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Lorentz symmetry is commonly assumed to be an intrinsic requirement of the(2+1)d deconfined quantum phase transition (DQPT), and the conformal fieldtheory (CFT) can be utilized. The dynamics of DQPT in the Kagome lattice areexplored by using a combination of large-scale quantum Monte Carlo simulationsand stochastic analytic continuation. In the valence-bonded solid phase, thefragmentation of a nearly flat band with a finite energy gap is observed aroundthe K point. At the deconfined quantum critical point, besides the lineardispersion at the $\Gamma$ point, another one is found at the K point.Counterintuitively, these two gapless modes take different speeds equal to0.319(8) and 0.101(9), indicating the absence of Lorentz symmetry. Aftercarefully inspecting the snapshot of the simulation, we discovered the fastmode at $\Gamma$ point corresponding to the deconfinement of spinons(fractional charges), and the slow mode at K point is related to the quantumstring ( generalized symmetry). Our work will extend the understanding of phasetransition, and intrigue the field of topological quantum field theory.

Does Deconfined Quantum Phase Transition Have to Keep Lorentz Symmetry? Two Velocities of Spinon and String