Symmetry-protected topological (SPT) order is a kind of order in zero-temperature quantum-mechanical states of matter that have a symmetry and a finite energy gap. To derive the results in a most-invariant way, renormalization group methods are used (leading to equivalence classes corresponding to certain fixed points). The SPT order has the following defining properties: (a) distinct SPT states with a given symmetry cannot be smoothly deformed into each other without a phase transition, if the deformation preserves the symmetry. (b) however, they all can be smoothly deformed into the same trivial product state without a phase transition, if the symmetry is broken during the deformation. The above definition works for both bosonic systems and fermionic systems, which leads to the notions of bosonic SPT order and fermionic SPT order. Using the notion of quantum entanglement, we can say that SPT states are states with a symmetry (by contrast: for long-range entanglement see topological order, which is not related to the famous EPR paradox). Since short-range entangled states have only trivial topological orders we may also refer the SPT order as Symmetry Protected "Trivial" order. (Wikipedia).
15 Properties of partially ordered sets
When a relation induces a partial ordering of a set, that set has certain properties with respect to the reflexive, (anti)-symmetric, and transitive properties.
From playlist Abstract algebra
Definition of a Topological Space
Please Subscribe here, thank you!!! https://goo.gl/JQ8Nys Definition of a Topological Space
From playlist Topology
Symmetries show up everywhere in physics. But what is a symmetry? While the symmetries of shapes can be interesting, a lot of times, we are more interested in symmetries of space or symmetries of spacetime. To describe these, we need to build "invariants" which give a mathematical represen
From playlist Relativity
Symmetry in Physics | Noether's theorem
▶ Topics ◀ Global / Local Symmetries, Continuous / Discrete Symmetries ▶ Social Media ◀ [Instagram] @prettymuchvideo ▶ Music ◀ TheFatRat - Fly Away feat. Anjulie https://open.spotify.com/track/1DfFHyrenAJbqsLcpRiOD9 If you want to help us get rid of ads on YouTube, you can support us on
From playlist Symmetry
Orbit of a set in abstract algebra
In this video we start to take a look at the orbit-stabilizer theorem. Our first stop is the orbit of a set. The orbit is created by taking an arbitrary element of a set and acting on that element by all the elements in the set of an an arbitrary group. In this video, we look at a few p
From playlist Abstract algebra
The Predictive Power Of Symmetry
From a bee’s hexagonal honeycomb to the elliptical paths of planets, symmetry has long been recognized as a vital quality of nature. Einstein saw symmetry hidden in the fabric of space and time. The brilliant Emmy Noether proved that symmetry is the mathematical flower of deeply rooted phy
From playlist Science Shorts and Explainers
http://www.teachastronomy.com/ A lot of fundamental concepts in physics are based on the idea of symmetry. Symmetry is familiar to us in an aesthetic sense. It often means things that have pleasing proportion, or look the same from every direction, or have a harmonious nature about them.
From playlist 23. The Big Bang, Inflation, and General Cosmology 2
Symmetric Groups (Abstract Algebra)
Symmetric groups are some of the most essential types of finite groups. A symmetric group is the group of permutations on a set. The group of permutations on a set of n-elements is denoted S_n. Symmetric groups capture the history of abstract algebra, provide a wide range of examples in
From playlist Abstract Algebra
This video was produced by Nina Qiu of Year 10 (2015).
From playlist Random
MagLab Theory Winter School 2019: Jennifer Cano "Topo Quantum Chem"
Topic: Topological quantum chemistry: Theory The National MagLab held it's seventh Theory Winter School in Tallahassee, FL from January 7th - 11th, 2019.
From playlist 2019 Theory Winter School
Symmetry-broken topological phases by Tanmoy Das
DISCUSSION MEETING NOVEL PHASES OF QUANTUM MATTER ORGANIZERS: Adhip Agarwala, Sumilan Banerjee, Subhro Bhattacharjee, Abhishodh Prakash and Smitha Vishveshwara DATE: 23 December 2019 to 02 January 2020 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Recent theoretical and experimenta
From playlist Novel Phases of Quantum Matter 2019
MagLab Theory Winter School 2018: Duncan Haldane - Bipartite Entanglement I
The National MagLab held it's sixth Theory Winter School in Tallahassee, FL from January 8th - 13th, 2018.
From playlist 2018 Theory Winter School
Xie Chen - Symmetry Protected Topological Phases - IPAM at UCLA
Recorded 02 September 2021. Xie Chen of the California Institute of Technology presents "Symmetry Protected Topological Phases" at IPAM's Graduate Summer School: Mathematics of Topological Phases of Matter. Abstract: This talk will give a brief introduction to symmetry protected topologica
From playlist Graduate Summer School 2021: Mathematics of Topological Phases of Matter
Topological Surface States in Topological Insulators, Superconductors and Beyond - M. Zahid Hasan
DISCUSSION MEETING : ADVANCES IN GRAPHENE, MAJORANA FERMIONS, QUANTUM COMPUTATION DATES Wednesday 19 Dec, 2012 - Friday 21 Dec, 2012 VENUE Auditorium, New Physical Sciences Building, IISc Quantum computation is one of the most fundamental and important research topics today, from both th
From playlist Advances in Graphene, Majorana fermions, Quantum computation
When Luttinger semimetal meets with ordered spin ice state in pyrochlore iridates by Gang Chen
Program The 2nd Asia Pacific Workshop on Quantum Magnetism ORGANIZERS: Subhro Bhattacharjee, Gang Chen, Zenji Hiroi, Ying-Jer Kao, SungBin Lee, Arnab Sen and Nic Shannon DATE: 29 November 2018 to 07 December 2018 VENUE: Ramanujan Lecture Hall, ICTS Bangalore Frustrated quantum magne
From playlist The 2nd Asia Pacific Workshop on Quantum Magnetism
Simple models of Symmetry Protected Topological phases
Simple models of Symmetry Protected Topological phases and Symmetry Enriched Topological phases of bosons in two and three dimensions Discussion Meeting: Quantum entanglement in macroscopic matter URL: http://www.icts.res.in/discussion_meeting/QEM2015/ Dates: Monday 12 Jan, 2015 - Friday
From playlist Discussion Meeting: Quantum entanglement in macroscopic matter
Quantum Spin Liquids in Kagome Lattice by Subhro Bhattacharjee
29 May 2017 to 02 June 2017 VENUE: Ramanujan Lecture Hall, ICTS Bangalore This program aims to bring together people working on classical and quantum systems with disorder and interactions. The extensive exploration, through experiments, simulations and model calculations, of growing cor
From playlist Correlation and Disorder in Classical and Quantum Systems
Generalized Global Symmetries: Nathan Seiberg
URL: https://strings2015.icts.res.in/talkTitles.php
From playlist Strings 2015 conference
My submission for the Summer of Math Exposition competition: https://www.youtube.com/watch?v=ojjzXyQCzso An introduction to the idea behind the mathematical definition of continuity. If you are familiar with the epsilon-delta definition of continuity, you may recognise it here, where I
From playlist Summer of Math Exposition Youtube Videos
Lattice realization of integer QHE of bosons by Subhro Bhattacharjee
New questions in quantum field theory from condensed matter theory URL: http://www.icts.res.in/discussion_meeting/qft2015/ Description:- The last couple of decades have seen a major revolution in the field of condensed matter physics, where the severe limitations of conventional paradigm
From playlist New questions in quantum field theory from condensed matter theory