Organizer: 王晴睿
Abstract: It is commonly believed that there are only two types of particle exchange statistics in quantum mechanics, fermions and bosons, with the exception of anyons in two dimension [1-3]. In principle, a second exception known as parastatistics, which extends outside of two dimensions, has been considered [4] but was believed to be physically equivalent to fermions and bosons [5,6]. In this talk I present a recent work of mine [7] which shows that nontrivial parastatistics inequivalent to either fermions or bosons can exist in physical systems. I first formulate a second quantization theory of paraparticles that is significantly different from previous theories, which turns out to be the key to get new physics. I then present a family of exactly solvable quantum spin models where free paraparticles emerge as quasiparticle excitations. Next, I demonstrate a distinctive physical consequence of parastatistics by proposing a challenge game [8] that can only be won using physical systems hosting paraparticles, which also gives a quantum information application of parastatistics. I then mention a categorical description of emergent paraparticles in 2D or 3D gapped phases in the framework of tensor category theory, where I find that parastatistics correspond to an exotic type of symmetric fusion categories. I will end by discussing several recent developments and future directions, including generalized symmetries of paraparticle systems, Bogoliubov-type Hamiltonians that describe "paraparticle superconductors", and R-quantized relativistic field theories that may model elementary paraparticles.
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[2] F. Wilczek, Phys. Rev. Lett. 48, 1144 (1982); Phys. Rev. Lett. 49, 957 (1982).
[3] C. Nayak, S. H. Simon, A. Stern, M. Freedman, and S. Das Sarma, Rev. Mod. Phys. 80, 1083 (2008).
[4] H. S. Green, Phys. Rev. 90, 270 (1953).
[5] S. Doplicher, R. Haag, and J. E. Roberts, Commun. Math. Phys. 23, 199 (1971); 35, 49 (1974).
[6] S. Doplicher and J. E. Roberts, Commun. Math. Phys. 28, 331 (1972).
[7] Z. Wang and K. R. A. Hazzard, Nature 637, 314 (2025).
[8] Z. Wang, arXiv:2412.13360 (2024).
Dr. Zhiyuan Wang received his B.S. in Physics from Peking University in 2016 and completed his Ph.D. in Physics at Rice University in 2022. He then started a postdoc position at the Max Planck Institute for Quantum Optics and will begin another postdoc at the Perimeter Institute this September. This summer, he is visiting YMSC as a researcher for two months, during July and August. His research interests lie in topological order and particle statistics—particularly from rigorous mathematical perspectives—as well as exactly solvable models in quantum many-body physics.
