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arXiv:1811.05985 · Physics Letters B

Post-quench evolution of complexity and entanglement in a topological system

Tibra Ali, Arpan Bhattacharyya, S. Shajidul Haque, Eugene H. Kim, Nathan Moynihan

Published Nov 5, 2020• 53 citations
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Abstract

We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of entanglement.

DOI
10.1016/j.physletb.2020.135919

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We investigate the evolution of complexity and entanglement following a quench in a one-dimensional topological system, namely the Su-Schrieffer-Heeger model. We demonstrate that complexity can detect quantum phase transitions and shows signatures of revivals; this observation provides a practical advantage in information processing. We also show that the complexity saturates much faster than the entanglement entropy in this system, and we provide a physical argument for this. Finally, we demonstrate that complexity is a less sensitive probe of topological order, compared with measures of entanglement.
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In this work, we find that the complexity of quantum many-body states, defined as a spread in the Krylov basis, may serve as a probe that distinguishes topological phases of matter. We illustrate this analytically in one of the representative examples, the Su-Schrieffer-Heeger model, finding that spread complexity becomes constant in the topological phase. Moreover, in the same setup, we analyze exactly solvable quench protocols where the evolution of the spread complexity shows distinct dynamical features depending on the topological vs nontopological phase of the initial state as well as the quench Hamiltonian.
We investigate phase transitions in the extended Su-Schrieffer-Heeger (SSH) model with next-nearest-neighbor hoppings and an imaginary staggered chemical potential. In the presence of small non-Hermiticity, exceptional points emerge in pairs from the gap-closing momenta near the topological phase boundaries of the Hermitian limit. Utilizing the Krylov spread complexity and entanglement entropy, we analyze two dynamical protocols: (i) preparing the non-Hermitian ground state via a unitary transformation, and (ii) evolving the system under the non-Hermitian Hamiltonian. We show that the spread complexity, and long-time spread complexity as well as entanglement entropy can effectively signal phase transitions in the first and second protocols, respectively. To unravel the detailed structure of the transitions, we introduce the momentum-resolved complexity that identifies the characteristic modes and tracks their evolution with the driving parameter. In the regime where the system possesses a purely imaginary spectrum, we further identify dynamical phases based on the saturation behavior of the spread complexity. The entanglement entropy is also found to exhibit similar saturation behavior, thereby providing a more experimentally accessible probe of the dynamical phases.
Research on topological models unveils fascinating physics, especially in the realm of dynamical quantum phase transitions (DQPTs). However, the understanding of entanglement structures and properties near DQPT in models with longer-range hoppings is far from complete. In this work, we study DQPTs in the quenched extended Su-Schrieffer-Heeger model. Anomalous DQPTs, where the number of critical momenta exceeds the winding number differences between the prequench and postquench phases, are observed. We find that the entanglement exhibits local maximum (minimum) around the anomalous DQPTs, in line with the level crossings (separations) around the middle of the correlation matrix spectrum. We further categorize the phases in the equilibrium model into two classes and distinctive features in the time evolution of the entanglement involving quenches within and across the two classes are identified. The findings pave the way to a better understanding of topological models with longer-range hoppings in the out-of-equilibrium regime.