Quantum scaling of the spin lattice relaxation rate in the checkerboardJ-Qmodel

Motivated by recent progress on the experimental realization of proximate deconfined quantum critical point in a frustrated quantum magnet, we study the low-energy spin dynamics of a related checkerboardJ-Qmodel by using quantum Monte Carlo simulations. The ground state of this model undergoes a weakly first-order quantum phase transition with an emergentO(4) symmetry between an antiferromagnetic state and a plaquette valence bond solid. The calculated spin lattice relaxation rate of nuclear magnetic resonance,1/T1, exhibits distinct low-temperature behaviors depending on the ground states. With decreasing the temperature,1/T1rises up on the antiferromagnetic side, characterizing a crossover to the renormalized classical regime, whereas1/T1drops exponentially on the side of valence bond solid, reflecting the gap opening in the plaquette ordered phase. The extracted spin gap scales with the distance to the transition point as a power-law with an exponentφ ≈ 0.3, consistent with the scaling ansatzϕ=νzwithν ≈ 0.3 andz = 1. Near the quantum phase transition, the temperature dependent1/T1shows a broad crossover regime where a universal scaling1/T1∼Tηwithη ≈ 0.6 is found. Our results suggest a quantum scaling regime associated with the emergent enhanced symmetry near this first-order quantum phase transition.