Twisted Boundary Conditions and the Adiabatic Ground State for the Attractive XXZ Luttinger Liquid

TL;DR

This paper investigates the adiabatic ground state of the attractive XXZ Luttinger liquid with twisted boundary conditions, revealing flux periodicity, bound state formation, and Berry's phase behavior depending on interaction parameters.

Contribution

It introduces the analysis of the adiabatic ground state and flux periodicity for the attractive XXZ chain with noninteger interaction parameters, highlighting bound state dynamics and Berry's phase.

Findings

Flux period is 2 flux quanta for noninteger p.

Formation of zero-energy bound states at Fermi surface during adiabatic process.

Berry's phase equals [p] times pi.

Abstract

The one-dimensional attractive lattice fermion gas equivalent to the Heisenberg-Ising spin 1/2 chain is studied for a ring geometry threaded by magnetic flux. We find that for charged fermions having interaction strength $\Delta=\cos(\pi / p)$ with $p$ {\it noninteger}, the adiabatic ground state is periodic in the magnetic flux threading the chain, with period 2 flux quanta, as found by Shastry and Sutherland for the repulsive case. We find that, at particular values of the threading field, a sequence of initially zero-energy bound states form at the Fermi surface during the adiabatic process, the largest containing $[p]$ (the integer part of $p$) fermions. This largest bound state moves around to the other Fermi point and sequentially unbinds. We find Berry's Phase for the whole process to be $[p] \pi$. For $p$ {\it integer}, as $\Phi$ increases, eventually all the particles in the system go into bound states of size $[p]$. The period in this case is of order the size of the system.