Broken discrete symmetries in a frustrated honeycomb antiferromagnet

The search for a quantum spin liquid – an insulatingmagnet with a gapless ground state which breaks neitherlattice nor spin symmetries – has been the focus of manystudies on two-dimensionalfrustrated quantum antiferro-magnets [1–4]. Such systems are assumed to be the maincandidates to describe a rich variety of unconventionalphases, phase transitions and critical points with decon-fined fractional excitations [5–7]. Frustration plays animportant role in classical systems as well. Within thiscontext, the phenomenon of order by disorder (OBD) [8]is the perfect example where the interplay of frustrationand fluctuations produces the emergence of unexpectedorder. OBD implies that certain low-temperature spinconfigurations are favored by higher entropy rather thanby lower energy. For instance, some frustrated spin mod-els may exhibit magnetization plateaus even at the clas-sical level [9, 10]. In this case fluctuations are responsi-ble for stabilizing particular collinear spin configurationsthat have softer excitation spectra compared to a gen-eral noncollinear spin state. Another nontrivial fluctua-tion effect is a finite-temperature transition in 2D Heisen-berg antiferromagnets related to breaking (discrete) lat-tice symmetries in the absence of a long-range magneticorder [11]. Studying various fluctuation-induced types ofmagnetic order is important in order to establish robust-ness of a hypothetical spin-liquid state.Here, we consider the Heisenberg antiferromagnet ona honeycomb lattice, model realized in a number of realmagnetic materials [12–15]. Recent interest in this modelis largely motivated by the experimental realization ofthe spin-liquid state in Bi