Thermodynamics and phase transitions for the Heisenberg model on the pinwheel distorted kagome lattice

Abstract

We study the Heisenberg model on the pinwheel distorted Kagome lattice as observed in the material Rb2Cu3SnF12. Experimentally relevant thermodynamic properties at finite temperatures are computed utilizing numerical linked-cluster expansions. We also develop a Lanczos-based zerotemperature numerical linked-cluster expansion to study the approach of the pinwheel distorted lattice to the uniform Kagome lattice Heisenberg model. We find strong evidence for a phase transition before the uniform limit is reached, implying that the ground state of the Kagome lattice Heisenberg model is likely not pinwheel dimerized and is stable to finite pinwheel dimerizing perturbations.

Numerical linked-cluster expansions for disordered lattice models

“…A similar idea was implemented to study the valence-bond solid to spin liquid transition of the pinwheel distorted kagome lattice Heisenberg model. 36 As a final case study we turn to the disordered frustrated Heisenberg model on the checkerboard lattice. We adopt the NLCE with a square expansion, where the building block is the corner-sharing 2 × 2 plaquette with crossed next-nearest-neighbor bonds as opposed to a single site; the order of the expansion indicates Lines are the same as in Fig.…”

Quantum phase transition between disordered and ordered states in the spin-12kagome lattice antiferromagnet(Rb1−xCsx<

“…1(c). 32,33,35,36 The gapped ground state in Rb 2 Cu 3 SnF 12 arises from the inequivalence of the exchange interactions, i.e., J 1 /k B = 216 K, J 2 = 0.95J 1 , J 3 = 0.85J 1 and J 4 = 0.55J 1 .…”

Numerical linked-cluster expansion for the distorted kagome lattice Heisenberg model

“…We also point out the clear deviation of the ED results with the 12-site cluster from NLCE at 0.1 < T < 0.5 [see e.g., Figure 4(a)]. The results for other values of λ [25] show that the convergence in NLCE at low temperatures is lost before λ reaches unity. Therefore, it is natural to ask, what is the value of λ beyond which NLCE no longer converges at low temperatures?…”

“…We calculate the bond energies, B α , for the four different types of bonds that exist on the lattice. The difference between B 1 (corresponding to the pinwheel dimers) and any other bond can be used as the VBS order parameter [25]. Here, we choose this difference to be between B 1 and the average of the other three, (B 2 +B 3 +B 4 )/3−B 1 .…”