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

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[π(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.

9 pages, 6 figures. v2: accepted version

References in corpus (6)

• Connecting distant ends of one-dimensional critical systems by a sine-square deformation
• Boundary effects in the density-matrix renormalization group calculation
• Exact ground state of the sine-square deformed XY spin chain
• Suppression of finite-size effects in one-dimensional correlated systems
• Hyperbolic Deformation on Quantum Lattice Hamiltonians
• Scaling Relation for Excitation Energy Under Hyperbolic Deformation

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