Spherical Deformation for One-dimensional Quantum Systems

TL;DR

This paper investigates how a spherical deformation of interaction strengths in one-dimensional quantum systems improves the convergence of ground-state energy calculations, demonstrating a 1/N^2 correction rate for finite-size effects.

Contribution

It introduces a spherical deformation method that accelerates the convergence of ground-state energy in 1D quantum systems with open boundaries.

Findings

Finite-size correction scales as 1/N^2 with spherical deformation.

Spherical deformation leads to faster convergence of energy per site.

The approach is explained via spherical geometry insights.

Abstract

System-size dependence of the ground-state energy E^N is investigated for N-site one-dimensional (1D) quantum systems with open boundary condition, where the interaction strength decreases towards the both ends of the system. For the spinless Fermions on the 1D lattice we have considered, it is shown that the finite-size correction to the energy per site, which is defined as E^N / N - \lim_{N \to \infty} E^N / N, is of the order of 1 / N^2 when the reduction factor of the interaction is expressed by a sinusoidal function. We discuss the origin of this fast convergence from the view point of the spherical geometry.