Scientific Series

Hank Chen, Perimeter Institute and University of Waterloo

Drinfel’d double symmetry of the 4d Kitaev model

We construct the 2-Drinfel'd double associated to a finite 2-group G, and compute its braided 2-category of 2-representations, in order to characterize the topological excitations in the 4d toric code and its spin-Z_2 variant. This work relates the categorical and field theoretical approaches toward characterizing higher-dimensional topological phases in existing literature. In particular, we show that particular twists of the underlying 2-Drinfel'd double is responsible for much of the higher-structural properties that arise in gapped topological phases in 4d. We emphasize that this work also displays the first ever instance of higher Tannakian duality for 2-categories.

The Berry phase, discovered by M.V. Berry in 1984, has been applied to the construction of various invariants in topological phase of matters. The Berry phase measures the non-triviality of a uniquely gapped system as a family and takes its value in $H^2({parameter space};Z)$.

In recent years, there have been several attempts to generalize it to higher-dimensional many-body lattice systems[1,2,3,4], called the “higher” Berry phase. In the case of spatial dimension d it is believed that the higher Berry phase takes its value in $H^{d+2}({parameter space};Z)$. However, in general dimensions, the definition of the higher Berry phase in lattice systems is not yet known.

In my talk, I’ll explain about the way to extract the higher Berry phase in 1-dimensional systems by using the “higher inner product” of three matrix product states and how to construct the topological invariant which takes its value in $H^3({parameter space};Z)$. This talk is based on [3] and [4].

Refs:
[1] A. Kapustin and L. Spodyneiko Phys. Rev. B 101, 235130
[2] X. Wen, M. Qi, A. Beaudry, J. Moreno, M. J. Pflaum, D. Spiegel, A. Vishwanath and M. Hermele arXiv:2112.07748
[3] S. Ohyama, Y. Terashima and  K. Shiozaki arXiv:2303.04252
[4] S. Ohyama and S. Ryu arXiv:2304.05356  

Zoom link:  https://pitp.zoom.us/j/93720709850?pwd=RTliMDNMRWo2V2k1MnBKUjlRMjBqZz09

Gravity is exciting from both theoretical and observational perspectives. In this talk, I will discuss how gravitational observables, such as waveforms, can be determined from scattering amplitudes in quantum field theory. We can therefore use the full arsenal of theoretical collider physics to compute gravitational waveforms. As an example, I will describe the waveform generated in a scattering process at next-to-leading order. I will finish by discussing how amplitudes can further be used to understand non-radiative aspects of gravity, including the curvature of the Kerr metric itself. This leads to a network of “double copy” relations between classical solutions of the Maxwell and Einstein equations.

Zoom link:  https://pitp.zoom.us/j/92038383246?pwd=RjQwVHo1VWR6VDl0a3VPZEU0ZXFyUT09

A new approach for the first quantization of superstrings, called B-RNS-GSS formalism, is being constructed. It consists of quantizing embeddings of super surfaces into superspaces. As in the classical theory of super-embeddings, it has twistor-like variables. In this talk, besides motivating the need for such a formalism, I will review the work done in hep-th: 2211.06899, where the hetetoric supergravity equations of motion were derived from BRST nilpotency.

Zoom link:  https://pitp.zoom.us/j/98656433153?pwd=NjlpcUtITDAwWlgycUtUZUVsZ3QrQT09

Tensor Processing Units are application specific integrated circuits (ASICs) built by Google to run large-scale machine learning (ML) workloads (e.g. AlphaFold). They excel at matrix multiplications, and hence can be repurposed for applications beyond ML. In this talk I will explain how TPUs can be leveraged to run large-scale density matrix renormalization group (DMRG) calculations at unprecedented size and accuracy. DMRG is a powerful tensor network algorithm originally applied to computing ground-states and low-lying excited states of strongly correlated, low-dimensional quantum systems. For certain systems, like one-dimensional gapped or quantum critical Hamiltonians, or small, strongly correlated molecules, it has today become the gold standard method for computing e.g. ground-state properties. Using a TPUv3-pod, we ran large-scale DMRG simulations for a system of 100 spinless fermions, and optimized matrix product state wave functions with a bond dimension of more than 65000 (a parameter space with more than 600 billion parameters). Our results clearly indicate that hardware accelerator platforms like Google's latest TPU versions or NVIDIAs DGX systems are ideally suited to scale tensor network algorithms to sizes that are beyond capabilities of traditional HPC architectures.

Zoom link:  https://pitp.zoom.us/j/99337818378?pwd=SGZvdFFValJQaDNMQ0U1YnJ6NU1FQT09

Polyaromatic hydrocarbons (PAHs) such as acenes have long been studied due to its interesting optical properties and low singlet triplet gaps. Earlier studies have already noticed that use of complete valence active space is imperative to the understanding of its qualitative and quantitative properties. Since complete active space based methods cannot be applied to such large active spaces, we have used density matrix renormalization group (DMRG) based approaches. Further small modification to the PAH topology shows interesting new phases of behaviour in its optical gaps. We have understood the effect of these effects based on spin frustration due to the presence of odd membered rings. In this talk, I will discuss these observations from molecular and model Hamiltonian perspectives.Further developments based on artificial neural network based configuration interaction for strongly correlated systems will also be discussed.5  The similarities between the ANNs and the MPS wavefunctions will be leveraged for 2D systems.

