scholarly journals Sufficient symmetry conditions for Topological Quantum Order

2009 ◽  
Vol 106 (40) ◽  
pp. 16944-16949 ◽  
Author(s):  
Z. Nussinov ◽  
G. Ortiz
Keyword(s):  
Topological Quantum ◽  
Quantum Order

scholarly journals Topological quantum order: Stability under local perturbations

2010 ◽  
Vol 51 (9) ◽  
pp. 093512 ◽  
Author(s):  
Sergey Bravyi ◽  
Matthew B. Hastings ◽  
Spyridon Michalakis
Keyword(s):  
Local Perturbations ◽  
Topological Quantum ◽  
Quantum Order

scholarly journals A symmetry principle for topological quantum order

2009 ◽  
Vol 324 (5) ◽  
pp. 977-1057 ◽  
Author(s):  
Zohar Nussinov ◽  
Gerardo Ortiz
Keyword(s):  
Symmetry Principle ◽  
Topological Quantum ◽  
Quantum Order

scholarly journals Gauging permutation symmetries as a route to non-Abelian fractons

2019 ◽  
Vol 7 (5) ◽  
Author(s):  
Abhinav Prem ◽  
Dominic Williamson
Keyword(s):  
General Procedure ◽  
Three Dimensional ◽  
Lattice Models ◽  
Field Theories ◽  
Quantum Field Theories ◽  
Quantum Field ◽  
Quasi Particle ◽  
Code Model ◽  
Topological Quantum ◽  
Quantum Order

We discuss the procedure for gauging on-site Z_2Z2 global symmetries of three-dimensional lattice Hamiltonians that permute quasi-particles and provide general arguments demonstrating the non-Abelian character of the resultant gauged theories. We then apply this general procedure to lattice models of several well known fracton phases: two copies of the X-Cube model, two copies of Haah’s cubic code, and the checkerboard model. Where the former two models possess an on-site Z_2Z2 layer exchange symmetry, that of the latter is generated by the Hadamard gate. For each of these models, upon gauging, we find non-Abelian subdimensional excitations, including non-Abelian fractons, as well as non-Abelian looplike excitations and Abelian fully mobile pointlike excitations. By showing that the looplike excitations braid non-trivially with the subdimensional excitations, we thus discover a novel gapped quantum order in 3D, which we term a ‘panoptic" fracton order. This points to the existence of parent states in 3D from which both topological quantum field theories and fracton states may descend via quasi-particle condensation. The gauged cubic code model represents the first example of a gapped 3D phase supporting (inextricably) non-Abelian fractons that are created at the corners of fractal operators.

scholarly journals Zero modes, bosonization, and topological quantum order: The Laughlin state in second quantization

2015 ◽  
Vol 91 (8) ◽  
Author(s):  
Tahereh Mazaheri ◽  
Gerardo Ortiz ◽  
Zohar Nussinov ◽  
Alexander Seidel
Keyword(s):  
Second Quantization ◽  
Zero Modes ◽  
Topological Quantum ◽  
Quantum Order

Topology knots and hierarchy problem

2019 ◽  
Author(s):  
Vitaly Kuyukov
Keyword(s):  
Quantum Theory ◽  
String Theory ◽  
Quantum Gravity ◽  
Dimensional Space ◽  
Space Time ◽  
Elementary Particles ◽  
Hierarchy Problem ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
New Formula

Many approaches to quantum gravity consider the revision of the space-time geometry and the structure of elementary particles. One of the main candidates is string theory. It is possible that this theory will be able to describe the problem of hierarchy, provided that there is an appropriate Calabi-Yau geometry. In this paper we will proceed from the traditional view on the structure of elementary particles in the usual four-dimensional space-time. The only condition is that quarks and leptons should have a common emerging structure. When a new formula for the mass of the hierarchy is obtained, this structure arises from topological quantum theory and a suitable choice of dimensional units.

Sign in / Sign up

Export Citation Format

Share Document