Title: Free-Fermion entanglement and Time and Band Limiting
Speaker: Luc Vinet (Centre de Recherches Mathématiques (CRM))
Abstract: We shall discuss entanglement open finite free-Fermion chains associated with families of discrete orthogonal polynomials and present a simple construction for a tridiagonal matrix T that commutes with the hopping matrix for the entanglement Hamiltonian H. We shall rely on the notion of algebraic Heun operator attached to bispectral problems, and the parallel between entanglement studies and the theory of time and band limiting. As examples, we will examine Fermionic chains related to the Chebychev and Krawtchouk polynomials. For the former case, which corresponds to a homogeneous chain, the outcome of the construction coincides with recent results of Eisler and Peschel; the latter case yields commuting operators for a particular inhomogeneous chain. Since T is tridiagonal and non-degenerate, it can be readily diagonalized numerically, which in turn can be used to calculate the spectrum of H, and therefore the entanglement entropy.
Time: Thursday, 5 September 2019, 2:30pm
Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS,
10 Burlington Road, Dublin 4
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Last Updated: 29th August 2019 by George Rogers
Thursday 5th September : Free-Fermion Entanglement and Time and Band Limiting
Title: Free-Fermion entanglement and Time and Band Limiting
Speaker: Luc Vinet (Centre de Recherches Mathématiques (CRM))
Abstract: We shall discuss entanglement open finite free-Fermion chains associated with families of discrete orthogonal polynomials and present a simple construction for a tridiagonal matrix T that commutes with the hopping matrix for the entanglement Hamiltonian H. We shall rely on the notion of algebraic Heun operator attached to bispectral problems, and the parallel between entanglement studies and the theory of time and band limiting. As examples, we will examine Fermionic chains related to the Chebychev and Krawtchouk polynomials. For the former case, which corresponds to a homogeneous chain, the outcome of the construction coincides with recent results of Eisler and Peschel; the latter case yields commuting operators for a particular inhomogeneous chain. Since T is tridiagonal and non-degenerate, it can be readily diagonalized numerically, which in turn can be used to calculate the spectrum of H, and therefore the entanglement entropy.
Time: Thursday, 5 September 2019, 2:30pm
Location: Lecture Room, 1st Floor, School of Theoretical Physics, DIAS,
10 Burlington Road, Dublin 4
Category: Regular seminars, School of Theoretical Physics News & Events
Big thank you to @MartinaPQuinn of @helloalicepr for moderating the discussion, and of course to our panel @NeasaMcG @CormacORafferty and @laoneill111
@CormacORafferty "to cut yourself off from fundamental research means you could miss out on some of the biggest ideas"
@laoneill "it's our job as researchers to keep reminding governments how important basic research is" "For Dev basic research being carried out in Ireland was a badge of pride"
@NeasaMcG Schrödinger's work in causality was not well received by the religious authorities at the time At the same time DIAS did have Catholic priests working on research projects in the early days, so there was not the conflict you might think between science and religion
@laoneill111 Schrödinger was very popular in social circles in Dublin, a bit of a renaissance man
@CormacORafferty Schrödinger was gifted at explaining difficult concepts
@CormacORafferty on how unsuccessful work, in Schrödinger's case, unified field theory, is just as important part of science. And no one has managed to crack it yet! And not forgetting the cat
@laoneill111 how Schrödinger's book inspired scientists to change fields and result in the finding of the double helix.
@NeasaMcG explaining how DIAS came about and how Schrödinger was attracted to Ireland #DIASdiscovers
Panel Discussion getting underway! @laoneill111 @CormacORafferty @NeasaMcG @MartinaPQuinn
We're half way through the documentary... Join us for the rest and the fascinating discussion to follow DM for link
@Stella15882 @NeasaMcG @HistFest @lukeoneil47 @CormacORafferty @MartinaPQuinn Stella, send me an email. I'll get a link to you communications@dias.ie
Starting in just over an hour we have limited tickets left for tonights broadcast and panel discussion. Get your free ticket now twitter.com/DIAS_Dublin/st…
Culture Night 2020 Booking Links! - Virtual Tour of DIAS Dunsink Observatory: eventbrite.ie/e/118043576515 - Earthquakes and other Geohazards: eventbrite.ie/e/earthquakes-… - Taifeadaí Cartlainne ó Scoil an Léinn Cheiltigh: eventbrite.ie/e/taifeadai-ca… Join us from 5pm! #CultureNight2020
@dias_geophysics have developed something special for @galway2020 in collaboration with composer David Stalling. It is an audio-visual composition “Palace of Ships,” based on sounds, images and seismic data from DIAS’ @SEA_SEIS Expeditions. More: dias.ie/2020/09/14/dia…
Meet some of our panelists for tomorrows discussion on the impact and legacy of the work carried out by Erwin Schroedinger during his time in Ireland as our first Director of Theoretical Physics Grab a free ticket here: eventbrite.ie/e/115984908985