Resonating-Valence-Bond Physics Is Not Always Governed by the Shortest Tunneling Loops

Arnaud Ralko (1) , Ioannis Rousochatzakis (2, 3)

1 NEEL - TMC - Théorie de la Matière Condensée
2 School of Physics and Astronomy [Minneapolis]
3 MPI-PKS - Max-Planck-Institut für Physik komplexer Systeme

It is well known that the low-energy sector of quantum spin liquids and other magnetically disordered systems is governed by short-ranged resonating valence bonds (RVB). Here we show that the standard minimal trunca-tion to the nearest-neighbor valence bond (NNVB) basis fails completely even for systems where it should work the most, according to received wisdom. This paradigm shift is demonstrated for the quantum spin-1 2 square-kagome, where strong geometric frustration, similar to the kagome, prevents magnetic ordering down to zero temperature. The shortest tunneling events bear the strongest longer-range singlet fluctuations, leading to amplitudes that do not drop exponentially with the length of the loop L, and to an unexpected loop-six valence bond crystal (VBC), which is otherwise very high in energy at the minimal truncation level. 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. Introduction-The search for quantum spin liquids has been an active topic in condensed matter physics for many years [1-6, 18-21]. Recently, this search has gained new impetus from the discovery [7-15] of a series of layered spin-1 2 kagome an-tiferromagnets (AFMs), whose ideal nearest-neighbor (NN) Heisenberg limit stands out as the prime candidate for a Z 2 topological spin liquid [16, 17]. One of the earliest fundamental insights from the theory side is that the low-energy sector of all magnetically disordered AFMs should be governed by resonances between sufficiently short-ranged singlet or valence bond (VB) pair-ings [6, 18-21]. Casting this very physical picture into an effective Hamiltonian has been challenging for many years [22-31]. While one aspect of the problem, the non-orthogonality of the VBs [23], was essentially resolved recently [28-31], the really serious problem turns out to be the truncation to the NNVB basis, a problem that goes back to Zeng and Elser [24]. This is the second study that focuses on the impact of virtual singlets outside the NNVB basis to the tunneling physics. Ref. [31] has dealt with the 2D kagome, where the delicate competition between different resonances leads to a VBC [32-35] which is very fragile [29, 30, 36], and virtual singlets are essential to stabilize the Z 2 spin liquid [31]. The aim of this work is to show that virtual singlets have a strong qualitative effect in all disordered AFMs, even when the minimal NNVB truncation is expected to work the most, according to received wisdom. To this end, we have chosen an extreme case of an AFM, the square-kagome [37-42] of Fig. 1, which features a huge tunneling energy separation at the minimal truncation level. This happens because this system manifests the shortest resonances possible, the squares [ 4 in Fig. 1 (b)], with NNVB amplitudes that are five times stronger than the second-shortest, 'loop-six' events. This energy separation leads to the very robust 'pinwheel' VBC of Fig. 1 (c, left) [37, 40], well separated in energy from competing RVB states. Yet, even for such a system, virtual singlets change the physics qualitatively because they have very different impact

Domaines: Physique [physics]

Arnaud Ralko, Ioannis Rousochatzakis. Resonating-Valence-Bond Physics Is Not Always Governed by the Shortest Tunneling Loops. Physical Review Letters, 2015, 115 (16), pp.167202. ⟨10.1103/PhysRevLett.115.167202⟩. ⟨hal-01874533⟩