Weak Finite-Size Dependence of Velocity and Strong Phase Dependence of Central Charge

摘要

We study the finite-size scaling behavior of velocity and central charge for different coupling constantsand different phases in (1+1)-dimensional lattice model in very short chains. Using XXZ spin 1/2 chains with 15 orfewcr sites, we demonstrate the weak finite-size dependence of spinon velocity for any magnitude of coupling strengthJz and the strong phase dependence of central charge. This behavior of velocity and central charge in different couplingconstants and different phases gives a method to determine phase transitions of (1+1)-dimensional mnodels. This methodis simple and cfficient by utilizing only the ground state energy of very short finite-size chains. It is also general andpowerful for various one-dimensional lattice models and it uncovers even the weakest Berezinsk Kosterlitz-Thoulessphase transitions.