Level Spectroscopy in Quantum Antiferromagnets Using Monte Carlo Simulations

The low-energy spectrum of antiferromagnets reveal valuable information about the nature of the phase or phase transition in such systems. I review the recent works done in collaboration with Suwa and Sandvik (Phys Rev B 92 195145 (2015), Phys Rev B 94 144416 (2016)) on how to probe the dispersion of the excitations in a variety of SU(2) symmetric S = 1/2 spin systems using quantum Monte-Carlo methods. Various applications are discussed in both one and two dimensions, which include probing the critical excitations for conventional and unconventional quantum critical points. In the latter case, the excitation spectrum is highly unusual and has additional gapless modes and possible emergent symmetries which are not present otherwise.