scholarly journals Topological Quantum Fluids

1996 ◽  
Vol 49 (1) ◽  
pp. 183 ◽  
Author(s):  
Nguyen Van Hieu
Keyword(s):  
Quantum Hall ◽  
Experimental Tests ◽  
Quantum Fluids ◽  
Topological Order ◽  
Long Distance ◽  
Fractional Quantum Hall ◽  
Quantum Antiferromagnets ◽  
Topological Quantum ◽  
Topological Field ◽  
Many Body Systems

We discuss quantum-mechanical many-body systems interacting with a topological field, known as topological quantum fields. Several topics on the theory of quantum fluids are examined. First we establish the existence of topological gauge fields in high-T c superconductors and in Heisenberg quantum antiferromagnets. Then we consider typical topological quantum fluids, known as quantum Hall fluids, which are systems exhibiting the fractional quantum Hall effect (FQHE). A theoretical model of these fluids is described in detail. We also discuss the long distance physics of topological quantum fluids, their topological order parameter and possible experimental tests of the theory.

BRAIDING AND ENTANGLEMENT IN NONABELIAN QUANTUM HALL STATES

2009 ◽  
Vol 23 (12n13) ◽  
pp. 2727-2736 ◽  
Author(s):  
G. ZIKOS ◽  
K. YANG ◽  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
S. H. SIMON
Keyword(s):  
Quantum Computation ◽  
Quantum Information Processing ◽  
Fault Tolerant ◽  
Dimensional Space ◽  
Quantum Hall ◽  
Topological Order ◽  
Fractional Quantum Hall ◽  
Quantum Hall States ◽  
Topological Quantum ◽  
Hall States

Certain fractional quantum Hall states, including the experimentally observed ν = 5/2 state, and, possibly, the ν = 12/5 state, may have a sufficiently rich form of topological order (i.e. they may be nonabelian) to be useful for quantum information processing. For example, in some cases they may be used for topological quantum computation, an intrinsically fault tolerant form of quantum computation which is carried out by braiding the world lines of quasiparticle excitations in 2+1 dimensional space time. Here we briefly review the relevant properties of nonabelian quantum Hall states and discuss some of the methods we have found for finding specific braiding patterns which can be used to carry out universal quantum computation using them. Recent work on one-dimensional chains of interacting quasiparticles in nonabelian states is also reviewed.

scholarly journals Competing ν = 5/2 fractional quantum Hall states in confined geometry

2016 ◽  
Vol 113 (44) ◽  
pp. 12386-12390 ◽  
Author(s):  
Hailong Fu ◽  
Pengjie Wang ◽  
Pujia Shan ◽  
Lin Xiong ◽  
Loren N. Pfeiffer ◽  
...  
Keyword(s):  
Quantum Computation ◽  
Filling Factor ◽  
Fault Tolerant ◽  
Quantum Hall ◽  
Point Contact ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Topological Quantum ◽  
Quantum Point ◽  
Topological Quantum Computation

Some theories predict that the filling factor 5/2 fractional quantum Hall state can exhibit non-Abelian statistics, which makes it a candidate for fault-tolerant topological quantum computation. Although the non-Abelian Pfaffian state and its particle-hole conjugate, the anti-Pfaffian state, are the most plausible wave functions for the 5/2 state, there are a number of alternatives with either Abelian or non-Abelian statistics. Recent experiments suggest that the tunneling exponents are more consistent with an Abelian state rather than a non-Abelian state. Here, we present edge-current–tunneling experiments in geometrically confined quantum point contacts, which indicate that Abelian and non-Abelian states compete at filling factor 5/2. Our results are consistent with a transition from an Abelian state to a non-Abelian state in a single quantum point contact when the confinement is tuned. Our observation suggests that there is an intrinsic non-Abelian 5/2 ground state but that the appropriate confinement is necessary to maintain it. This observation is important not only for understanding the physics of the 5/2 state but also for the design of future topological quantum computation devices.

QUANTUM COMPUTING WITH NON-ABELIAN QUASIPARTICLES

2007 ◽  
Vol 21 (08n09) ◽  
pp. 1372-1378 ◽  
Author(s):  
N. E. BONESTEEL ◽  
L. HORMOZI ◽  
G. ZIKOS ◽  
S. H. SIMON
Keyword(s):  
Dimensional Space ◽  
Quantum Hall ◽  
Three Dimensional ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Quantum Operations ◽  
Topological Quantum ◽  
Dimensional Space Time ◽  
Two Space Dimensions ◽  
Topological Quantum Computation

In topological quantum computation quantum information is stored in exotic states of matter which are intrinsically protected from decoherence, and quantum operations are carried out by dragging particle-like excitations (quasiparticles) around one another in two space dimensions. The resulting quasiparticle trajectories define world-lines in three dimensional space-time, and the corresponding quantum operations depend only on the topology of the braids formed by these world-lines. We describe recent work showing how to find braids which can be used to perform arbitrary quantum computations using a specific kind of quasiparticle (those described by the so-called Fibonacci anyon model) which are thought to exist in the experimentally observed ν = 12/5 fractional quantum Hall state.

scholarly journals Beyond anyons

2018 ◽  
Vol 33 (28) ◽  
pp. 1830011
Author(s):  
Zhenghan Wang
Keyword(s):  
Black Holes ◽  
Quantum Gravity ◽  
Quantum Hall ◽  
Group Symmetry ◽  
Topological Order ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Btz Black Holes ◽  
Modular Tensor Categories ◽  
Interesting Direction

The theory of anyon systems, as modular functors topologically and unitary modular tensor categories algebraically, is mature. To go beyond anyons, our first step is the interplay of anyons with conventional group symmetry due to the paramount importance of group symmetry in physics. This led to the theory of symmetry-enriched topological order. Another direction is the boundary physics of topological phases, both gapless as in the fractional quantum Hall physics and gapped as in the toric code. A more speculative and interesting direction is the study of Banados–Teitelboim–Zanelli (BTZ) black holes and quantum gravity in 3d. The clearly defined physical and mathematical issues require a far-reaching generalization of anyons and seem to be within reach. In this short survey, I will first cover the extensions of anyon theory to symmetry defects and gapped boundaries. Then, I will discuss a desired generalization of anyons to anyon-like objects — the BTZ black holes — in 3d quantum gravity.

Incompressible Quantum Fluids of Ideal Anyons in a Strong Magnetic Field

1991 ◽  
Vol 05 (10) ◽  
pp. 1725-1729
Author(s):  
F. C. Zhang ◽  
M. Ma
Keyword(s):  
Magnetic Field ◽  
Strong Magnetic Field ◽  
Ground State ◽  
Similarity Transformation ◽  
Quantum Hall ◽  
Quantum Fluids ◽  
Fractional Quantum ◽  
Fractional Quantum Hall ◽  
Integer Quantum Hall Effect ◽  
Integer Quantum

Ideal anyons with statistics ν in a strong magnetic field are studied by means of a similarity transformation. The ground state exhibits "integer" quantum Hall effect at filling factor 1/ν with quasiparticle excitations of charge q/ν and statistics -1/ν. Certain electron FQH states can be considered as realization of this, for example, the sequence 2/5, 3/7, … hierarchy of the 1/3 state. This may explain the observed quasiparticle-quasihole asymmetry in the fractional quantum Hall hierarchy.

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