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arXiv:2209.11119

Anyon condensation, topological quantum information scrambling, and Andreev-like reflection of non-Abelian anyons in quantum Hall interfaces

Ken K. W.

Published Sep 22, 2022• 1 citation
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Abstract

Quantum information scrambling is the spread of local information into correlation throughout the entire quantum many-body system. This concept has become a central topic in different contexts. In this work, we restate the connection between anyon condensation and topological quantum information scrambling in quantum Hall interfaces. We consider the interface between the Abelian Halperin-330 state and the non-Abelian Read-Rezayi state. We verify explicitly that the interface can be fully gapped. This allows the transmutation of local pseudospin information carried by an Abelian anyon into topological information stored entirely by the anyons in the non-Abelian quantum Hall liquid, with no scrambled information stored at the interface. In combination with our previous work [K. K. W. Ma and K. Yang, Phys. Rev. B 105, 045306 (2022)], our results demonstrate the dependence of the scrambling mechanism on the gapfulness of the interface. Possible Andreev-like reflection of non-Abelian anyons in the fully gapped interface is also discussed.

DOI
10.48550/arxiv.2209.11119

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The black hole information paradox has been hotly debated for the last few decades without a full resolution. This makes it desirable to find analogues of this paradox in simple and experimentally accessible systems, whose resolutions may shed light on this longstanding and fundamental problem. Here, we review and resolve the apparent "information paradox" in two different interfaces separating Abelian and non-Abelian quantum Hall states. In both cases, the information carried by the pseudospin degree of freedom of the Abelian anyons get scrambled when they cross the interface and enter the non-Abelian quantum Hall liquid. Nevertheless, it is found that the scrambling mechanism depends on the nature of the interface. The corresponding analogues of different concepts in black hole physics such as event horizon, black hole interior, Hawking radiation, and Page curve will also be discussed.
Topologically ordered phases of matter can be characterized by the presence of a universal, constant contribution to the entanglement entropy known as the topological entanglement entropy (TEE). The TEE can be calculated for Abelian phases via a ``cut-and-glue'' approach by treating the entanglement cut as a physical cut, coupling the resulting gapless edges with explicit tunneling terms, and computing the entanglement between the two edges. We provide a first step towards extending this methodology to non-Abelian topological phases, focusing on the generalized Moore-Read (MR) fractional quantum Hall states at filling fractions $\ensuremath{\nu}=1/n$. We consider interfaces between different MR states, write down explicit gapping interactions, which we motivate using an anyon condensation picture, and compute the entanglement entropy for an entanglement cut lying along the interface. Our work provides new insight towards understanding the connections between anyon condensation, gapped interfaces of non-Abelian phases, and TEE.
We find a series of possible continuous quantum phase transitions between fractional quantum Hall states at the same filling fraction in two-component quantum Hall systems. These can be driven by tuning the interlayer tunneling and/or interlayer repulsion. One side of the transition is the Halperin (p,p,p-3) Abelian two-component state, while the other side is the non-Abelian Z4 parafermion (Read-Rezayi) state. We predict that the transition is a continuous transition in the 3D Ising class. The critical point is described by a Z2 gauged Ginzburg-Landau theory. These results have implications for experiments on two-component systems at ν=2/3 and single-component systems at ν=8/3.
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We study the trapping of Abelian anyons (quasiholes and quasiparticles) by a local potential (e.g., induced by an atomic force microscopy tip) in a microscopic model of fractional quantum Hall liquids with long-range Coulomb interaction and edge confining potential. We find, in particular, that at Laughlin filling fraction $\ensuremath{\nu}=1∕3$, both quasihole and quasiparticle states can emerge as the ground state of the system in the presence of the trapping potential. As expected, we find that the presence of an Abelian quasihole has no effect on the edge spectrum of the quantum liquid, unlike in the non-Abelian case [X. Wan et al., Phys. Rev. Lett. 97, 256804 (2006)]. Although quasiholes and quasiparticles can emerge generically in the system, their stability depends on the strength of the confining potential and the strength and the range of the trapping potential. We discuss the relevance of the calculation to the high-accuracy generation and control of individual anyons in potential experiments, in particular, in the context of topological quantum computing.