Talks

The charge resistivity/conductivity can take universal values in various scenarios of two-dimensional condensed matter systems. Well-known examples of universal resistivity include 2+1d quantum critical points, (fractional) quantum Hall effects, the criterion of two-dimensional “bad metal”, and the universal resistivity jump predicted at the interaction-driven metal-insulator transition. We construct examples of two-dimensional metallic states with the following exotic behaviors: (1) at low temperature this state is a “bad metal” whose resistivity can be much larger than the Mott-Ioffe-Regel limit; (2) while increasing temperature T the resistivity ρ(T) crosses over from a bad metal at low T to a good metal at intermediate T; (3) at low temperature the metallic state has a large Lorenz number, which strongly violates the Wiedemann-Franz law; (4) the state also has a large thermopower (Seebeck coefficient). Motivated by the recent experiment in transition metal dichalcogenides, an exotic interaction-driven metal-insulator transition will also be constructed. The universal resistivity jump at this transition far exceeds what was proposed in previous theory.

Zoom Link: https://pitp.zoom.us/j/93625929658?pwd=Y284ZTZpWFM1RnduSmhXdDZBRjgyQT09

I study the dynamics of a gyroscope far from an isolated source of gravitational waves. With respect to a local frame 'tied to the distant stars', the gyroscope precesses when gravitational waves cross its path, resulting in a net `orientation memory', carrying information on the gravitational wave profile. I show that the precession rate is given by the so-called "dual covariant mass aspect", providing a celestially local measurement protocol for this quantity. Moreover, I show that the net memory effect can be derived from the flux-balance equations for superrotation charges in the "generalized BMS" algebra. Finally, I show how the spin memory effect à la Pasterski et al. is reproduced as a special case.

Fractons are relatively new types of quasiparticles which have recently been inspiring activity within several branches of physics. I will offer some motivations and perspectives from quantum information theory, condensed matter physics, and high energy physics, focusing mainly on my work in the latter two subjects. This talk is primarily based on https://arxiv.org/abs/2108.08322 and a paper to appear shortly with Dominic Williamson.

Guided by the principles of effective field theory (EFT), I will discuss three avenues to constrain physics beyond General Relativity with black-hole observations.

1) Shadows: Without specifying any particular gravitational dynamics, I will discuss image features of black-hole shadows in general parameterizations and their relation to fundamental-physics principles like (i) regularity (no remaining curvature singularity), (ii) simplicity (a single new-physics scale), and (iii) locality (a new-physics scale set by local curvature).

2) Stability: Specifying the linearized dynamics around black-hole spacetimes determines the onset of potential instabilities and connects to the ringdown phase of gravitational waves. I will delineate how said instabilities can constrain the EFT of gravity, theories of low-scale dark energy, as well as ultralight dark matter.

3) Nonlinear evolution: The larger the probed curvature scale, the tighter the constraints on new gravitational physics. Making full use of experimental data, thus relies on predictions in the nonlinear regime of binary mergers. I will present recent progress towards achieving stable numerical evolution for the EFT of gravity up to quadratic order in curvature.

Zoom Link: https://pitp.zoom.us/j/98276687334?pwd=UnM2dElacWNtempQUHJMNVlaNHgyUT09

Conformal field theories have played an important role in understanding the origin of gravitational entropy, as the Cardy formula accounts for the entropy of three-dimensional BTZ black holes or black holes with an AdS3 near-horizon region. More recently, Cardy-type formulas have also been derived for different field theories, such as warped conformal field theories, which are two-dimensional field theories invariant under chiral scaling symmetry.

In this talk I discuss a particular class of three-dimensional spacetimes, dubbed warped flat spaces. I will present their geometric and thermodynamic properties, focusing on their causal structure. I will explain how their entropy can be accounted for through a dual description in terms of a warped conformal field theory.

When an interacting quantum many-body system is cooled down to its ground state, there can be discrete "topological invariants" that characterize the properties of such ground states. This leads to the concept of "topological phases of matter" distinguished by these topological invariants. Experimental manifestations of these topological phases of matter include the integer and fractional quantum Hall effect, as well as topological insulators.

