Extended Aharonov-Bohm period analysis of strongly correlated electron systems

The 'extended Aharonav-Bohm (AB) period' recently proposed by [K. Kusabahe and H. Aoki: J. Phys. Sec, Jpn. 85 (1996) 2772] is extensively studied numerically for finite size systems of strongly correlated electrons. While the extended AB period is the system length times the flux quantum for noninteracting systems; we have found the existence of the boundary across which the period is halved or another boundary into an et-en shorter period on the phase diagram for these models, If me compare this result with the phase diagram predicted From the Tomonaga-Luttinger theory, devised for low-energy physics, the halved period (or shorter periods) has a one-to-one correspondence to the existence of the pairing (phase separation or metal-insulator transition) in these models, We have also found for the t-J model that the extended AB period does not change across the integrable-nonintegrable boundary despite the totally different level statistics.