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

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.

6 pages, revtex, 3 figures available on request, to appear in J. Phys. Soc. Jpn

References in corpus (4)

• Twisted Boundary Conditions and the Adiabatic Ground State for the Attractive XXZ Luttinger Liquid
• Exact solution and spectral flow for twisted Haldane-Shastry model
• GAPS IN THE HEISENBERG-ISING MODEL
• Transport coefficients, effective charge and mass for multicomponent systems with fractional exclusion statistics

Cited by in corpus (10)

• Twist Boundary Conditions of Quantum Spin Chains near the Gaussian Fixed Points
• $SU(2)/Z_2$ symmetry of the BKT transition and twisted boundary conditio n
• Magnetization-plateau state of the S=3/2 spin chain with single ion anisotropy
• Breakdown of the magnetization plateau of the S=1/2 ferromagnetic-ferromagnetic-antiferromagnetic trimerized spin chain with anisotropy
• Bifurcation at the c=3/2 Takhtajan-Babujian point to the c=1 critical lines
• Spectral flow of non-hermitian Heisenberg spin chain with complex twist
• Polarization amplitude near quantum critical points
• Bosonization with a background $U(1)$ gauge field
• Bloch oscillations in the spin-1/2 XXZ chain
• SU(ν) Generalization of Twisted Haldane-Shastry Model