Chisa Hotta : Formation of quantum spin liquids

Since Anderson’s resonating-valence-bond (RVB) picture was proposed, quantum spin liquids (QSLs) have been actively studied in a variety of theoretical models, including the triangular-lattice Hubbard, kagome, and (J_1)-(J_2) Heisenberg models, as well as the Kitaev honeycomb model. Experimental efforts have also identified several candidate materials, including K-ET₂Cu₂(CN)₃, ZnCu₃(OH)₆Cl₂ (Herbertsmithite), a-RuCl₃, and NaYbSe₂. Initially, the absence of magnetic ordering down to the lowest accessible temperatures was often taken as a key signature of QSL behavior More recently, advances in quantum many-body theory have enabled a more microscopic characterization based on entanglement and topological order. In this picture, a QSL exhibits fluctuating loop degrees of freedom subject to nonlocal constraints, which give rise to distinct topological sectors. However, how these loops and constraints emerge from microscopic spin Hamiltonians is hidden, particularly in Heisenberg models.

Here we address this question by examining the many-body wave functions of QSLs. We recently obtained an exact tensor-network representation of the complete set of eigenstates of the Kitaev honeycomb model, allowing us to directly trace the emergence of topological entanglement. We then extend this perspective to the kagome QSL using parton theory. We find that the Gutzwiller projection, which converts a fermionic parton state into a physical spin state, generates the underlying loop structure and the characteristic (-ln 2) contribution associated with Z₂ topological order.

We apply this framework to understand Herbertsmithite, where magnetic impurities located between kagome spin-liquid layers can interact through the intervening QSL. We show that the resulting RKKY interaction has a structure fundamentally different from previous treatments based on free Majorana fermions, which do not fully incorporate the gauge constraints essential to topological order.