In this talk, after a general overview of topological phases of matter, I will explain how to define topological invariants that are specific to the ground states of regular crystals, i.e. systems that are periodic in space. I will discuss the physical manifestations of the resulting "crystalline topological phases", including implications for the properties of crystalline defects such as dislocations and disclinations. Then, I will explain how these ideas can be generalized to quasicrystals, which are a different class of materials that have long-range spatial order without exact periodicity. These ideas ultimately lead to a general classification principle for crystalline and quasicrystalline topological phases of matter.

Classical shadow tomography provides an efficient method for predicting functions of an unknown quantum state from a few measurements of the state. It relies on a unitary channel that efficiently scrambles the quantum information of the state to the measurement basis. However, it is quite challenging to realize deep unitary circuits on near-term quantum devices, and an unbiased reconstruction map is non-trivial to find for arbitrary random unitary ensembles. In this talk, I will discuss our recent progress on combining classical shadow tomography with quantum chaotic dynamics. Particularly, I will introduce two new families of shadow tomography schemes: 1) Hamiltonian-driven shadow tomography and 2) Classical shadow tomography with locally scrambled quantum dynamics. In both works, I’ll derive the unbiased reconstruction map, and analyze the sample complexity. In the Hamiltonian-driven scheme, I will illustrate how to use proper time windows to achieve a more efficient tomography. In the second work, I will demonstrate advantages of shadow tomography in the shallow circuit region. Then I’ll conclude by discussing approximate shadow tomography with local Hamiltonian dynamics, and demonstrate that a single quench-disordered quantum spin chain can be used for approximate shadow tomography.

References:
[1] Hong-Ye Hu, Yi-Zhuang You. “Hamiltonian-Driven Shadow Tomography of Quantum States”. arXiv:2102.10132 (2021)
[2] Hong-Ye Hu, Soonwon Choi, Yi-Zhuang You. “Classical Shadow Tomography with Locally Scrambled Quantum Dynamics”. arXiv: 2107.04817 (2021)

Zoom Link: https://pitp.zoom.us/j/99011187936?pwd=OVU3VkpyZ21YcXRCOW5DOHlnSWlVQT09

This talk will be very informal: I will discuss ongoing research with open questions and partial results. We study the asymptotic consistency of modern interpolating methods, including deep networks, in both classification and regression settings. That is, we consider learning methods which scale the data size while simultaneously scaling the model size, in a way which always interpolates the train set. We present empirical evidence that, perhaps contrary to intuitions in theory, many natural interpolating learning methods are *inconsistent* for a wide variety of distributions. That is, they do not approach Bayes-optimality even in the limit of infinite data. The message is, in settings with nonzero Bayes risk, overfitting is not benign: interpolating the noise significantly harms the classifier, to the point of preventing consistency. This work is motivated by: (1) understanding differences between the overparameterized and underparameterized regime, (2) guiding theory towards more "realistic" assumptions to capture deep learning practice, and (3) understanding common structure shared by "natural" interpolating methods. Based on joint work with: Neil Mallinar, Amirhesam Abedsoltan, Gil Kur, and Misha Belkin. And is a follow-up work to the paper "Distributional Generalization", joint with Yamini Bansal.

I will first give a brief overview of my research in the field of out-of-equilibrium quantum many-
body physics, ranging from the theory of many-body localization, to the recent application of Tensor

Processing Units for accelerating simulations of quantum dynamics. I’ll then focus on (1) the

experimental observation and theoretical explanation of subdiffusive dynamics in a “tilted” Fermi-
Hubbard system [PRX 10, 011042 (2020)], and (2) a “freezing” phase transition between weak and

strong ergodicity breaking in systems with particles that are immobile by themselves, but undergo
coordinated pair hopping [PRB 101, 214205 (2020)]. These topics contain the common thread of
either an emergent or microscopic conservation of the dipole moment (center of mass of the particle
distribution), and I will provide simple pictures for how this leads to the subdiffusion and ergodicity
breaking.