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arXiv:1207.2198 · Physical Review B

Thermal instability of protected end states in a one-dimensional topological insulator

Oscar Viyuela, ́Angel Rivas, Miguel Angel Martin-Delgado

Published Oct 23, 2012• 63 citations
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Abstract

We have studied the dynamical thermal effects on the protected end states of a topological insulator (TI) when it is considered as an open quantum system in interaction with a noisy environment at a certain temperature $T$. As a result, we find that protected end states in a TI become unstable and decay with time. Very remarkably, the interaction with the thermal environment (fermion-boson) respects chiral symmetry, which is the symmetry responsible for the protection (robustness) of the end states in this TI when it is isolated from the environment. Therefore, this mechanism makes end states unstable while preserving their protecting symmetry. Our results have immediate practical implications in recently proposed simulations of TIs using cold atoms in optical lattices. Accordingly, we have computed lifetimes of topological end states for these physical implementations that are useful to make those experiments realistic.

DOI
10.1103/physrevb.86.155140

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We have studied the dynamical thermal effects on the protected end states of a topological insulator (TI) when it is considered as an open quantum system in interaction with a noisy environment at a certain temperature TTT. As a result, we find that protected end states in a TI become unstable and decay with time. Very remarkably, the interaction with the thermal environment (fermion-boson) respects chiral symmetry, which is the symmetry responsible for the protection (robustness) of the end states in this TI when it is isolated from the environment. Therefore, this mechanism makes end states unstable while preserving their protecting symmetry. Our results have immediate practical implications in recently proposed simulations of TIs using cold atoms in optical lattices. Accordingly, we have computed lifetimes of topological end states for these physical implementations that are useful to make those experiments realistic.
The existence of gapless boundary states is a key attribute of any topological insulator. Topological band theory predicts that these states are robust against static perturbations that preserve the relevant symmetries. In this article, using Floquet theory, we examine how chiral symmetry protection extends also to states subject to time-periodic perturbations---in one-dimensional Floquet topological insulators as well as in ordinary one-dimensional time-independent topological insulators. It is found that, in the case of the latter, the edge modes are resistant to a much larger class of time-periodic symmetry-preserving perturbations than in Floquet topological insulators. Notably, boundary states in chiral time-independent topological insulators also exhibit an unexpected resilience against a certain type of symmetry-breaking time-periodic perturbations. We argue that this is a generic property for topological phases protected by chiral symmetry. Implications for experiments are discussed.
We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a ppp-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, and therefore our main focus is the time evolution of the string order parameter, entanglement spectrum, and the topologically protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.
Topological insulators (TIs) are an exciting discovery because of their robustness against disorder and interactions. Recently, second-order TIs have been attracting increasing attention, because they host topologically protected 1D hinge states in 3D or 0D corner states in 2D. A significantly critical issue is whether the second-order TIs also survive interactions, but it is still unexplored. We study the effects of weak Coulomb interactions on a 3D second-order TI, with the help of renormalization-group calculations. We find that the 3D second-order TIs are always unstable, suffering from two types of topological phase transitions. One is from second-order TI to TI, the other is to normal insulator. The first type is accompanied by emergent time-reversal and inversion symmetries and has a dynamical critical exponent κ=1. The second type does not have the emergent symmetries but has nonuniversal dynamical critical exponents κ<1. Our results may inspire more inspections on the stability of higher-order topological states of matter and related novel quantum criticalities.
Two-dimensional topological insulators, characterized by symmetry-protected anomalous boundary modes, have been generalized to the strongly correlated regime for both bosonic and fermionic systems. As correlated topological insulators (TI) approach experimental realization in quantum simulators, conventional probes, such as transport measurements, are not easily applicable to these synthetic platforms. In this study, we focus on two examples of correlated TI: a bosonic TI protected by Z2×U(1)\mathbb{Z}_2\times U(1)Z2​×U(1) symmetry and the fermionic quantum spin Hall insulator protected by time-reversal symmetry. We propose a unified, readily implementable protocol based on measuring the disorder parameter ⟨exp⁡(iθQ^A)⟩\langle\exp(\mathrm{i}θ\hat{Q}_A)\rangle⟨exp(iθQ^​A​)⟩ for a large subregion AAA, with Q^A\hat{Q}_AQ^​A​ the total charge operator within AAA. Our key finding is that this quantity exhibits non-analytical dependence on θθθ for correlated TI, a signature robust against decoherence. We establish this diagnostic through both numerical simulations and analytical derivations. This protocol is well-suited for implementation on near-term quantum simulation platforms, providing a direct route to experimentally confirm correlated TI.
Symmetry plays a fundamental role in understanding complex quantum matter, particularly in classifying topological quantum phases, which have attracted great interests in the recent decade. An outstanding example is the time-reversal invariant topological insulator, a symmetry-protected topological (SPT) phase in the symplectic class of the Altland-Zirnbauer classification. We report the observation for ultracold atoms of a noninteracting SPT band in a one-dimensional optical lattice and study quench dynamics between topologically distinct regimes. The observed SPT band can be protected by a magnetic group and a nonlocal chiral symmetry, with the band topology being measured via Bloch states at symmetric momenta. The topology also resides in far-from-equilibrium spin dynamics, which are predicted and observed in experiment to exhibit qualitatively distinct behaviors in quenching to trivial and nontrivial regimes, revealing two fundamental types of spin-relaxation dynamics related to bulk topology. This work opens the way to expanding the scope of SPT physics with ultracold atoms and studying nonequilibrium quantum dynamics in these exotic systems.
The stability of quantum entanglement has been a bottleneck in the design of scalable quantum computing architectures, especially due to decoherence and environmental noise in traditional quantum materials. Topological insulators (TIs), which have bulk-insulating states and conducting surface states protected by time-reversal symmetry, offer a promising platform for enhancing entanglement resilience. This paper explores the mechanism of quantum entanglement in two-dimensional topological insulator systems and assesses their potential for next-generation quantum computing. -Using tight-binding Hamiltonian simulations and time-dependent density-matrix simulations, we study the evolution of entanglement as a function of temperature, disorder strength, spin-orbit coupling, etc. The entanglement is measured using concurrence and von Neumann entropy measures among a variety of system setups. Simulations Findings TI-based qubit systems have been found to have a 35-48 percent improvement in entanglement lifetime over conventional semiconductor qubits with comparable noise levels. Remarkably, coherence times of over 120 m are observed at temperatures lower than 50 mK, and an estimated 42% slows down the rate of entanglement degradation in the presence of moderate non-magnetic disorder. Moreover, the statistical analysis of 1,000 simulation runs shows that the standard deviation of entanglement fluctuations has decreased by a factor of 31, leading to better stability and reproducibility. These data demonstrate the inherent fault-tolerant properties of the topological surface states and their ability to maintain quantum correlations over longer periods of operation. Finally, the conclusions indicate that topological insulators provide a viable, scalable material platform for maintaining quantum entanglement, with important implications for quantum logic models and error-tolerant quantum computing. This paper justifies the incorporation of topological materials into future quantum information processing systems.