariance in the ground-state wave function. In particular, for a certain one-dimensional system with SSD, it is shown that the ground state is exactly identical with the Fermi sea of the uniform periodic chain. We also apply the SSD to two-dimensional systems and show that the SSD is able to suppress the boundary modulations from the open edges extremely well, demonstrating that the SSD works in any dimensions and in any directions.