Quantum Matter

Snapshots are the standard data produced in many quantum simulators. In this talk we demonstrate that they encode far more information than conventional correlation functions. I’ll show how snapshot data can probe conformal boundaries and defects in quantum many-body systems. In particular, from local-spin snapshots we can extract the universal conformal defect (boundary) entropy of the Ising CFT, as well as the “line of defect fixed points”. The protocol extends naturally to higher-dimensional CFTs. I’ll then discuss a construction of a strongly interacting spin-liquid wave function using free or weakly interacting fermions available on current simulators, and I’ll share preliminary results applying our proposal to real experimental data.

I will discuss the phenomenology of superconductors hosting both order parameter vortices and fractionally charged anyon excitations. I will demonstrate that in such systems superconductivity and topological order are intertwined under applied magnetic fields, leading to surprising observable consequences departing from traditional superconductivity from electronic pairing. In particular,  I will show that vortices nucleated by perpendicular magnetic fields must trap anyons in their cores. However, because only some vortices can trap an integer number of anyons, this places a constraint on the vortex phase winding. In general, rather than the expected hc/2e quantization of superconducting vortices, we find instead the enhanced flux quantum of hc/e, which I will argue should affect a wide range of observables. I will further develop a general Landau-Ginzburg theory describing vortex fluctuations and discuss the phase diagram as perpendicular magnetic field is increased, showing that condensation of the intertwined vortices leads to exotic insulating phases hosting neutral anyons and a nonvanishing thermal Hall effect.

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]