Probing Entanglement and Symmetry Breaking Orders via Spectroscopies and Machine Learning
Quantum materials are essential components in the development of advanced technologies, including magnetic-field sensors, energy-related technologies, and quantum computers. Especially, the search of highly entangled quantum materials is crucial, because entanglement is a resource in quantum informa...
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| Format: | Thesis |
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Massachusetts Institute of Technology
2023
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| Online Access: | https://hdl.handle.net/1721.1/152761 https://orcid.org/0000-0002-9532-4061 |
| Summary: | Quantum materials are essential components in the development of advanced technologies, including magnetic-field sensors, energy-related technologies, and quantum computers. Especially, the search of highly entangled quantum materials is crucial, because entanglement is a resource in quantum information applications. A key step towards finding and fabricating highly-entangled materials is to develop experimental and theoretical methods to characterize entanglement. In large-scale solid-state systems, the experimental characterization relies on spectroscopies, including X-ray and neutron spectroscopies. Among different conceptual and mathematical formalisms of entanglement, multipartite entanglement has gained significance due to its accessibility through local probe techniques such as spectroscopies. The resonant inelastic X-ray scattering (RIXS) is an advanced X-ray spectroscopic technique that can probe collective excitations arising from charge, spin, and orbital degrees of freedom, which makes it suitable to characterize multipartite entanglement. RIXS also exhibits potential that extends beyond current understandings, under exceptional precision, it can measure four-point correlations beyond the capability of other spectra techniques, which inspires new entanglement probes. This dissertation contains many aspects of probing entanglement and symmetry breaking orders using both spectroscopies and machine learning. In the first part about probing entanglement using spectroscopies, we will introduce a theoretical proposal for using RIXS to probe entanglement. We propose a new RIXS technique that can extract four-point correlations beyond the scope of the spin and charge structure factors. We verify our method using computational RIXS spectra and theoretically propose multipartite entanglement witnesses based on the four-point correlations for general fermion systems. Building upon the theme of extracting information from materials using spectroscopies, we further present two theoretical works that predict symmetry breaking orders in two-dimensional systems, which can be directly visualized using spectroscopic techniques. (1) We investigate local signatures of quantum Hall ferroelectric and nematic states arising near impurities that can be observed via Scanning Tunnelling Microscopy (STM). (2) We study charge orders at the fractional fillings in twisted transition metal dichalcogenide (TMD) bilayers that can be observed directly via STM. The second part is about the prediction of magnetic orders using machine learning. We’ll present a machine-learning model based on the Euclidean equivariant graph neural network (E3NN) which preserves the crystallographic symmetry, that is trained to predict magnetic orders (ferromagnetic, antiferromagnetic, and non-magnetic) and magnetic propagation vectors (zero or nonzero) with the crystal structures as input. The descriptor used has the advantage to encode general crystal structures of any space group while retaining all spatial information, this characteristic holds significant potential for advancing material science studies. |
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