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
Leave a Comment
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
The final #Syngeweek part is now live on our website. "Yet meet we shall, and part and meet again Where dead men meet, on lips of living men." dias.ie/2020/03/23/syn… Returning visitors don't forget to clear your cookies! #DIASdiscovers
Today is the 25th anniversary of the passing of Professor J.L Synge. Part 6 and the final #SyngeWeek installment will go live this evening on our website at 6pm #DIASdiscovers
What a great idea! 👩🚀👩🚀 twitter.com/SpaceStnExplor…
#SyngeWeek Part5 is now live on our website! "One of the attractions [of coming to DIAS] for me in 1948 was the prospect of being a colleague of Schrödinger. " Read more: dias.ie/2020/03/23/syn… Returning visitors remember to clear those cookies! #DIASdiscovers
Part 5 of #SyngeWeek covers his career with DIAS, the publication of "Relativity:The General Theory" which made DIAS the leading centre for research in General relativity for the following decade. Part 4 is availble until 6pm: dias.ie/2020/03/23/syn… #DIASdiscovers
On tonight! Don't miss your chance to see this fascinating documentary about Schroedinger's time in DIAS and the seminal discovery it lead to. Not forgetting he was DIAS' first Director of Theoretical Physics. @RTEOne #DIASdiscovers #schrodinger
Returning Visitors please remember to clear those cookies!
"...sometime early in 1944, I got a phone call from Oswald Veblen, asking me whether I would like to go to Europe attached to the American Army in a scientific capacity." #SyngeWeek Part 4: Columbus & Europe is now live on our website ➡️ dias.ie/2020/03/23/syn… #DIASdiscovers
Spring Newsletter just launched! See what has happened in 2020 so far: mailchi.mp/5ea85f227dce/d… Subscribe to our mailing list today to get future editions direct to your mailbox: dias.ie/mailinglistsub… #DIASdiscovers
"...he wanted to endow international medals in mathematics (a subject omitted from Nobel Prizes, on account of Nobel's jealousy of Mittag-Leffler..." #SyngeWeek Part 3: Toronto-Dublin-Toronto dias.ie/2020/03/23/syn… Returning visitors please remember to clear those cookies 🍪
"Long before 1916 I had become a Nationalist, but the idea that there might be an armed rebellion was nothing more than a whispered rumour..." #SyngeWeek part 3 will be posted on our website this evening at 6pm. Part 2: University is available until then: dias.ie/2020/03/23/syn…
Please note the reopening date of DIAS buildings is now 20 April. dias.ie/2020/03/13/ale… #coronavirus #StayHomeSaveLives
#SyngeWeek Part Two: University, is now live on our website. "...could force the rifle down the leg of his trousers, and we set out through the Front Gate of College; " ➡️dias.ie/2020/03/23/syn… Returning visitors please be sure to clear those cookies🍪 #DIASdiscovers
#SyngeWeek part 2 is coming this evening. This will cover his University years. J.L. Synge, an Irish mathematician & physicist, whose seven decade career included significant periods in Ireland (& DIAS) Canada, and the USA. Part 1 ➡️ dias.ie/2020/03/23/syn… #DIASdiscovers
"My mother was Ellen Frances Price (1861-1935), daughter of James Price, a distinguished Irish engineer. I believe that, in so far as it was genetic, my interest in mathematics came from this side of the family."- J.L Synge More: dias.ie/2020/03/23/syn… #SyngeWeek #DIASdiscovers