Quantum Critical Phenomena in the Thulium Vanadates and the long-range Transverse Field Ising Model

Thulium Vanadate materials exhibit ferro quadrupolar order which can be destabilized by application of a magnetic field leading to a quantum critical phenomena. The experimental observations exhibit a dichotomy between mean-field behavior with a jump in the heat capacity and a wipeout in Nuclear Magnetic Resonance spin-echo experiments inside a 'quantum-critical fan' implying gapless fluctuations with growing correlations and entanglement. We show that the infinite-range transverse field Ising model captures both these aspects. The Hilbert space of the long-range model breaks up into a large number of disconnected sectors allowing one to numerically study a system with thousands of spins and accurately model the quantum critical phenomena. The differences with mean-field theory will be highlighted.