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.
[1] J. M. Leinaas and J. Myrheim, Nuovo Cim. B 37, 1 (1977).
[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).
Organizer：Qingrui Wang 王晴睿
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Speaker
Zhiyuan Wang 王致远
Max Planck Institute for Quantum Optics
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Time
Wed., 14:00-15:30, July 9th, 2025
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Venue
C548, Shuangqing Complex Building A
Online Tencent: 995-283-0954
About the speaker
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.
