Chiral liquid phase of simple quantum magnets

We study a T = 0 quantum phase transition between a quantum paramagnetic state and a magnetically ordered state for a spin S = 1 XXZ Heisenberg antiferromagnet on a two-dimensional triangular lattice. The transition is induced by an easy-plane single-ion anisotropy D. At the mean-field level, the system undergoes a direct transition at a critical D = D-c between a paramagnetic state at D > D-c and an ordered state with broken U(1) symmetry at D < D-c. We show that beyond mean field the phase diagram is very different and includes an intermediate, partially ordered chiral liquid phase. Specifically, we find that inside the paramagnetic phase the Ising (Jz) component of the Heisenberg exchange binds magnons into a two-particle bound state with zero total momentum and spin. This bound state condenses at D > D-c, before single-particle excitations become unstable, and gives rise to a chiral liquid phase, which spontaneously breaks spatial inversion symmetry, but leaves the spin-rotational U(1) and time-reversal symmetries intact. This chiral liquid phase is characterized by a finite vector chirality without long-range dipolar magnetic order. In our analytical treatment, the chiral phase appears for arbitrarily small Jz because the magnon-magnon attraction becomes singular near the single-magnon condensation transition. This phase exists in a finite range of D and transforms into the magnetically ordered state at some D < D-c. We corroborate our analytic treatment with numerical density matrix renormalization group calculations.