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arXiv:2104.14097 · Physical Review Letters

Symmetry-Protected Topological Phases in a Rydberg Glass

Kai Li, Jiong-Hao Wang, Yan-Bin Yang, Yong Xu

Published Dec 23, 2021• 36 citations
arXivHTMLPDF

Abstract

Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.

DOI
10.1103/physrevlett.127.263004

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Recent theoretical studies predict that structural disorder, serving as a bridge connecting a crystalline material to an amorphous material, can induce a topological insulator from a trivial phase. However, to experimentally observe such a topological phase transition is very challenging due to the difficulty in controlling structural disorder in a quantum material. Given experimental realization of randomly positioned Rydberg atoms, such a system is naturally suited to studying structural disorder induced topological phase transitions and topological amorphous phases. Motivated by the development, we study topological phases in an experimentally accessible one-dimensional amorphous Rydberg atom chain with random atom configurations. In the single-particle level, we find symmetry-protected topological amorphous insulators and a structural disorder induced topological phase transition, indicating that Rydberg atoms provide an ideal platform to experimentally observe the phenomenon using state-of-the-art technologies. Furthermore, we predict the existence of a gapless symmetry-protected topological phase of interacting bosons in the experimentally accessible system. The resultant many-body topological amorphous phase is characterized by a Z_{2} invariant.
The topological orders in amorphous systems that lack crystalline symmetry have gained considerable attention recently. Here we propose the Floquet amorphous topological matter, among which the topological orders are explored in experimentally accessible one-dimensional array of randomly pointed Rydberg atoms with periodic driving. The topological properties are comprehensively characterized, considering both the single-particle and many-body perspectives. It is found that the periodic driving leads to rich topological phases of matter. At the single-particle level, we evaluate the real space winding numbers and polarization, revealing robust amorphous topological phases with 0-type and π-type edge modes. We show a structural disorder induced topological phase transition associated with localization transition in the nonequilibrium system. Remarkably, in the many-body case it is discovered that the amorphous topological order exists in the chain of hardcore bosons, captured by the topological entanglement entropy and the string order. Moreover, feasible experimental probe protocols are also elaborated. The topological phase in amorphous systems that lack long-range order brings a fresh perspective to the topological states of matter. Here, the authors propose the concept of Floquet amorphous topological order and consider its realization with periodically-driven Rydberg atoms.
The concept of topological phases is a powerful framework for characterizing ground states of quantum many-body systems that goes beyond the paradigm of symmetry breaking. Topological phases can appear in condensed-matter systems naturally, whereas the implementation and study of such quantum many-body ground states in artificial matter require careful engineering. Here, we report the experimental realization of a symmetry-protected topological phase of interacting bosons in a one-dimensional lattice and demonstrate a robust ground state degeneracy attributed to protected zero-energy edge states. The experimental setup is based on atoms trapped in an array of optical tweezers and excited into Rydberg levels, which gives rise to hard-core bosons with an effective hopping generated by dipolar exchange interaction.
Topological states of matter in disordered systems without translation symmetry have attracted great interest in recent years. These states with topological characters are not only robust against certain disorders, but also can be counterintuitively induced by disorders from a topologically trivial phase in the clean limit. In this review, we summarize the current theoretical and experimental progress on disorder-induced topological phases in both condensed-matter and artificial systems. We first introduce the topological Anderson insulators (TAIs) induced by random disorders and their topological characterizations and experimental realizations. We then discuss various extensions of TAIs with unique localization phenomena in quasiperiodic and non-Hermitian systems. We also review the theoretical and experimental studies on the disorder-induced topology in dynamical and many-body systems, including topological Anderson-Thouless pumps, disordered correlated topological insulators and average-symmetry protected topological orders acting as interacting TAI phases. Finally, we conclude the review by highlighting potential directions for future explorations.
Abstract Topological phases of matter can appear in noninteracting systems, as in band topology, or interacting systems, such as in spin models, with their defining features typically robust against weak disorder. Intriguingly, disorder itself can also induce topological phases--exemplified by the Anderson topological insulator in noninteracting systems. Experimental studies on disorder-induced topology have so far been limited to band topology. Here we report direct observations of disorder-induced many-body interacting average topological order in an atom array at half-filling, whereby random offsets to tweezer locations forming a lattice implement structural disorder, causing fluctuating long-range dipolar interactions between tweezer confined single atoms. The ground state degeneracy in disordered configurations is detected and compared to the regular lattice. The induced topological phase is vindicated by the spatially resolved atom-atom correlation functions for different forms of dimer compositions. By probing the quench dynamics of a highly excited state, we observe markedly slower decay of edge spin magnetization in comparison to the bulk spin, consistent with the presence of topologically protected edge modes in disordered lattices. Our experiments open a new direction for studying the interplay between disorder and strongly interacting topological matter in Rydberg atom arrays.
We investigate a symmetry-protected Z2{Z}_{2}Z2​ topological electron glass, a glassy equivalent of the Z2{Z}_{2}Z2​ topological band insulator in crystalline systems, and uncover associated quantum phase transitions in this three-dimensional amorphous network of atoms. Through explicit numerical calculations of the Witten effect, we show that the Z2{Z}_{2}Z2​ glass is characterized by an anomalous electromagnetic response, i.e., it can host dyons with 12\frac{1}{2}21​ electronic charge. We further study, using a variety of numerical diagnostics including such electromagnetic responses, the phase transitions of the Z2{Z}_{2}Z2​ glass into a metallic and/or a trivial insulating phase. We find that the phase transitions here are governed by subtle features of mobility edges and ``spectral inversion'' which are possibly unique to structurally amorphous systems. Our results provide a concrete setting to understand the general underpinnings of such phases, where strong structural disorder interplays with symmetry-protected topological order.
Protection of topological surface states by reflection symmetry breaks down when the boundary of the sample is misaligned with one of the high symmetry planes of the crystal. We demonstrate that this limitation is removed in amorphous topological materials, where the Hamiltonian is invariant on average under reflection over any axis due to continuous rotation symmetry. We show that the edge remains protected from localization in the topological phase, and the local disorder caused by the amorphous structure results in critical scaling of the transport in the system. In order to classify such phases we perform a systematic search over all the possible symmetry classes in two dimensions and construct the example models realizing each of the proposed topological phases. Finally, we compute the topological invariant of these phases as an integral along a meridian of the spherical Brillouin zone of an amorphous Hamiltonian.