Resonating valence bond physics is not always governed by the shortest tunneling loops

Abstract

It is well known that in quantum spin liquids and other magnetically disordered systems, the tunneling amplitudes between different nearest-neighbor valence bond (NNVB) configurations drop exponentially in the length L of the tunneling loops. Here we show that virtual excursions outside the NNVB basis can alter completely this fundamental quantum-mechanical notion even in extreme cases where the minimal NNVB truncation appears very robust. This paradigm shift is demonstrated for the quantum spin-1/2 square-kagome, where strong geometric frustration, similar to the two-dimensional kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events suffer from the strongest fluctuations, leading to amplitudes that do not drop exponentially with L, and to an unexpected loop-six valence bond crystal phase, which would otherwise be very far in the parameter space in the absence of virtual singlets. The low-energy effective description gives in addition a clear example of correlated loop processes that depend not only on the type of the loop but also on its lattice embedding, a direct manifestation of the long-range nature of the virtual singlets.

5 pages, 4 figures + supplementing material

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• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Tensor network study of the spin-1/2 Heisenberg anti-ferromagnet on the Shuriken lattice
• Non-Coplanar Magnetic Orders in Classical Square-Kagome Antiferromagnets
• Reentrance of disorder in the anisotropic shuriken Ising model
• Magnetism of the $s=1/2$ $J_1$-$J_2$ square-kagome lattice antiferromagnet
• $\require{mhchem}$Quantum paramagnetism in the decorated square-kagome antiferromagnet $\ce{Na6Cu7BiO4(PO4)4Cl3}$
• Static and resonant properties of decorated square kagome lattice compound KCu${}_7$(TeO${}_4$)(SO${}_4$)${}_5$Cl
• Competing orders in a frustrated Heisenberg model on the Fisher lattice
• The magnetization process of classical Heisenberg magnets with non-coplanar cuboc ground states
• Quantum phase diagram of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the square-kagome lattice: a tensor network study