Adiabatic Ground-State Properties of Spin Chains with Twisted Boundary Conditions

TL;DR

This paper investigates the adiabatic energy spectrum flow of Heisenberg spin chains with twisted boundary conditions, revealing the origins of spectral periodicity and its relation to irrelevant perturbations and fractional statistics.

Contribution

It demonstrates that spectral period 2 arises from irrelevant perturbations in the effective field theory, and distinguishes the origin of the period in the Haldane-Shastry model as related to fractional statistics.

Findings

Period 2 in energy spectrum is due to irrelevant perturbations.

Haldane-Shastry model's period reflects fractional statistics.

Spectral periodicity may be common in 1D interacting lattice models.

Abstract

We study the Heisenberg spin chain with twisted boundary conditions, focusing on the adiabatic flow of the energy spectrum as a function of the twist angle. In terms of effective field theory for the nearest-neighbor model, we show that the period 2 (in unit $2\pi$) obtained by Sutherland and Shastry arises from irrelevant perturbations around the massless fixed point, and that this period may be rather general for one-dimensional interacting lattice models at half filling. In contrast, the period for the Haldane-Shastry spin model with $1/r^2$ interaction has a different and unique origin for the period, namely, it reflects fractional statistics in Haldane's sense.