Metastable Kitaev Spin Liquids in Isotropic Quantum Heisenberg Magnets

Metastable states with surprising properties abound in Hilbert space. We study unfrustrated isotropic spin-\half Heisenberg models in honeycomb lattice and find emergence of $\mathit{\text{metastable}}\mathit{\text{Kitaev}}\mathit{\text{spin}}\mathit{\text{liquids}}\mathit{\text{having}}\mathit{\text{a}}\mathit{\text{2-spin}}\mathit{\text{nematic}}\mathit{\text{long}}\mathit{\text{range}}\mathit{\text{order}}$, via spontaneous symmetry breaking. Decomposition of isotropic Heisenberg Hamiltonian $H^H$ into an exact sum of 3 noncommuting (permuted) Kitaev Hamiltonians, $H^H$ = $H_{\mathrm{x}\mathrm{y}\mathrm{z}}^K+H_{\mathrm{y}\mathrm{z}\mathrm{x}}^K+H_{\mathrm{z}\mathrm{x}\mathrm{y}}^K,$ helps us build a degenerate $\mathit{\text{manifold}}\mathit{\text{of}}\mathit{\text{flux}}\mathit{\text{free}}\mathit{\text{metastable}}\mathit{\text{Kitaev}}\mathit{\text{spin}}\mathit{\text{liquid}}\mathit{\text{vacua}}$ and vector Fermionic (Goldstone like) collective modes. We introduce a method, $\mathit{\text{symmetric}}\mathit{\text{decomposition}}\mathit{\text{of}}\mathit{\text{Hamiltonians}}$, which might help craft $\mathit{\text{designer}}\mathit{\text{metalstable}}\mathit{\text{phases}}$. It is likely that small Kitaev interactions present in Jackeli-Khaliullin-Kitaev materials, with dominant Heisenberg couplings, bring in metastable Kitaev spin liquid features in real experiments. Present work opens possibilities of performing quantum computation and other tasks, using exotic quasiparticles and exotic metastable states, present in nonexotic real systems.