Sine-square deformation and supersymmetric quantum mechanics

Understand

We investigate the sine-square deformation (SSD) of free fermions in one-dimensional continuous space.

• On the basis of supersymmetric quantum mechanics, we prove the correspondence between the many-body ground state of the system with SSD and that of the uniform system with periodic boundary conditions.
• We also discuss the connection between the SSD in the continuous space and its lattice version, where the geometric correction due to the real-space deformation plays an important role in relating the eigenstates of the lattice SSD with those of the continuous SSD.