Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces

• URL: http://arxiv.org/abs/2004.14930v4
• Date: Sat, 15 May 2021 05:29:26 GMT
• Title: Quantum dynamical characterization and simulation of topological phases with high-order band inversion surfaces
• Authors: Xiang-Long Yu, Wentao Ji, Lin Zhang, Ya Wang, Jiansheng Wu and Xiong-Jun Liu
• Abstract summary: How to characterize topological quantum phases is a fundamental issue in the broad field of topological matter. We show that characterization of a d-dimensional (dD) topological phase can be reduced to lower-dimensional topological invariants in the high-order BISs. We experimentally build up a quantum simulator with spin qubits to investigate a 3D chiral topological insulator through emulating each momentum one by one.
• Score: 5.900548151067686
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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 post-quench 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 3D 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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