Friday Quantum Seminar

The two most prevalent classes of ordered states in quantum materials are those arising from spontaneous symmetry breaking (SSB) and from topological order. However, a systematic study for their coexistence in interacting systems is still lacking. In this talk, I will discuss how the topological configuration in order parameter spaces from SSB (classical topology) interplays with the symmetry protected/enriched topological orders (quantum topology) in two spatial dimensions (2d). Three examples of such systems will be given.

At the heart of modern quantum technologies is the interference in the radiation of quantum emitters mediated by common vacuum modes. When there are many atoms interfering in the emission process, one observes enhancement or suppression of decay rate coefficient, which is called superradiance and subradiance, respectively [1]. When there are transitions from different excited levels interfering in the emission process, the intensity of the emitted light is modulated at the frequency of the excited level splittings, which is called quantum beats.

The fundamental assumption of statistical mechanics is that the long-time average of any observable is equal to its average over the microcanonical ensemble. In classical mechanics, this stems from Boltzmann’s ergodic hypothesis, by which a generic initial state in an ergodic system visits the neighborhood of all states in phase space with the same energy. However, wavelike effects in quantum mechanics have made it difficult to identify what it even means for a quantum system to be ergodic, except on a case-by-case basis for individual observables.

A key goal in modern quantum science is to harness the complex behavior of quantum systems to develop new technologies. While precisely engineered platforms with ultracold atoms and trapped ions have emerged as powerful tools for this task, our limited ability to theoretically and computationally probe these systems poses immense challenges for their improved control and characterization.

In this talk, I will present a theory of interaction-induced band-flattening in strongly correlated electron systems. I will begin by illustrating an inherent connection between flat bands and index theorems and presenting a generic prescription for constructing flat bands by periodically repeating local Hamiltonians with topological zero modes. Specifically, a Dirac particle in an external, spatially periodic magnetic field can be cast in this form.

Abstract: In this talk, I will present a theory of interaction-induced band-flattening in strongly correlated electron systems. I will begin by illustrating an inherent connection between flat bands and index theorems and presenting a generic prescription for constructing flat bands by periodically repeating local Hamiltonians with topological zero modes. Specifically, a Dirac particle in an external, spatially periodic magnetic field can be cast in this form.

Optical experiments utilize excitons (electron-hole bound states) in moir ́e transition metal dichalcogenide bilayers as a quantum simulator of the Bose-Hubbard model. Nevertheless, we show that these excitations possess nonbosonic commutation relations due to their composite nature, limiting the size of phase space for them to occupy. Such an effect manifests at weak electron-hole correlation, and restricts the number of excitons to be less than 4 per site and valley for three different bilayers.

Abstract: Optical experiments utilize excitons (electron-hole bound states) in moiré transition metal dichalcogenide bilayers as a quantum simulator of the Bose-Hubbard model. Nevertheless, we show that these excitations possess nonbosonic commutation relations due to their composite nature, limiting the size of phase space for them to occupy. Such an effect manifests at weak electron-hole correlation, and restricts the number of excitons to be less than 4 per site and valley for three different bilayers.

Understanding the Hubbard model is crucial for investigating various quantum many-body states and its fermionic and bosonic versions have been largely realized separately. Recently, transition metal dichalcogenides heterobilayers have emerged as a promising platform for simulating the rich physics of the Hubbard model. In this work, we explore the interplay between fermionic and bosonic populations, using a WS2/WSe2 heterobilayer device that hosts this hybrid particle density.

A spontaneous symmetry-breaking order is conventionally described by a tensor-product wave-function of some few-body clusters. We discuss a type of symmetry-breaking orders, dubbed entanglement-enabled symmetry-breaking orders, which cannot be realized by any tensor-product state. Given a symmetry breaking pattern, we propose a criterion to diagnose if the symmetry-breaking order is entanglement-enabled, by examining the compatibility between the symmetries and the tensor-product description.