Quantum Matter

In this talk, I will introduce our recent studies on the effect of decoherence on fractional quantum Hall fluids and their robustness as topological quantum memories. Specifically, we examine the behavior of Laughlin states and Moore-Read states under dephasing noise using the plasma analogy as well as the field theory description. Notably, we identify a critical filling (which is 1/4 for the Renyi-2 case and between 1/4 and 1/8 in the replica limit) separating two regimes of mixed-state phase transition. Below the critical filling, a Berezinskii-Kosterlitz-Thousless (BKT) transition occurs at finite noise strength, separating the topologically ordered phase from a critical phase. This transition is characterized by quantum-information quantities that are non-linear functions of the density matrix. On a torus, the BKT transition marks the critical decoherence above which the quantum memory encoded in the ground state manifold is degraded. In contrast, above the critical filling, the quantum memory is extremely resilient against dephasing noise, with the transition occurring only at infinite noise strength. For the Moore-Read state, we further show that the transition also characterizes whether different fusion outcomes of non-Abelian anyons remain distinguishable under decoherence.

In this talk, we develop a comprehensive framework for realizing anyon condensation of topological orders within the string-net model by constructing a Hamiltonian that bridges the parent string-net model before and the child string-net model after anyon condensation. Our approach classifies all possible types of bosonic anyon condensation in any parent string-net model and identifies the basic degrees of freedom in the corresponding child models. Compared with the traditional UMTC perspective of topological orders, our method offers a finer categorical description of anyon condensation at the microscopic level. We also explicitly represent relevant UMTC categorical entities characterizing anyon condensation through our model-based physical quantities, providing practical algorithms for calculating these categorical data.

The so-called pseudo-potentials modeling fractional quantum Hall systems are quantum many-body Hamiltonians that are frustration free and have two symmetries, one related to the conservation of charge (particle number) and another to the conservation of dipole moment (angular momentum), in addition to translation invariance. We show that for such systems the minimum energy of charged excitations is bounded below by the minimum energy of neutral excitations. This property, which had been repeatedly observed in numerical simulations, has a surprisingly simple proof (joint work with Marius Lemm, Simone Warzel, and Amanda Young, arxiv:2410.11645).

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.