Scientific Series

We investigate topological order on fractal geometries embedded in n dimensions. In particular, we diagnose the existence of the topological order through the lens of quantum information and geometry, i.e., via its equivalence to a quantum error-correcting code with a macroscopic code distance or the presence of macroscopic systoles in systolic geometry. We first prove a no-go theorem that Z_N topological order cannot survive on any fractal embedded in 2D. For fractal lattice models embedded in 3D or higher spatial dimensions, Z_N topological order survives if the boundaries of the interior holes condense only loop or membrane excitations. Moreover, for a class of models containing only loop or membrane excitations, and are hence self-correcting on an n-dimensional manifold, we prove that topological order survives on a large class of fractal geometries independent of the type of hole boundaries. We further construct fault-tolerant logical gates using their connection to global and higher-form topological symmetries. In particular, we have discovered a logical CCZ gate corresponding to a global symmetry in a class of fractal codes embedded in 3D with Hausdorff dimension asymptotically approaching D_H=2+ϵ for arbitrarily small ϵ, which hence only requires a space-overhead Ω(d^(2+ϵ)) with d being the code distance. This in turn leads to the surprising discovery of certain exotic gapped boundaries that only condense the combination of loop excitations and gapped domain walls. We further obtain logical C^pZ gates with p≤n−1 on fractal codes embedded in nD. In particular, for the logical C^{n−1}Z in the nth level of Clifford hierarchy, we can reduce the space overhead to Ω(d^(n−1+ϵ)). Mathematically, our findings correspond to macroscopic relative systoles in fractals.

Zoom Link: https://pitp.zoom.us/j/96893356441?pwd=cnlxTVIwd0U5TW9uZDMweXRSa3oydz09

In this talk, I will connect physical properties of scattering amplitudes to the Riemann zeta function. Specifically, I will construct a closed-form amplitude, describing the tree-level exchange of a tower with masses m^2_n = \mu^2_n, where \zeta(\frac{1}{2}\pm i \mu_n) = 0. Requiring real masses corresponds to the Riemann hypothesis, locality of the amplitude to meromorphicity of the zeta function, and universal coupling between massive and massless states to simplicity of the zeros of \zeta. Unitarity bounds from dispersion relations for the forward amplitude translate to positivity of the odd moments of the sequence of 1/\mu^2_n.

Cosmic inflation provides an environment similar to particle colliders that can produce new particles and record the resulting signal. In this talk, I will describe a scenario in which new particles much heavier than the Hubble scale are produced during inflation via couplings to the inflaton. These heavy particles propagate classically and give rise to localized spots on the cosmic microwave background following their production. Momentum conservation during particle production dictates that these localized spots come in pairs. I will discuss the properties of such pairs of CMB spots and the prospect of their detection from the thermal fluctuation background in a position space search.

Critical states of matter are a class of highly entangled quantum matter with various interesting properties and form important bases for emergence of a variety of novel quantum phases. Such states pose serious challenges for the community due to their strongly interacting nature. In this talk, I will discuss our recent progress on tackling critical quantum matter using the method of conformal bootstrap. I will start with introducing several representative examples of critical quantum matter, including the familiar deconfined quantum phase transition, U(1) Dirac spin liquid phase, and the newly proposed Stiefel liquid phase. Next I will focus on the SU(N) deconfined phase transition (i.e. scalar QED), and demonstrate that they can be solved by conformal bootstrap, namely we have obtained their bootstrap kinks and islands.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO

In this talk we will introduce generalized hyperpolygons, which arise as Nakajima-type representations of a comet-shaped quiver, following recent work with Steven Rayan. After showing how to identify these representations with pairs of polygons, we shall associate to the data an explicit meromorphic Higgs bundle on a
genus-g Riemann surface, where g is the number of loops in the comet. We shall see that, under certain assumptions on flag types, the moduli space of generalized hyperpolygons admits the structure of a completely integrable Hamiltonian system. Finally, we shall look into the appearance of branes within the moduli space of generalized hyperpolygons as well as of Higgs bundles, and consider mirror symmetry for such branes. Time permitting, we will mention some other recent results in various areas of science. 

Zoom Link: https://pitp.zoom.us/j/91592778202?pwd=WnM2VS9pS2c0QVIxVWFOdGhFMTdEdz09

The incorporation of classical general relativity into the framework of quantum field theory yielded a rather surprising result -- thermodynamic particle production. In short, for fundamental deformations in the structure of spacetime, quantum mechanics necessitates the creation of thermalized particles from the vacuum. One such phenomenon, known as the Unruh effect, causes empty space to effervesce a thermal bath of particles when viewed by an observer undergoing uniformly accelerated motion. These highly accelerated systems will also have an associated Rindler horizon which produces this Unruh radiation at the celebrated Fulling-Davies-Unruh temperature. For accelerated charges, the emission and absorption of this Unruh radiation will not only affect the associated Rindler horizon in accordance with the Bekenstein-Hawking area-entropy law, but will also imprint the FDU temperature on any photons emitted and subsequently detected in the laboratory. A recent series of high energy channeling experiments carried out by the NA63 collaboration at CERN have finally brought about the first observations and insights into the nature of the Unruh effect. In this presentation, I will discuss the various aspects of acceleration-induced thermality measured by these experiments at NA63.