Zoom link:  https://pitp.zoom.us/j/92159136836?pwd=ZFJBcXZ3R3czSUcxcThOci9ueStBZz09

Jacob Barnett, Perimeter Institute

Locality and Exceptional Points in Pseudo-Hermitian Physics

This talk discusses the role of non-Hermitian operators in fundamental and effective theories of physics. An implicit assumption of the tensor product model of locality is that the inner product factorizes with the tensor product. Quasi-Hermitian quantum frameworks can be used to lift this assumption while preserving the reality of spectra and unitarity. After characterizing local observable algebras and expectation values, I will examine Bell's inequality and its generalizations, the nonlocal games, in the setting of quasi-Hermitian theories. Pseudo-Hermitian operators characterize systems with time-reversal symmetry. These operators exhibit rich perturbative and symmetry-breaking properties that are unparalleled in the Hermitian regime. I will convey some geometric and topological aspects of these features, with emphasis placed on non-interacting many-body systems.
 

I will first review the construction of quiver Yangians for the quiver and superpotential from string theory on general toric Calabi-Yau threefolds; they serve as BPS algebras of these systems and their characters reproduce the unrefined BPS indices. I will then explain how to generalize the construction to arbitrary quivers and how to incorporate refined BPS indices. The entire construction allows for straightforward generalizations to trigonometric, elliptic, and generalized cohomologies. Time permitting, I will discuss some applications, such as on BPS counting and on Gauge/Bethe correspondence. 

Zoom link:  https://pitp.zoom.us/j/96812116687?pwd=RjlsSVhDaUVBREtUUnd5S04rQjhpZz09

Despite first observing cosmic rays with energies above an EeV (10^18 eV) in the 1960s, the source of these particles remains an open question. Modern observatories, in particular the Pierre Auger Observatory and Telescope Array, have firmly established that the cosmic ray spectrum continues up to ~10^20.3 eV and have significantly advanced our understanding of these particles. However, limited statistics, uncertainties in particle physics, and significant deflections in the Galactic magnetic field have made progress towards discovering their astrophysical source extremely challenging. One key astrophysical input needed to understand ultrahigh energy cosmic ray data is the distribution of their sources, or the source evolution. In this talk, I will focus on multimessenger observations which have the potential to pin down the source evolution for the very first time.

Zoom Link:  https://pitp.zoom.us/j/94054513261?pwd=aHRNWE04VDI2cDA2RmRYQmtNRnd3dz09

Highly magnetized neutron stars are a source of extreme transients observed in different bands, like the fast radio burst (FRB) and associated hard X-ray burst from the Galactic magnetar SGR 1935+2154. The origin of such outbursts, hard X-rays on the one hand and millisecond duration FRBs on the other hand, is still unknown. We present a global model for various kinds of such magnetar outbursting activities. Crustal surface motions are expected to twist the inner magnetar magnetosphere by shifting the frozen-in footpoints of magnetic field lines. We discuss criteria for the development of various instabilities of 3D twisted flux bundles in the force-free dipolar magnetospheres and compare their energetic properties to observations of magnetar X-ray flares. We then review a recently developed FRB generation mechanism in the outer magnetosphere of a magnetar. The strong magnetic pulse induced by a magnetar flare collides with the current sheet of the magnetar wind, compresses and fragments it into a self-similar chain of magnetic islands. Time-dependent plasma currents created during their collisions produce relatively narrow-band GHz emission with luminosities sufficient to explain bright extragalactic FRBs.

Zoom ink:  https://pitp.zoom.us/j/96469987183?pwd=N1UzVkh6RGZUeWV6TFZJLzk0M3VWZz09

Gravitational scattering provides valuable insight into classical dynamics and is likely of fundamental importance in quantum gravity.  However, a complete framework for gravitational scattering does not yet exist.  The lack of a clear framework hinders progress; for example, different groups have reported different results for the loss of angular momentum in post-Minkowskian scattering.  In this talk I will report on recent work 2303.17124 with Compere and Wei constructing a general framework for classical gravitational scattering of finite-sized massive bodies in four spacetime dimensions.  We formulate assumptions and definitions such that the five asymptotic regions (past/future timelike/null infinity and spatial infinity) share a single Bondi-Metzner-Sachs (BMS) group of symmetries and associated charges and derive global conservation laws stating that the total change in charge is balanced by the corresponding radiative flux.  Our assumptions are compatible with all known properties of scattering spacetimes, including certain logarithmic corrections that invalidate common falloff assumptions.  Among the new implications are rigorous definitions for quantities like initial/final spin, scattering angle, and impact parameter in multi-body spacetimes, without the use of any preferred background structure.  We show that spin is supertranslation-invariant, while impact parameter is not.  To complement these derivations I will emphasize a helpful "puzzle piece" diagram that faithfully represents all five asymptotic regions, illustrating their roles in the scattering problem.

Zoom link:  https://pitp.zoom.us/j/94358515412?pwd=cUFocVNjQ1pqUmp4MDN0RmRLbjE0QT09