Scientific Series

This talk applies effective field theory to the back-reaction of sources with finite size but infinite mass. The main tool for calculating back-reaction is a general relation between a source's effective action and the boundary conditions of `bulk’ fields in the near-source limit. As applied to the Maxwell (or Einstein) fields for point sources this boundary condition reproduces standard Gauss’ Law expressions, but the same arguments imply source-dependent boundary conditions for the Schrodinger (or Dirac) field of an orbiting particle. As applied to the quantum mechanics of a particle interacting with a source through an inverse-square potential EFTs remove the guess-work from the (well-known) ambiguities in the determination of boundary conditions at the origin, and provides a simple interpretation of the classical renormalization effects that are known to arise in this case. EFT arguments show why the RG evolution associated with this classical renormalization is likely universal for a great many types of point sources. The EFT boundary conditions also modify how finite-size effects alter bound-state orbits in the Coulomb problem, and in particular give them a non-standard dependence on the mass of the orbiting particle. It is argued that this might provide a solution to the `proton-radius puzzle’, in which experiments seem to indicate a different proton radius depending on whether or not it is measured using electrons or muons.

Motivated by the question about reconstructing a Conformal field theory from the data of a subfactor of finite index, Jones studied the continuous limit of the periodic quantum spin chain which Thompson group acts on. Based on planar algebras, the topological axiomatization of subfactors, we will illustrate the idea of the correspondence between the skein theory of planar algebras and presentation of Thompson groups.

The affine Grassmannian is the analog of the Grassmannian for the loop group. They are very important objects in mathematical physics and the Geometric Langlands program. In this talk, I will explain my recent work on the central degeneration of semi-infinite orbits, Iwahori orbits and Mirkovic-Vilonen cycles in the affine Grassmannian. I will also use lots of convex polytopes to illustrate my results. In addition, I will explain the connections between my work and other parts of geometric representation theory and combinatorial algebraic geometry.  

Bosonic symmetric protected topological (BSPT) phases are bosonic anagolue of electron topological insulators and superconductors. Despite the theoretical progresses of classifying these states, little attention has been paid to experimental realization of BSPT states in dimensions higher than 1. We propose bilayer graphene system in a out-of-plane magnetic field with Coulomb interaction is a natural platform for BSPT states with $U(1)\times U(1)$ symmetry. We also propose that the quantum phase transition between the BSPT state and the trivial state, which may be tuned by an out-of-plane electric field, could be a novel transition with only gapless bosonic degrees of freedom. In the second part of the talk we will discuss the out-of-time-order correlation (OTOC) and its application in many-body localized and marginal MBL systems. We demonstrate, in marginal MBL systems, the scrambling time follows a stretched exponential scaling with the distance between the operators, which demonstrates Sinai diffusion of quantum information and the enhanced scrambling by the quantum criticality in non-chaotic systems.

In this talk, I will focus on cosmologies that replace the big bang with a big bounce. I will explain how, in these scenarios, the large-scale structure of the universe is determined during a contracting phase before the bounce and will describe the recent development of the first well-behaved classical (non-singular) cosmological bounce solutions.

The matrix product state (MPS) ansatz makes possible computationally-efficient representations of weakly entangled many-body quantum systems with gapped Hamiltonians near their ground states, notably including massive, relativistic quantum fields on the lattice. No Wick rotation is required to apply the time evolution operator, enabling study of time-dependent Hamiltonians. Using free massive scalar field theory on the 1+1 Robertson-Walker metric as a toy example, I present early efforts to exploit this fact to model quantum fields in curved spacetime. We use the ADM formalism to write the appropriate Hamiltonian witnessed by a particular class of normal observers. Possible applications include simulations of gravitational particle production in the presence of interactions, studies of the slicing-dependence of entanglement production, and inclusion of the expectation of the stress-energy tensor as a matter source in a numerical relativity simulation.

