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Center for Nonlinear Studies |
Most continuous phase transitions are described by the Landau-Ginzburg-Wilson (LGW) paradigm where an effective action is expanded in powers of an order parameter and its derivatives. For more than a decade, the deconfined quantum criticality has caught a great deal of attention as a highly non-trivial phase-transition point beyond the LGW paradigm. The low-energy (or long-length-scale) physics will be described not by the original degrees of freedom manifest in the model Hamiltonian but by an internal degrees of freedom emerging as fractional excitation. The existence or the stability of such a deconfined quantum-critical point has been debated for the Neel to the valence-bond-solid transition in the two-dimensional quantum spin systems, the three-dimensional non-compact CP$^{N-1}$ action, the loop, and the dimer models. We have studied the excitation energy around the deconfined quantum-critical point in the two-dimensional quantum spin system, the SU(2) J-Q model, by means of the unbiased worldline quantum Monte Carlo method. The energy gaps are estimated by the generalized moment method capturing the asymptotic behavior of the imaginary-time correlation. The transition point is located by the level spectroscopy using the lowest gaps. We find strong quantitative evidence for deconfined linearly dispersing spinons with multiple gapless points at ${\bf k}=(0,0)$, $(\pi,0)$, $(0,\pi)$, and $(\pi,\pi)$, as inferred from two-spinon excitations (S=0 and S=1 states) around these points. We also observe a duality between singlet and triplet excitations at the critical point and inside the ordered phases, in support of an enhanced symmetry, possibly SO(5).
Host: Kipton Barros