Quantum phase transitions in the 
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-layer Ising toric code

L., Schamriss,; Lenke, L.; Mühlhauser, M.; Schmidt, K. P.

doi:10.1103/physrevb.105.184425

Cited by 3 publications

(1 citation statement)

References 63 publications

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“…As a consequence, it has been an attractive starting point for many investigations to understand the physical properties of topologically ordered quantum matter, e.g., the effect of external perturbations and the properties of induced quantum phase transitions [18][19][20][21][22][23][24][25][26][27][28][29], the consequences of thermal fluctuations [30][31][32], the properties of entanglement measures [33,34] or dynamical correlation functions [35] as well as non-equilibrium properties [36,37]. Further, generalization of the perturbed toric code have been investigated in 3D [38][39][40][41][42], in layered systems [43,44] and for frustrated geometries [45,46].…”

Section: Introductionmentioning

confidence: 99%

Incorporating non-local anyonic statistics into a graph decomposition

Mühlhauser,

Kott,

Schmidt

2024

SciPost Phys. Core

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In this work we describe how to systematically implement a full graph decomposition to set up a linked-cluster expansion for the topological phase of Kitaev’s toric code in a field. This demands to include the non-local effects mediated by the mutual anyonic statistics of elementary charge and flux excitations. Technically, we describe how to consistently integrate such non-local effects into a hypergraph decomposition for single excitations. The approach is demonstrated for the ground-state energy and the elementary excitation energies of charges and fluxes in the perturbed topological phase.

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Section: Introductionmentioning

confidence: 99%

Incorporating non-local anyonic statistics into a graph decomposition

Mühlhauser,

Kott,

Schmidt

2024

SciPost Phys. Core

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Gauge field dynamics in multilayer Kitaev spin liquids

Joy,

Rosch

2024

npj Quantum Mater.

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The Kitaev spin liquid realizes an emergent static $${{\mathbb{Z}}}_{2}$$ Z 2 gauge field with vison excitations coupled to Majorana fermions. We consider Kitaev models stacked on top of each other, weakly coupled by Heisenberg interaction ∝ J⊥. This inter-layer coupling breaks the integrability of the model and makes the gauge fields dynamic. Conservation laws and topology keep single visons immobile. However, an inter-layer vison pairs can hop with a hopping amplitude linear in J⊥ confined to the layer, but their motion is strongly influenced by the type of stacking. For AA stacking, an interlayer pair has a two-dimensional motion but for AB or ABC stacking, sheet conservation laws restrict its motion to a one-dimensional channel within the plane. For all stacking types, an intra-layer vison-pair is constrained to move out-of-plane only. Depending on the anisotropy of the Kitaev couplings Kx, Ky, Kz, the intra-layer vison pairs can display either coherent tunnelling or purely incoherent hopping. When a magnetic field opens a gap for Majorana fermions, there exist two types of intra-layer vison pairs - a bosonic and a fermionic one. Only the bosonic pair obtains a hopping rate linear in J⊥. We use our results to identify the leading instabilities of the spin liquid phase induced by the inter-layer coupling.

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Anyon condensation and confinement transition in a Kitaev spin liquid bilayer

Hwang

2024

Phys. Rev. B

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Transitions between quantum spin liquids (QSLs) are fundamental problems lying beyond the Landau paradigm and requiring a deep understanding of the entanglement structures of QSLs called topological orders. The novel concept of anyon condensation has been proposed as a theoretical mechanism, predicting various possible transitions between topological orders, but it has long been elusive to confirm the mechanism in quantum spin systems. Here, we introduce a concrete spin model that incarnates the mechanism of the anyon condensation transition. Our model harbors two topological QSLs in different parameter regions, a non-Abelian Kitaev spin liquid (KSL) bilayer state and a resonating valence bond (RVB) state. The bilayer-KSL-to-RVB transition indeed occurs by the mechanism of anyon condensation, which we identify by using parton theories and exact diagonalization studies. Moreover, we observe “anyon confinement” phenomena in our numerical results, akin to the quark confinement in high-energy physics. Namely, non-Abelian Ising anyons of the bilayer KSL are confined in the transition to the RVB state. Implications and extensions of this study are discussed in various aspects such as (i) anyon-condensed multilayer construction of Kitaev's 16-fold way of anyon theories, (ii) an additional vison condensation transition from the RVB to a valence bond solid in the Kitaev bilayer system, (iii) dynamical anyon condensation in a non-Hermitian Kitaev bilayer, (iv) generalizations of our model to other lattice geometries, and (v) experimental realizations. This work puts together the two fascinating QSLs that are extensively studied in modern condensed matter and quantum physics into a concrete spin model, offering a comprehensive picture that unifies the anyon physics of the Kitaev spin liquids and the resonating valence bonds. Published by the American Physical Society 2024

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Quantum phase transitions in the K -layer Ising toric code

Cited by 3 publications

References 63 publications

Incorporating non-local anyonic statistics into a graph decomposition

Incorporating non-local anyonic statistics into a graph decomposition

Gauge field dynamics in multilayer Kitaev spin liquids

Anyon condensation and confinement transition in a Kitaev spin liquid bilayer

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