Possibility of hole confinement in the weak coupling regime of one dimensional ising antiferromagnet and the emergence of spin-charge separation in the bulk limit

TL;DR

This paper investigates hole dynamics in a one-dimensional Ising antiferromagnet, revealing confinement effects in weak coupling and free propagation with spin-charge separation in the bulk limit, supported by exact diagonalization results.

Contribution

It demonstrates the transition from hole confinement to free propagation and spin-charge separation in the bulk limit using exact diagonalization.

Findings

Power-law energy description in weak coupling regime

Hole confinement tends to break down as system size increases

Spin-charge separation observed in the bulk limit

Abstract

The energy of one hole in one dimensional Ising antiferromagnet is calculated using exact diagonalization (ED) method on finite systems with number of sites N ranging from 4 to 50. This study gives a power-law description for the hole energy in the weak coupling region (0.001 less than or equal to Jz/t and Jz/t less than or equal to 0.1).This power-law description can otherwise be understood as a weak string-like energy that tends to compromise the motion of the hole by confining it to its birth site. However, for large N, the hole is found to escape from this confinement and hence propagates as a free particle in agreement with theoretical results in the bulk limit and experimental observations from angle resolved photoemission spectroscopy (ARPES) of spin-charge separation. In the strong coupling regime (Jz/t greater than 1), the energy of the hole is found to be independent of the system size. Accordingly, the velocities corresponding to charge and spin degrees of freedom in this regime become comparable. Under this situation, the hole may be treated as a localized particle.