Welcome to the home page of the online seminars on **Tensor Networks in High Energy Physics**!

This is a joint initiative of the *Gravity, Quantum Fields and Information* group at the **Albert Einstein Institute** in Potsdam (Michal Heller, Sukhi Singh), **DESY** in Zeuthen (Karl Jansen), the **Max-Planck Institute for Quantum Optics** in Garching (Mari-Carmen Banuls), and the Tensor Network initiative (Stefan Kuhn, Bianca Dittrich, Adam Lewis) at the **Perimeter Institute for Theoretical Physics** in Canada.

Our aim is to provide an online platform for researchers working on this topic all around the globe to present their work from anywhere they like! (Office, home, restaurant, airport, or even the beach.) We hope this seminar series can make a small contribution towards cutting down costs, unnecessary travel, and carbon emissions.

**How does it work?** A link to the virtual seminar room for each talk is sent out to participating groups via our mailing list. Anyone with the link can tune-in remotely to the live stream, ask questions, and participate in discussion.

In addition, the talks are typically recorded and posted on our YouTube channel: https://www.youtube.com/c/GravityQuantumFieldsandInformationAEI, in case you miss the live stream, and/or want to revisit the talk.

If you are interested in being added to the mailing list to receive information (including the link to the virtual seminar room) please contact Sukhi Singh

## Upcoming Seminars

#### 1. Adam G. M. Lewis

**When:** February 28, 2020 @ 15.30 (GMT +1 hour, Berlin time)

**Title:** Fermionic Hartle-Hawking Vacua From a Staggered Lattice Scheme

**Abstract:** I will discuss work in collaboration with Guifré Vidal towards simulation of quantum fields in curved spacetimes. We eventually mean to simulate strongly interacting fields, out of equilibrium, coupled to spacetime curvature in various ways. This study concerns the more modest goal of computing renormalized, quadratic expectation values of free Dirac fields installed upon fixed, two dimensional Lorentzian spacetimes. First, we use a staggered-fermion discretization to generate a sequence of lattice theories yielding the desired QFT in the continuum limit. Numerically-computed lattice correlators are then used to approximate, through extrapolation, those in the continuum. Finally, we use so-called point-splitting regularization and Hadamard renormalization to remove divergences, and thus obtain finite, renormalized expectation values of quadratic operators in the continuum. As illustrative applications, we show how to recover the Unruh effect in flat spacetime, how to compute renormalized expectation values in the Hawking-Hartle vacuum of a 2-dimensional "Schwarzschild" black hole, and how to do the same in the Bunch-Davies vacuum of dS2.

## Past Seminars

#### 1. Ignacio Cirac (Opening seminar of the series)

**When:** November 8, 2019 @ 15.00 (GMT +1 hour, Berlin time)

**Title:** *Tensor Networks and Lattice Gauge Theories*

**Abstract:** Certain Quantum Many-body states can be efficiently described in terms of tensor networks. Those include Matrix Product States (MPS), Projected Entangled-Pair Etates (PEPS), or the Multi-scale Entanglement Renormalization Ansatz. They play an important role in quantum computing, error correction, or the description of topological order in condensed matter physics, and are widely used in computational physics. In the last years, it has also been realized their suitability to describe Lattice Gauge Theories, at least in the context of MPS in low dimensions. In this talk I will review some of the basic ideas about tensor networks and their applications to lattice gauge theories, and explain current efforts to extend them to higher dimensions using PEPS.

**YouTube link: **https://www.youtube.com/watch?v=hdb82b1kazw&feature=youtu.be

#### 2. Bartlomiej Czech

**When:** December 6, 2019 @ 15.30 (GMT +1 hour, Berlin time)

**Title:** *What does the Chern-Simons formulation of AdS3 gravity tell us about complexity?*

**Abstract:** I will explain how to realize the wavefunction of a CFT2 ground state as a network of Wilson lines in the Chern-Simons formulation of AdS3 gravity. The position and shape of the network encode the scale at which the wavefunction is defined. The structure of the network is that of a Matrix Product State (MPS) whose constituent tensors effect the Operator Product Expansion. A general argument suggests identifying the "density of complexity" of this MPS network with the extrinsic curvature of the bulk cutoff surface, which by the Gauss-Bonnet theorem agrees with the Complexity = Volume proposal. The viewpoint I offer departs from the circuit paradigm of complexity and dispenses with reference states. Instead, recognizing that field theory states are functionals which send observables to their expectation values, I propose to think of state complexity as the algorithmic complexity of constructing such functionals.

**YouTube link: **https://www.youtube.com/watch?v=2p-mo-LdZxw

#### 3. Frank Verstraete

**When:** January 24, 2020 @ 15.30 (GMT +1 hour, Berlin time)

**Title:** Quantum symmetries in tensor networks

**Abstract:** Tensor networks and more specifically matrix product operators provide a natural framework for describing nonlocal symmetries in lattice spin systems. It will be argued that those matrix product operators form representations of tensor fusion categories, and that they lead to simple lattice representations of topological and conformal field theories. We will construct algebraic equations defining the topological / conformal sectors, and construct explicitly all excitations using the operator-state correspondence.

**YouTube link: **https://www.youtube.com/watch?v=IHe5YYsEK7k.

#### 4. Simone Montangero

**When:** February 14, 2020 @ 15.30 (GMT +1 hour, Berlin time)

**Title:** Tensor network methods applied to high energy physics problems

**Abstract:** We briefly introduce tensor network methods, a classical numerical approach that promises to become a powerful tool to support future quantum simulations and computations, providing guidance, benchmarking and verification of the quantum computation and simulation results. We review some of the latest achievements we obtained: the gauge-invariant formulation of tensor networks and their application to abelian and non-abelian, one- and two-dimensional lattice gauge theories in regimes where Monte Carlo methods efficiency is hindered by the sign problem. Finally, we present the application of tensor network machine learning techniques to the event classification of LHCb simulated data.

**YouTube link: **https://youtu.be/vrZHkyDvYhI