Condensed Matter and Statistical Mechanics

The Infinite HaPPY Code

Speaker: 
Monica Jinwoo Kang
Date: 
Wed, Nov 4, 2020
Location: 
University of Saskatchewan
Centre for Quantum Topology and Its Applications
Zoom
Conference: 
quanTA CRG Seminar
CRG: 
quantum-topology
Abstract: 

I will construct an infinite-dimensional analog of the HaPPY code as a growing series of stabilizer codes defined respective to their Hilbert spaces. These Hilbert spaces are related by isometries that will be defined during this talk. I will analyze its system in various aspects and discuss its implications in AdS/CFT. Our result hints that the relevance of quantum error correction in quantum gravity may not be limited to the CFT context.

For other events in this series see the quanTA events website.

Class: 

Conformal field theories and quantum phase transitions: an entanglement perspective

Speaker: 
William Witczak-Krempa
Date: 
Wed, Sep 30, 2020
Location: 
Zoom
University of Sasktachewan
Conference: 
quanTA CRG Seminar
CRG: 
quantum-topology
Abstract: 

Quantum phase transitions occur when a quantum system undergoes a sharp change in its ground state, e.g. between a ferro- and para-magnet. I will present a remarkable set of transitions, called quantum critical, that are described by conformal field theories (CFTs). I will focus on 2 and 3 spatial dimensions, where the conformal symmetry is powerful yet less constraining than in 1 dimension. We will probe these scale-invariant theories via the structure of their quantum entanglement. The methods will include large-N expansions, the AdS/CFT duality from string theory, and large-scale numerical simulations. Finally, we’ll see that certain quantum Hall states, which are topological in nature, possess very similar entanglement properties. This hints at broader principles that relate very different quantum states.

For other events in this series see the quanTA events website.

Class: 

Conformal Invariance and Universality in the 2D Ising Model

Speaker: 
Stalislav Smirnov
Date: 
Mon, Jul 6, 2009
Location: 
University of New South Wales, Sydney, Australia
Conference: 
1st PRIMA Congress
Abstract: 

It is conjectured that many 2D lattice models of physical phenomena (percolation, Ising model of a ferromagnet, self avoiding polymers, ...) become invariant under rotations and even conformal maps in the scaling limit (i.e. when "viewed from far away"). A well-known example is the Random Walk (invariant only under rotations preserving the lattice) which in the scaling limit converges to the conformally invariant Brownian Motion.

Assuming the conformal invariance conjecture, physicists were able to make a number of striking but unrigorous predictions: e.g. dimension of a critical percolation cluster is almost surely 91/48; the number of simple length N trajectories of a Random Walk is about N11/32·mN, with m depending on a lattice, and so on.

We will discuss the recent progress in mathematical understanding of this area, in particular for the Ising model. Much of the progress is based on combining ideas from probability, complex analysis, combinatorics.

Class: 

Modelling Aperiodic Solids: Concepts and Properties of Tilings and their Physical Interpretation

Author: 
Franz Gaehler
Date: 
Thu, Aug 1, 2002
Location: 
University of Victoria, Victoria, Canada
Conference: 
Aperiodic Order, Dynamical Systems, Operator Algebras and Topology
Abstract: 

Topics: Quasicrystals, Quasiperiodicity, Translation module, Repetitivity, Local Isomorphism, Mutual Local Derivability, Matching Rules, Covering Rules, Maximal Coverings

Class: