Dzyaloshinskii transition in a classical chiral Heisenberg model and analogy to DQC*

Magnetic systems with broken chirality can display diverse spin textures with a rich phase diagram due to competing interactions and fields [1]. A similar phenomenon has been realized even in a nonmagnetic valence-bond solid (VBS) state, where the chiral term favors a winding of the VBS order parameter [2]. This leads to new perspectives on deconfined quantum criticality (DQC) [3], a quantum phase transition beyond the Ginzburg-Landau (GL) paradigm, as a multicritical point in the extended phase diagram.

Here, as an effective model for the extended DQC phase diagram observed in [2], we numerically study a Heisenberg model with both the Dzyaloshinskii-Moriya interaction as well as three-fold clock-type anisotropy. The model exhibits two ordered phases: (i) a low-temperature clock ordered phase, and (ii) an intermediate incommensurate winding phase. Interestingly, the phase transition seems to be consistent with another beyond-GL criticality predicted by Dzyaloshinskii [4]. We discuss the details of the phase diagram, including the possibility of multicriticality in the effective model. 

[1] X. Z. Yu et. al., Nature 465, 901 (2010), Y. Nishikawa and K. Hukushima, Phys. Rev. B 94, 064428 (2016)

[2] B. Zhao, J. Takahashi, and A. W. Sandvik, Phys. Rev. Lett. 125, 257204 (2020)

[3] T. Senthil, et. al., Science 303, 1490 (2004)

[4] E. Dzyaloshinskii, Sov. Phys. JETP 20, 665 (1965)