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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.

The quest for Anderson localization of light is at the center of many experimental and theoretical activities. Cold atoms have emerged as interesting quantum system to study coherent transport properties of light. Initial experiments have established that dilute samples with large optical thickness allow studying weak localization of light, which has been well described by a mesoscopic model. Recent experiments on light scattering with cold atoms have shown that Dicke super- or subradiance occurs in the same samples, a feature not captured by the traditional mesoscopic models. The use of a long range microscopic coupled dipole model allows to capture both the mesoscopic features of light scattering and Dicke super- and subradiance in the single photon limit. I will review experimental and theoretical state of the art on the possibility of Anderson localization of light by cold atoms.

Condensation of topological defects is the foundation of the modern theory of bulk-boundary correspondence, also known as topological holography. In this talk, I discuss string condensation in 3+1D topological orders, which plays a role analogous to anyon condensation in 2+1D topological orders. I will demonstrate through examples how they correspond to 2+1D symmetry enrichd phases, including both gapped and gapless phases. Then I give a detailed analysis of string condensaiton in 3+1D discrete gauge theories. I compute the outcome of the condensation, namely the category of excitations surviving the condensation. The results suggest that a complete topological holography for 2+1D phases can only be established by taking into account all possible ways of condensing strings in the bulk 3+1D topological order.

Scientists are always working on the forefront of technology, developing new ideas and solving important problems. But many researchers don’t realize that their work can be protected—and potentially monetized for a profit!—by filing a patent application. In this presentation, we will talk about the types of inventions that can be patented, and the benefits of getting a patent for your invention. We will also discuss practical aspects of the patent process, and how you can best prepare yourself for success.

A computational phase transition in a classical or quantum system is a non-analytic change in behavior of an order parameter which can only be observed with the assistance of a nontrivial classical computation. Such phase transitions, and the computational observables which detect them, play a crucial role in the optimal decoding of quantum error-correcting codes and in the scalable detection of measurement-induced phenomena. We show that computational phase transitions and observables can also provide important physical insight on the phase diagram of a classical statistical physics system, specifically in the context of the dislocation-mediated melting of a two-dimensional antiferromagnetic (AF) crystal. In the solid phase, elementary dislocations disrupt the bipartiteness of the underlying square lattice, and as a result, pairs of dislocations are linearly confined by string-like AF domain walls. It has previously been argued that a novel AF tetratic phase can arise when double dislocations proliferate while elementary dislocations remain bound. We will argue that, although there is no thermodynamic phase transition separating the AF and paramagnetic (PM) tetratic phases, it is possible to algorithmically construct a nonlocal order parameter which distinguishes the AF and PM tetratic regimes and undergoes a continuous computational phase transition. We discuss both algorithm-dependent and "intrinsic" algorithm-independent computational phase transitions in this setting, the latter of which includes a transition in one's ability to consistently sort atoms into two sublattices to construct a well-defined staggered magnetization.

Why is the future different from the past? The most poignant property about the world around us is that time is always moving forward, yet, as odd as it may seem, our current theories of physics cannot account for this property. In all of fundamental physics, the future and the past are entirely similar. We select time increasing solutions by hand and call on extremely unlikely initial conditions at the big bang to justify this choice. I will address this question and describe attempts to restore the irreversibility of time as the building block of our understanding of nature.

This talk was delivered at ISSYP 2019, Perimeter's high school summer program.