Condensed Matter

Like ordinary symmetries, non-invertible symmetries can characterize Symmetry-Protected Topological (SPT) phases. In this talk, we will discuss weak SPTs protected by projective non-invertible symmetries. Projective symmetries are ubiquitous in quantum spin models and can be leveraged to constrain their phase diagram and entanglement structure, e.g., Lieb-Schultz-Mattis (LSM) theorems. We will show how, surprisingly, projective non-invertible symmetries do not always imply LSM theorems. We will first discuss a simple, exactly solvable 1+1D quantum spin model in an SPT phase protected by both translation and non-invertible symmetries forming a non-trivial projective algebra. We will then generalize this example to a class of projective non-invertible Rep(G) x G x translation symmetries. For some finite groups G, this projectivity implies an LSM theorem. When it does not, we prove it still provides a constraint through an SPT-LSM theorem: any unique and gapped ground state is necessarily a non-invertible weak SPT state with non-trivial entanglement. [This talk is based on arXiv:2409.18113]

The exactly solvable spin-1/2 Kitaev model on a honeycomb lattice has drawn significant interest, as it offers a pathway to realizing the long-sought after quantum spin liquid. Building upon the Kitaev model, Yao and Lee introduced another exactly solvable model on an unusual star lattice featuring non-abelian spinons. The additional pseudospin degrees of freedom in this model could provide greater stability against perturbations, making this model appealing. However, a mechanism to realize such an interaction in a standard honeycomb lattice remains unknown. I will present a microscopic theory to obtain the Yao-Lee model on a honeycomb lattice by utilizing strong spin-orbit coupling of anions edge-shared between two eg ions in the exchange processes. This mechanism leads to the desired bond-dependent interaction among spins rather than orbitals, unique to our model, implying that the orbitals fractionalize into gapless Majorana fermions and fermionic octupolar excitations emerge. Since the conventional Kugel-Khomskii interaction also appears, the phase diagram including these interactions using classical Monte Carlo simulations and exact diagonalization techniques will be presented. Several open questions will be also discussed.

UTe₂ is an intriguing recently discovered superconductor that exhibits a wide range of exotic properties. Experimental evidence increasingly supports spin-triplet pairing, and under pressure or in magnetic fields, UTe₂ displays multiple superconducting phases, including a remarkable reentrant phase above 40 T. However, conflicting results persist regarding the presence of chiral and time-reversal symmetry breaking. Recent STM measurements have identified a charge density wave in the normal state, which couples with the superconducting state at lower temperatures to form a pair density wave. In this talk, I will provide an overview of the latest developments in understanding the unconventional superconductivity of UTe₂.