Sine-square deformation and supersymmetric quantum mechanics

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.

18 pages, 3 figures; v2: typos corrected, references updated

References in corpus (8)

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Cited by in corpus (13)

• Evolution operators in conformal field theories and conformal mappings: the entanglement Hamiltonian, the sine-square deformation, and others
• Quantum dynamics in sine-square deformed conformal field theory: Quench from uniform to non-uniform CFTs
• Floquet conformal field theories with generally deformed Hamiltonians
• Sine-square deformation and Mobius quantization of two-dimensional conformal field theory
• Holographic Duals of Inhomogeneous Systems: The Rainbow Chain and the Sine-Square Deformation Model
• Dipolar quantization and the infinite circumference limit of two-dimensional conformal field theories
• Magnetic susceptibility of quantum spin systems calculated by sine square deformation: one-dimensional, square lattice, and kagome lattice Heisenberg antiferromagnets
• Zero-energy states in conformal field theory with sine-square deformation
• Conformal Quantum Mechanics and Sine-Square Deformation
• Time development of conformal field theories associated with $L_1$ and $L_{-1}$ operators
• Sine-square deformed mean-field theory
• Analysis for Lorentzian conformal field theories through sine-square deformation
• Energy Scale Deformation on Regular Polyhedra