In recent years there has been quite some effort to apply Matrix Product States (MPS) and more general Tensor Networks (TN) to lattice gauge theories. Contrary to the standard Euclidean-time Monte Carlo approach, which faces a major obstacle in the sign problem, numerical methods based on TN are free from the sign problem and allow to some extent simulating time evolution. Moreover, TN are also a suitable tool to explore proposals for potential future quantum simulators for lattice gauge theories.

In this talk I am going to present some examples where these possibilities allow novel insight into lattice gauge theories. After briefly introducing MPS, I will mainly focus on two models: The first part of the talk is going to be about the Schwinger model. I will show how MPS can help to explore proposals for potential future quantum simulators for this model by studying their spectral properties and simulating adiabatic preparation protocols for the interacting vacuum.

Furthermore, I will show an explicit example where TN allow to overcome the Monte Carlo sign problem in a lattice calculation by studying the zero-temperature phase structure for the two-flavor case at non-zero chemical potential with MPS.

In the second part, I am focusing on a non-Abelian gauge model, namely a 1+1 dimensional SU(2) lattice gauge theory. Using MPS, the phenomenon of string breaking in this theory can be studied in real time, thus allowing to gain new insight into this process. Moreover, I will show how the gauge field can be integrated out for systems with open boundary conditions and how to obtain a formulation which allows to address the model more efficiently with MPS.

Quantum tomography is an important tool for characterizing the parameters of unknown states, measurements, and gates.  Standard quantum tomography is the practice of estimating these parameters with known measurements, states, or both, respectively.  In recent years, it has become important to address the issue of working with systems where the ``devices'' used to prepare states and make measurements both have significant errors.  Of particular concern to me is whether such state-preparation and measurement errors are correlated with each other.  In this talk, I will share a solution to assessing such correlations with an object called a partial determinant.  Further, I will show how this technique suggests a perspective for such correlated quantum states and observables (over the space of device settings) is analogous to the non-holonomic perspectives of thermodynamic heat and work (over the macroscopic state space.)

In this talk I will give a short introduction into Projected Entangled-Pair States (PEPS), and their infinite variant iPEPS, a class of tensor network Ansatz targeted at the simulation of 2D strongly correlated systems. I will present work on two recent

projects: the first will be an application of the iPEPS algorithm to a Kitaev-Heisenberg model, a model which through-out recent years has received a lot of attention due to its potential connection to the physics of a subclass of the so-called Iridate compounds. The second will be work related to the development of the iPEPS method to specifically target cylindrical geometries. Here I will present some preliminary results where we apply the methods to the Heisenberg and Fermi-Hubbard models and evaluate their performance in comparison to infinite Matrix Product States. As a final part of my talk I will, depending on time, elaborate somewhat on potential future topics including (but not restricted to):  the main challenges of iPEPS simulations from a numerical perspective and what pre-steps we have experimented with to tackle these, the possibility of applying recent proposals for finite-temperature calculations within the PEPS framework to frustrated spin systems and the use of Tensor Network Renormalization for the study of RG flows.

Unlike entanglement entropy and mutual information which may mix both classical and quantum correlations, entanglement negativity received extensive interest recently, for its merit of measuring the pure quantum entanglement in the system. In this talk, I will introduce the entanglement negativity in 2+1 dimensional topologically ordered phases. For a bipartitioned or tripartitioned spatial manifold, we show how the universal part of entanglement negativity depends on the presence of quasiparticles and the choice of ground states. Besides interpreting recent results in exactly solvable lattice models, we give new results on non-Abelian topologically ordered phases.

Seminal work of Steve Lack showed that universal algebraic theories (PROPs) may be composed to produce more sophisticated theories.  I’ll apply this method to construct an axiomatic version of the theory of a pair of complementary observables starting from the theory of monoids.  How far can we get with this?  Quite far!  We’ll get a large chunk of finite dimensional quantum theory this way —but the fact that quantum systems have non-trivial dynamics means that it’s (always) possible to present the resulting theory as a composite PROP in Lack’s sense.  If time permits, I’ll also discuss how this approach can serve as a way of constructing toy models with specific properties.
TRIGGER WARNING: category theory, blasphemy.