---
abstract: '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.'
address:
- 'Department of Physics, Faculty of Science, Niigata University, Japan'
- 'Department of Physics, Graduate School of Science, University of Tokyo, Japan '
author:
- Kouichi Okunishi
- Hosho Katsura
title: ' Sine-square deformation and supersymmetric quantum mechanics '
---

[*Keywords*]{}: sine-square deformation, SUSY quantum mechanics

Introduction
============

Recently, spatial deformations of interaction couplings in low-dimensional quantum many-body systems have attracted much attention [@GendiarKN2009; @HikiharaN2011; @GendiarDLN2011; @Katsura2011; @Katsura2011B; @ShibataH2011; @Hotta2; @Hotta; @Hikihara_Suzuki; @Tada:2014kza; @Ishibashi; @MaruyamaKH2011; @exponential; @rainbow; @cosh]. A smooth cutoff of the coupling encoded in the real space is generally expected to suppress the scattering at the boundaries [@VekicW1993]. Among the various schemes, the sine-square deformation (SSD) in one-dimensional 