arXiv subjects

Arist Zhenyuan Yang

Publications and source records attributed to Arist Zhenyuan Yang.

3 recordsLinked to original sources

arXiv2026

On the Symmetries of Anisotropic Spin Interaction Models

We show that anisotropic spin interactions do not merely break spin-space group (SSG) symmetries, but instead twist them through cohomology invariants, yielding symmetry classes beyond subgroups of $ O(3)\times \operatorname{Isom}(\mathbb{R}^3) $. This requires redefining the spin-only group $ S_0 $ in terms of proper spin rotations. Based on this unitary $ S_0 $, we formulate a twisted SSG (tSSG) theory that captures the complete set of spin-space symmetries. We then study a spin-1 model with tSSG symmetry using linear flavor wave theory and find $\mathbb{Z}_2$ topological quadrupolar excitations defined on a spin Brillouin Klein bottle. Specifically, the quadrupolar excitations possess a momentum-space glide-reflection symmetry and the edge states exhibit a nonlocal momentum twist. These results establish the symmetry language required for interacting spin systems, whether realized in magnetic materials or on programmable quantum simulators, and open a route to unconventional magnetism.

cond-mat.str-el↗

arXiv2026

Spin-Charge Groups for Fermions in Fluids and Crystals: General Structures and Physical Consequences

Known symmetry groups are insufficient to describe the various couplings among spin, charge, and spatial degrees of freedom in fermionic systems. To address this problem, we introduce spin-charge groups (SCGs), which provide a unified framework for fermionic symmetries. SCGs incorporate spin and charge operations as `internal' symmetries, spatial and temporal operations as `external' symmetries, together with their couplings and projective twists. After deriving the general group structure of SCGs, we explore their applications in concrete physical systems, including $^3$He superfluids, charge-4e superconductors, collinear magnets with spin-fluxes, and superconductors with coexisting magnetic orders. We show that SCGs can enforce additional band degeneracies, Chern numbers and cross spin-charge responses. Hence SCGs provide a symmetry-based route toward the classification and exploration of new phases of matter even when strong interactions are included.

cond-mat.str-el↗

arXiv2024

Representation Theory for Massless Quasiparticles in Bogoliubov-de Gennes Systems

Gapless quasiparticles can exist in the Bogoliubov-de Gennes (BdG) Hamiltonians in the mean field description of superconductors (SCs), fermionic superfluids (SFs) and quantum spin liquids (QSLs). The mechanism of gapless quasiparticles in superconductors was studied in literature based on the homotopy theory or symmetry-indicators. However, important properties of the gapless quasiparticles including the degeneracy, the energy-momentum dispersion and the responses to external probe fields need to be determined. In the present work, we investigate gapless quasiparticles in general BdG systems by using projective representation theory for the full `symmetry' groups formed by combinations of lattice, spin and charge operations. We find that (I) charge conjugation (or effective charge conjugation) symmetry can yield gapless quasiparticles with linear, quadratic or higher order dispersions at high symmetry points of the Brillouin zone; (II) different quantum numbers protected level crossing can give rise to zero modes along high symmetry lines; (III) combined spatial inversion and time reversal symmetry can protect zero modes appearing at generic $k$ points. To obtain the low energy properties of gapless quasiparticles, the $k\cdot p$ theory is provided using a high efficient method--the Hamiltonian approach. Based on generalized band representation theory for BdG systems, several lattice models are constructed to illustrate the above results. Our theory provides a method to classify nodal SCs/SFs/QSLs with given symmetries, and enlightens the realization of Majorana type massless quasiparticles in condensed matter physics.

cond-mat.str-el↗