Anyons in One Dimension: Quantum Pairing and Quantum Dissipative Baths

• Applicants: Privatdozent Dr. Axel Pelster; Professor Dr. Michael Thorwart
• Subject Area: Theoretical Condensed Matter Physics
• Term: since 2025
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 547748180

A rather intriguing property of quantum mechanics is the indistinguishability of identical particles. This has far-reaching consequences for their statistical behaviour when two particles are spatially exchanged. In three dimensions, many-body wave functions are either symmetric or anti-symmetric with respect to this exchange and fundamental properties of particles obeying bosonic or fermionic statistics, respectively, arise. In reduced spatial dimensions, the many-particle configuration space may become topologically non- trivial instead, leading to fractional statistics of anyons, which interpolate between bosons and fermions. In two dimensions, the consequences are drastically manifest in the fractional quantum Hall effect, which physically originates from electrons with flux quanta behaving as anyons, thereby constituting a novel state of matter. Reducing further to one-dimensional (1D) anyons renders the topic even more interesting, since a spatial exchange is then intimately connected to strong particle interactions. The conceptual description of 1D anyons currently advances in new directions via anyon-Hubbard models which have attracted attention due to fascinating proposals to realize them in optical lattices with ultracold bosonic or fermionic atoms. These systems show exotic physical properties as, for instance, a quasi-condensation at finite momenta, statistically induced quantum phase transitions between insulating and superfluid phases, and an asymmetrically distributed light cone dynamics. All these are particular manifestations of the exotic quantum statistical features of anyonic systems. The present research proposal intends to reveal further key properties of 1D anyons, aiming at three objectives. The first one analyzes in a minimal model how two anyons can form pairs in an analogous way, as Cooper pairs of electrons are formed. With this, an anyonic connection between the pairing mechanisms in a two- component Fermi gas and a two-component Bose gas can be established, yielding anyonic superfluidity, where parity breaking is expected. The second objective shall reveal how quantum systems relax or dephase when coupled to anyonic quantum statistical baths. We focus on both the low-energy Luttinger-liquid and the weak- interaction Bogoliubov description of the anyon-Hubbard model. Concerning the central quantum system immersed in an anyonic bath, the paradigmatic cases of the quantum anyonic Brownian motion and the spin-anyon model are treated. The third objective represents a topical bracket and focuses on the common mathematical background for a field-theoretical description of 1D anyons. Starting from the canonical field quantization we will work out a path integral quantization for anyons, which necessitates an anyonic generalization of Grassmann numbers. We foresee the discovery of more exotic states of quantum matter and an advanced understanding of their properties.

• DFG Programme: Research Grants
• International Connection: USA
• Cooperation Partner: Professor Dr. Nathan Harshman