Phase transition in a noisy Kitaev toric code model

We consider various aspects of Kitaev's toric code model on a plane in the C*-algebraic approach to quantum spin systems on a lattice. In particular, we show that elementary excitations of the ground state can be described by localized endomorphisms of the observable algebra. The structure of these endomorphisms is analyzed in the spirit of the Doplicher–Haag–Roberts program (specifically, through its generalization to infinite regions as considered by Buchholz and Fredenhagen). Most notably, the statistics of excitations can be calculated in this way. The excitations can equivalently be described by the representation theory of [Formula: see text], i.e. Drinfel'd's quantum double of the group algebra of ℤ2.

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Low-energy effective theory of the toric code model in a parallel magnetic field

Physical Review B ◽

10.1103/physrevb.79.033109 ◽

2009 ◽

Vol 79 (3) ◽

Cited By ~ 84

Author(s):

Julien Vidal ◽

Sébastien Dusuel ◽

Kai Phillip Schmidt

Keyword(s):

Magnetic Field ◽

Low Energy ◽

Effective Theory ◽

Parallel Magnetic Field ◽

Code Model ◽

Toric Code

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Quenching the Kitaev honeycomb model

SciPost Physics ◽

10.21468/scipostphys.7.5.071 ◽

2019 ◽

Vol 7 (5) ◽

Cited By ~ 1

Author(s):

Louk Rademaker

Keyword(s):

Phase Transition ◽

Steady State ◽

Time Evolution ◽

Valence Bond ◽

Antiferromagnetic Order ◽

Dynamical Phase Transition ◽

Dynamical Phase ◽

Equilibrium Response ◽

Valence Bond Solid ◽

Toric Code

I studied the non-equilibrium response of an initial Néel state under time evolution with the Kitaev honeycomb model. With isotropic interactions (J_x = J_y = J_zJx=Jy=Jz) the system quickly loses its antiferromagnetic order and crosses over into a steady state valence bond solid, which can be inferred from the long-range dimer correlations. There is no signature of a dynamical phase transition. Upon including anisotropy (J_x = J_y \neq J_zJx=Jy≠Jz), an exponentially long prethermal regime appears with persistent magnetization oscillations whose period derives from an effective toric code.

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Homological codes and abelian anyons

Reviews in Mathematical Physics ◽

10.1142/s0129055x19500387 ◽

2019 ◽

Vol 31 (10) ◽

pp. 1950038

Author(s):

Péter Vrana ◽

Máté Farkas

Keyword(s):

Homotopy Type ◽

Ground States ◽

Chain Complex ◽

Cochain Complex ◽

Locally Finite ◽

Code Model ◽

Cw Complex ◽

Localized Excitations ◽

Proper Homotopy ◽

Toric Code

We study a generalization of Kitaev’s abelian toric code model defined on CW complexes. In this model, qudits are attached to [Formula: see text]-dimensional cells and the interaction is given by generalized star and plaquette operators. These are defined in terms of coboundary and boundary maps in the locally finite cellular cochain complex and the cellular chain complex. We find that the set of energy-minimizing ground states and the types of charges carried by certain localized excitations depends only on the proper homotopy type of the CW complex. As an application, we show that the homological product of a CSS code with the infinite toric code has excitations with abelian anyonic statistics.

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Dispersive toric code model with fusion and defusion

Physical Review B ◽

10.1103/physrevb.101.115105 ◽

2020 ◽

Vol 101 (11) ◽

Author(s):

Bruno Nachtergaele ◽

Nicholas E. Sherman

Keyword(s):

Code Model ◽

Toric Code

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Defects in the 3-dimensional toric code model form a braided fusion 2-category

Journal of High Energy Physics ◽

10.1007/jhep12(2020)078 ◽

2020 ◽

Vol 2020 (12) ◽

Author(s):

Liang Kong ◽

Yin Tian ◽

Zhi-Hao Zhang

Keyword(s):

Topological Defects ◽

Spatial Dimension ◽

Topological Order ◽

Mathematical Result ◽

3 Dimensional ◽

Code Model ◽

Model Form ◽

Degeneracy Condition ◽

Toric Code

Abstract It was well known that there are e-particles and m-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional ℤ2 topological order. Recent mathematical result, however, shows that there are additional string-like topological defects in the 3-dimensional ℤ2 topological order. In this work, we construct all topological defects of codimension 2 and higher, and show that they form a braided fusion 2-category satisfying a braiding non-degeneracy condition.

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