Sine-square deformation and supersymmetric quantum mechanics
Kouichi Okunishi, Hosho Katsura
TL;DR
This paper explores the sine-square deformation in continuous free fermion systems, establishing a supersymmetric quantum mechanics framework that links the deformed and uniform ground states, and discusses lattice-continuous space connections.
Contribution
It introduces a supersymmetric quantum mechanics approach to analyze SSD in continuous systems and clarifies the relationship between lattice and continuous SSD eigenstates.
Findings
Proves the ground state correspondence between SSD and uniform systems
Highlights the role of geometric correction in lattice-continuous space connection
Provides a theoretical foundation for understanding SSD in continuous quantum systems
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.
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