Phase transitions and critical behaviors of XXZ ladders

Abstract

We study the phase transitions and critical behaviors of the two-leg dimerized XXZ ladders by extensive Monte Carlo simulations and finite-size scaling analysis. For the Heisenberg model on the staggered ladder, we verify that the phase transition between the two topological phases belongs to the four-state Potts universality class; for the XY case (), the phase diagram is similar to the Heisenberg case, but the critical behavior belongs to a new universality class; for the Ising case (), we find three topological phases, in which one of them has both the topological orders and the local magnetic order; the two phase transitions associated with these phases also belong to the Ising universality class. On the columnar ladder, we have not found any phase transition for all the three cases. Furthermore, we find that the magnetic field can also induce phase transitions for both the staggered and columnar models, and the topological phases are in certain magnetic plateaux. For the staggered model, we study the phase transition associated with the plateau of zero magnetization; we find that the critical behavior of the string order parameter belongs to the 2D classical Ising model, and the scaling behavior of the uniform magnetization is different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class. For the columnar model, we study the phase transition associated with the plateau whose magnetization is half of the saturation value, which has fractional quantized Berry phase; in this case, the conventional string order parameters are not applicable as order parameters, we determine the critical point of this phase transition by the scaling behavior of the uniform magnetization which is also different from the Dzhaparidze–Nersesyan–Pokrovsky–Talapov universality class.