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Entanglement-Spectrum Crossing and Momentum-Time Skyrmions in Quench Dynamics

Zongping Gong, Masahito Ueda

Published Oct 15, 2017• 2 citations
OpenAlex

Abstract

By studying the quench dynamics in one-dimensional superlattice systems with inversion symmetry, we find robust crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The physics behind this phenomenon is the emergence of a dynamical Chern number accompanied by unitarily created momentum-time Skyrmions. We also discuss a possible experimental situation based on Bloch-state tomography in ultracold atomic systems. Our work identifies the unique role of topology in quantum dynamics far from equilibrium.

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Chinese Physics Letters•Jun 1, 2020•4 citations
By studying the quench dynamics in one-dimensional superlattice systems with inversion symmetry, we find robust crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The physics behind this phenomenon is the emergence of a dynamical Chern number accompanied by unitarily created momentum-time Skyrmions. We also discuss a possible experimental situation based on Bloch-state tomography in ultracold atomic systems. Our work identifies the unique role of topology in quantum dynamics far from equilibrium.
We unveil the stable (d+1)-dimensional topological structures underlying the quench dynamics for all of the Altland-Zirnbauer classes in d=1 dimension, and we propose to detect such dynamical topology from the time evolution of entanglement spectra. Focusing on systems in classes BDI and D, we find crossings in single-particle entanglement spectra for quantum quenches between different symmetry-protected topological phases. The entanglement-spectrum crossings are shown to be stable against symmetry-preserving disorder and faithfully reflect both Z (class BDI) and Z_{2} (class D) topological characterizations. As a by-product, we unravel the topological origin of the global degeneracies temporarily emerging in the many-body entanglement spectrum in the quench dynamics of the transverse-field Ising model. These findings can experimentally be tested in ultracold atoms and trapped ions with the help of cutting-edge tomography for quantum many-body states. Our work paves the way towards a systematic understanding of the role of topology in quench dynamics.
Topology in quench dynamics gives rise to intriguing dynamic topological phenomena, which are intimately connected to the topology of static Hamiltonians yet challenging to probe experimentally. Here we theoretically characterize and experimentally detect momentum-time skyrmions in parity-time [Formula: see text]-symmetric non-unitary quench dynamics in single-photon discrete-time quantum walks. The emergent skyrmion structures are protected by dynamic Chern numbers defined for the emergent two-dimensional momentum-time submanifolds, and are revealed through our experimental scheme enabling the construction of time-dependent non-Hermitian density matrices via direct measurements in position space. Our work experimentally reveals the interplay of [Formula: see text] symmetry and quench dynamics in inducing emergent topological structures, and highlights the application of discrete-time quantum walks for the study of dynamic topological phenomena.
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.
We study the effect of strong disorder on topology and entanglement in quench dynamics. Although disorder-induced topological phases have been well studied in equilibrium, the disorder-induced topology in quench dynamics has not been explored. In this paper, we predict a disorder-induced topology of postquench states characterized by the quantized dynamical Chern number and the crossings in the entanglement spectrum in (1+1)(1+1)(1+1) dimensions. The dynamical Chern number undergoes transitions from zero to unity and back to zero when increasing the disorder strength. The boundaries between different dynamical Chern numbers are determined by delocalized critical points in the postquench Hamiltonian with the strong disorder. An experimental realization in quantum walks is discussed.
We study the topological properties of one-dimensional systems undergoing unitary time evolution. We show that symmetries possessed both by the initial wave function and by the Hamiltonian at all times may not be present in the time-dependent wave function-a phenomenon which we dub "dynamically induced symmetry breaking." This leads to the possibility of a time-varying bulk index after quenching within noninteracting gapped topological phases. The consequences are observable experimentally through particle transport measurements. With reference to the entanglement spectrum, we explain how the topology of the wave function can change out of equilibrium, both for noninteracting fermions and for symmetry-protected topological phases protected by antiunitary symmetries.
One of the appealing features of topological systems is the presence of robust edge modes. Under a sudden quantum quench, the edge modes survive for a characteristic time that scales with the system size, during which the nontrivial topology continues to manifest in entanglement properties, even though the post-quench Hamiltonian belongs to a trivial phase. We exemplify this in the quench dynamics of a two-dimensional Haldane model with the help of one-particle entanglement spectrum and the probability density of its mid-states. We find that, beyond our knowledge in one-dimensional models, the momentum dependence of the transverse velocity plays a crucial role in the out-of-equilibrium evolution of the entanglement properties.