Talks

It is well-known that one-dimensional systems at finite temperature, such as the classical Ising model, cannot spontaneously break a discrete symmetry due to the proliferation of domain walls. The validity of this statement rests on a few assumptions, including the spatial locality of interactions. In a situation where a one-dimensional system exists as a defect in a critical, higher-dimensional bulk system, the coupling between defect and bulk can induce an effective long-range interaction on the defect. It is thus natural to ask if long-range order can be stabilized on a defect in a critical bulk, which amounts to asking whether domain walls on the defect are relevant or not in the renormalization group sense. I will explore this question in the context of Ising conformal field theory in two and higher dimensions in the presence of a localized symmetry-breaking field. With both perturbative techniques and numerical conformal bootstrap, I will provide evidence that indeed the defect domain wall must be relevant when 2 < d < 4. For the bootstrap calculations, it is essential to include “endpoint” primary fields of the defect, which lead to a rigorous and powerful way to input bulk data. I will additionally give tight estimates of a number of other quantities, including  scaling dimensions of defect operators and the defect entropy, and I will conclude with a discussion of future directions.

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Zoom link https://pitp.zoom.us/j/92671628591?pwd=WjNma3VEV2M4T011dFlLMzM2ZUJiUT09

Costello, Witten and Yamazaki proposed a 4d Chern-Simons theory as a unified way to engineer integrable models. In the presence of 'Disorder' defects (for non-ultralocal 2d theories), this correspondence has been established only classically. As a first quantum check, I will derive the matching of 1-loop divergences between the 4d and 2d theories. My assumptions are general and seem to isolate sigma-models among the 2d theories. (Based on 2309.16753)

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Zoom link https://pitp.zoom.us/j/99362983669?pwd=NE1uQ3FmWityQ1R0NUVnZkRPZTRUdz09

Significant effort has been devoted to searching for new fundamental forces of nature. At short length scales (below approximately 10 nm), many of the strongest experimental constraints come from neutron scattering from individual nuclei in gases. The leading experiments at longer length scales instead measure forces between macroscopic test masses. I will present a proposal that combines these two approaches: scattering neutrons off of a target that has spatial structure at nanoscopic length scales. Such structures will give a coherent enhancement to small-angle scattering, where the new force is most significant. This can considerably improve the sensitivity of neutron scattering experiments for new forces in the 0.1 - 100 nm range. I will discuss the backgrounds due to Standard Model interactions and a variety of potential target structures that could be used, estimating the resulting sensitivities. I will show that, using only one day of beam time at a modern neutron scattering facility, our proposal has the potential to detect new forces as much as four orders of magnitude beyond current laboratory constraints at the appropriate length scales.

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Zoom link https://pitp.zoom.us/j/98201041537?pwd=MS9weFpNcHVFTVIwMTVoYmpxeTd6Zz09

The deep learning architecture associated with ChatGPT and related generative AI products is known as transformers. Initially applied to Natural Language Processing, transformers and the self-attention mechanism they exploit have gained widespread interest across the natural sciences. We will present the mathematics underlying the attention mechanism and describe the basic transformer architecture. We will then describe applications to time series and imaging data in astronomy and discuss possible foundation models.

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Zoom link https://pitp.zoom.us/j/91226066758?pwd=TWZ5RVliMjVKYXdLcHdya09lNWZhQT09

Quantum state tomography (QST) is the art of reconstructing an unknown quantum state through measurements. It is a key primitive for developing quantum technologies. Neural network quantum state tomography (NNQST), which aims to reconstruct the quantum state via a neural network ansatz, is often implemented via a basis-dependent cross-entropy loss function. State-of-the-art implementations of NNQST are often restricted to characterizing a particular subclass of states, to avoid an exponential growth in the number of required measurement settings. In this talk, I will discuss an alternative neural-network-based QST protocol that uses shadow-estimated infidelity as the loss function, named “neural-shadow quantum state tomography” (NSQST). After introducing NNQST and the classical shadow formalism, I will present numerical results on the advantage of NSQST over NNQST at learning the relative phases, NSQST’s noise robustness, and NSQST’s advantage over direct shadow estimation. I will also briefly discuss the future prospects of the protocol with different variational ansatz and randomized measurements, as well as its experimental feasibility.

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Zoom link https://pitp.zoom.us/j/94167105773?pwd=TXR3TUtwNjV4VFB4SEpvTkhqd29SUT09