Exact plaquette singlet phases in an orthogonal-plaquette model

Abstract

We introduce a quantum spin-1/2 model hosting two exact plaquette singlet ground states in extended parameter regimes. There is an exact phase transition between both phases, at which the system has an extensive ground-state degeneracy. Further, the model exhibits an extensive number of conserved quantities, which allow the prediction of additional phases. We exploit this feature and explore the phase diagram in detail for two specific parameter regimes. The model is based solely on Heisenberg interactions and seems sufficiently simple to be realized in quantum materials. A general scheme to determine exact singlet product states is briefly discussed. (a) 1 J J v J h J (b) 1 0 2 4 1 3 pyramid plaquette p J 2 J v 2 J h 2 arXiv:1912.09060v1 [cond-mat.str-el]

A quantum magnetic analogue to the critical point of water

“…We note that the colour scales in c and d are truncated such that they do not include the peak values of C/T and ξ. e, Dimer spin-spin correlation function, ⟨S i • S j ⟩, showing a discontinuity with J/J D at low temperatures but continuous behaviour throughout the supercritical regime. The dashed black line, the equivalent of the critical isochore in water, shows the locus of points where this order parameter is constant at its critical-point value, ⟨S i • S j ⟩ = −0.372 (30).…”

“…1b), whereas the Shastry-Sutherland model favours singlets on the 'empty' plaquettes. From the sensitive energetic competition between the empty-plaquette and full-plaquette phases 30 , it is not surprising that the additional three-dimensional and Dzyaloshinskii-Moriya terms in SrCu 2 (BO 3 ) 2 could cause this discrepancy, and we expect the state we observe above 18 kbar and below 2 K to be the full-plaquette phase. Because both plaquette phases have twofold degenerate ground states (only half of the plaquettes may form singlets), the thermal transition has Ising symmetry independent of their empty-plaquette or full-plaquette nature, and our results are not affected by this issue.…”

“…The accuracy of the ansatz is controlled by the bond dimension, D, of the tensors (Methods). Whereas iPEPS has been applied previously to discuss the ground state of the Shastry-Sutherland model 14,15,30 , here we apply recently developed methods 17,22 for representing the thermal states of the system. We analyse the pure Shastry-Sutherland model, by which is meant a single 2D layer (Fig.…”

Valence-bond solids, vestigial order, and emergent SO(5) symmetry in a two-dimensional quantum magnet

“…Beyond the sign-problematic (in the most interesting parameter regimes) Shastry-Sutherland model and extensions of it [105], sign-free 2D J-Q models with twofold degenerate PVBS ground states can also be designed. In a "checker-board" J-Q (CBJQ) model, an unusual first-order transition between the AFM state and a Z 2 breaking PVBS ground state was found [65].…”