We consider the effect of the coupling between two-dimensional (2D) quantum rotors near an XY ferromagnetic quantum critical point and spins of itinerant fermions. We analyze how this coupling affects the dynamics of rotors and the self-energy of fermions. A common belief is that near a q=0 ferromagnetic transition, fermions induce an ω/q Landau damping of rotors (i.e., the dynamical critical exponent is z=3) and Landau overdamped rotors give rise to non-Fermi liquid fermionic self-energy ς∝ω2/3. This behavior has been confirmed in previous quantum Monte Carlo (QMC) studies. Here we show that for the XY case the behavior is different. We report the results of large-scale quantum Monte Carlo simulations, which show that at small frequencies z=2 and ς∝ω1/2. We argue that the new behavior is associated with the fact that a fermionic spin is by itself not a conserved quantity due to spin-spin coupling to rotors, and a combination of self-energy and vertex corrections replaces 1/q in the Landau damping by a constant. We discuss the implication of these results to experiments.
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We thank R. M. Fernandes, M. H. Christensen, Y. Schattner, X. Wang, and E. Berg for valuable discussions. Y.Z.L., W.L.J., and Z.Y.M. acknowledge support from the RGC of Hong Kong SAR of China (Grants No. 17303019, No. 17301420, and No. AoE/P-701/20) and the Strategic Priority Research Program of the Chinese Academy of Sciences (Grant No. XDB33000000). We thank the Center for Quantum Simulation Sciences in the Institute of Physics, Chinese Academy of Sciences, the Computational Initiative at the Faculty of Science and the Information Technology Services at the University of Hong Kong and the Tianhe supercomputing platforms at the National Supercomputer Centers in Tianjin and Guangzhou for their technical support and generous allocation of CPU time. YW acknowledges support from NSF under Award No. DMR-2045871. The work by AVC was supported by the Office of Basic Energy Sciences, U.S. Department of Energy, under award DE-SC0014402. A.K. and A.V.C. acknowledge the hospitality of KITP at UCSB, where part of the work has been conducted. The research at KITP is supported by the National Science Foundation under Grant No. NSF PHY-1748958.
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