Zoom Link: https://pitp.zoom.us/j/97257949405?pwd=Ung4TXVwbHJDdm9LbEVRSExQTzI4Zz09

At some length scale, Einstein's theory of general relativity (GR) must break down and be reconciled with quantum mechanics in a quantum theory of gravity. Binary black hole mergers probe the strong field, non-linear, highly dynamical regime of gravity, and thus gravitational waves from these systems could contain beyond-GR signatures. While LIGO presently performs model-independent and parametrized tests of GR, in order to perform model-dependent tests, we must have access to numerical relativity binary black hole waveform predictions in beyond-GR theories through full inspiral, merger, and ringdown. In this talk, I will discuss our results in producing full numerical relativity waveforms in beyond-GR theories, including dynamical Chern-Simons gravity and Einstein dilaton Gauss-Bonnet gravity, and performing gravitational wave data analysis on these waveforms.

Zoom Link: https://pitp.zoom.us/j/91782607606?pwd=SkpaYlF6a04zVDNXS2ZlWjJwdUpkQT09

Designing encoding and decoding circuits to reliably send messages over many uses of a noisy channel is a central problem in communication theory. When studying the optimal transmission rates achievable with asymptotically vanishing error it is usually assumed that these circuits can be implemented using noise-free gates. While this assumption is satisfied for classical machines in many scenarios, it is not expected to be satisfied in the near term future for quantum machines where decoherence leads to faults in the quantum gates. As a result, fundamental questions regarding the practical relevance of quantum channel coding remain open. By combining techniques from fault-tolerant quantum computation with techniques from quantum communication, we initiate the study of these questions. As our main result, we prove threshold theorems for quantum communication, i.e. we show that coding near the (standard noiseless) classical or quantum capacity is possible when the gate error is below a threshold.

In this talk, I will present a general approach to obtain effective field theories for topological crystalline insulators whose low-energy theories are described by massive Dirac fermions. We show that these phases are characterized by the responses to spatially dependent mass parameters with interfaces. These mass interfaces implement the dimensional reduction procedure such that the state of interest is smoothly deformed into a network of defects (dubbed topological crystal), where each defect supports a short-ranged entangled state. Effective field theories are obtained by integrating out the massive Dirac fermions, and various quantized topological terms are uncovered. I will describe how to apply this strategy through a few simple examples and comment on the relation to the topological elasticity theory. 

In this talk we discuss aspects of the non-relativistic two-body problems in AdS spacetime and their CFT duals. Specifically, we focus on understanding the spectrum of double-twist operators in the dual CFT as well as realizing the flat space scattering and bound states from the CFT correlator.

To understand the double-twist operator spectrum we use quantum perturbation theory in the bulk. We then match the result with the inversion formula for consistency. Next, we show how to obtain the flat space scattering from the correlator by using Euclidean time evolution to construct the scattering states; finally we demonstrate how to get the bound states through the WKB approximation. Time permitting, we will also discuss how to obtain physical quantities such as precession of the near-circular orbits in AdS from the data of the double twist operators lying on the first two Regge trajectories.

The COHERENT collaboration made the first measurement of coherent elastic neutrino nucleus scattering(CEvNS) in 2017 using a low-background, 14.6-kg CsI[Na] detector at the SNS. Since initial detection, this detector has opened a new era of precision CEvNS measurements by doubling the detector exposure and improving understanding of the detector response. We these improvements, we now use CsI[Na] data to make competitive constraints of beyond-the-standard-model physics.
We will focus on our recent search for dark matter particles produced at the SNS. With our experience measuring CEvNS, we are sensitive to analogous coherent dark matter induced recoils in our detector. This is a novel approach for accelerator-based dark matter experiments. Searching in this channel is also very powerful, allowing relatively small detectors to explore new parameter space inaccessible to much larger detectors. We will briefly discus other BSM opportunities with COHERENT, showing current results from CsI[Na] along with future sensitivity.

Twisted bilayer graphene (TBG) realizes an exquisitely tunable, strongly interacting system featuring superconductivity and various correlated insulating states. In this talk I will introduce gate-defined wires in TBG as an enticing platform for Majorana-based fault-tolerant qubits. Our proposal notably relies on “internally” generated superconductivity in TBG – as opposed to “external” superconducting proximity effects commonly employed in Majorana devices – and may operate even at zero magnetic field. I will also describe how electrical measurements of gate-defined wires can reveal the nature of correlated insulators and shed light on the Cooper-pairing mechanism in TBG.

Zoom Link: https://pitp.zoom.us/meeting/register/tJcqc-ihqzMvHdW-YBm7mYd_XP9Amhypv5vO