Vector Chiral Phases in the Frustrated 2D $XY$ Model and Quantum Spin Chains

The phase diagram of the frustrated 2D classical and 1D quantum $XY$ models is calculated analytically. Four transitions are found: the vortex unbinding transitions triggered by strong fluctuations occur above and below the chiral transition temperature. Vortex interaction is short range on small and logarithmic on large scales. The chiral transition, though belonging to the Ising universality class by symmetry, has different critical exponents due to nonlocal interaction. In a narrow region close to the Lifshitz point a reentrant phase transition between paramagnetic and quasiferromagnetic phase appears. Applications to antiferromagnetic quantum spin chains and multiferroics are discussed.

Figure 1

Left panel: Phase diagram of the HXY model as a function of $K_2/K_0$, calculated from (18). The bold lines mark the BKT transition, the dashed line marks the chiral transition. Right panel: Quantum critical regions, $T>T_{p,c}$ for the chiral and $T>T_{p,\mathrm{KT}}$ for the magnetic transition, respectively, of a frustrated quantum spin chain. The thick arrow denotes the parameter region accessible in $\mathrm{Gd}{(hfac)}_3\mathrm{NITiPr}$.