Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Chinese Physics Letters

Dynamics of the Entanglement Spectrum of the Haldane Model under a Sudden Quench*

Lin-Han Mo, Qiu-Lan Zhang, Xin Wan

Published Jun 1, 2020• 4 citations
Publisher

Abstract

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.

DOI
10.1088/0256-307x/37/6/060301

Related papers

Dynamics of the Entanglement Zero Modes in the Haldane Model under a Quantum Quench

Heng-Xi Ji, Lin-Han Mo, Xin Wan

We investigate evolution of entanglement spectra of the Haldane model for Chern insulators upon a sudden quench within the same topological phase. In particular, we focus on the location of the entanglement spectrum crossing, which signifies the bulk topology. It is shown that the coplanarity condition for the pseudomagnetic field of the model, which can be used to determine the crossing in the equilibrium case, needs to be relaxed. We analytically derive the non-equilibrium condition with the help of an edge-state wave function ansatz and a dynamically induced length-scale cutoff. With spectral analyses, it is realized that the oscillatory behavior of the crossing is dominated by the interband excitations at the van Hove singularities.

Chinese Physics Letters•Mar 1, 2022•3 citations

Dynamical geometry of the Haldane model under a quantum quench

Liwei Qiu, Lih-King Lim, Xin Wan

We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for nonequilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the prequench equilibrium state relaxes to the postquench equilibrium state in an oscillatory fashion, whose amplitude decay as ${t}^{1/2}$. In the process, however, the characteristic winding vector of the nonequilibrium system can evolve to regimes that are not reachable with equilibrium states.

arXiv:2405.12470•Physical review. B./Physical review. B•Sep 26, 2024•0 citations

Quench dynamics of edge modes revealed by entanglement spectrum in a dimerized chain with dilute impurities

Qiu-Lan Zhang

We study the evolution of the one-particle entanglement spectrum for the one-dimensional dimerized chain in the presence of impurities. When the system quenches from a topologically nontrivial phase to a trivial phase with disorder, the spectrum features the split of two zero-energy edge modes due to their interaction with impurities. Our observations demonstrate the feasibility of using entanglement spectrum to study the quench dynamics of topological systems.

International Journal of Modern Physics B•Jul 19, 2018•0 citations

Dynamics of edge currents in a linearly quenched Haldane model

Sougata Mardanya, Utso Bhattacharya, Amit Agarwal +1 more

In a finite-time quantum quench of the Haldane model, the Chern number determining the topology of the bulk remains invariant, as long as the dynamics is unitary. Nonetheless, the corresponding boundary attribute, the edge current, displays interesting dynamics. For the case of sudden and adiabatic quenches the postquench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite-time ($\ensuremath{\tau}$) linear quench in a Haldane nanoribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $\ensuremath{\tau}$ and has a turning point at a characteristic time scale $\ensuremath{\tau}={\ensuremath{\tau}}_{0}$. For small $\ensuremath{\tau}$, the excited states lead to a huge unidirectional surge in the edge current of both edges. On the other hand, in the limit of large $\ensuremath{\tau}$, the edge current saturates to its expected equilibrium ground-state value. This competition between the two limits lead to the observed nonmonotonic behavior. Interestingly, ${\ensuremath{\tau}}_{0}$ seems to depend only on the Semenoff mass and the Haldane flux. A similar dynamics for the edge current is also expected in other systems with topological phases.

arXiv:1801.07015•Physical review. B./Physical review. B•Mar 26, 2018•17 citations

Post-Quench Entanglement and Fluctuations in the Haldane Model

Anmol Dhar

Topological insulators are materials that behave like an insulator in the bulk but have conducting edge states. These edge states are topologically protected and exhibit unique properties. Studying the dynamics of these systems far-from equilibrium can provide information on the stability of these edge states and provide insight on the propagation of entanglement which is of interest in quantum information. In this thesis, I study the far-from-equilibrium dynamics of the Haldane model. Various quenches between different topological phases are performed, and the dynamics of both the entanglement and particle numbers are analyzed. Using a correlation matrix, the time evolution of the entanglement and charge fluctuations are calculated. The dynamics of the entanglement and charge fluctuations provides insight on the evolution of this system following a quench. The charge fluctuations allow us to probe the entanglement of these systems using a quantity that can be measured experimentally. I showed that for the various quenches, the charge fluctuations mirrors the entanglement entropy providing examples for which the second moment provides the majority of the weight. Additionally, I showed that the entanglement entropy drastically increases immediately following a quench until the system reaches a steady state. By analyzing the entanglement spectrum I showed that the bulk states contribute to the entanglement following a quench. This thesis establishes a framework that can be applied to other topological systems.

•Jan 1, 2018•0 citations

Dynamics of Quenched Topological Edge Modes

Pedro D Sacramento

A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be understood as changes of the parameters of the Hamiltonian. These changes may be sudden or carried out at a fixed rate. In general, the edge modes decay in the thermodynamic limit, but for finite systems a revival time is found that scales with the system size. The dynamics of fermionic edge modes and Majorana modes are compared. The effect of periodic perturbations is also referred allowing the appearance of edge modes out of a topologically trivial phase.

arXiv:1701.03567•Nov 26, 2017•1 citation
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.
We investigate evolution of entanglement spectra of the Haldane model for Chern insulators upon a sudden quench within the same topological phase. In particular, we focus on the location of the entanglement spectrum crossing, which signifies the bulk topology. It is shown that the coplanarity condition for the pseudomagnetic field of the model, which can be used to determine the crossing in the equilibrium case, needs to be relaxed. We analytically derive the non-equilibrium condition with the help of an edge-state wave function ansatz and a dynamically induced length-scale cutoff. With spectral analyses, it is realized that the oscillatory behavior of the crossing is dominated by the interband excitations at the van Hove singularities.
We explore the time evolution of a topological system when the system undergoes a sudden quantum quench within the same nontrivial phase. Using Haldane's honeycomb model as an example, we show that equilibrium states in a topological phase can be distinguished by geometrical features, such as the characteristic momentum at which the half-occupied edge modes cross, the associated edge-mode velocity, and the winding vector about which the normalized pseudospin magnetic field winds along a great circle on the Bloch sphere. We generalize these geometrical quantities for nonequilibrium states and use them to visualize the quench dynamics of the topological system. In general, we find the prequench equilibrium state relaxes to the postquench equilibrium state in an oscillatory fashion, whose amplitude decay as t1/2{t}^{1/2}t1/2. In the process, however, the characteristic winding vector of the nonequilibrium system can evolve to regimes that are not reachable with equilibrium states.
In a finite-time quantum quench of the Haldane model, the Chern number determining the topology of the bulk remains invariant, as long as the dynamics is unitary. Nonetheless, the corresponding boundary attribute, the edge current, displays interesting dynamics. For the case of sudden and adiabatic quenches the postquench edge current is solely determined by the initial and the final Hamiltonians, respectively. However for a finite-time ($\ensuremath{\tau}$) linear quench in a Haldane nanoribbon, we show that the evolution of the edge current from the sudden to the adiabatic limit is not monotonic in $\ensuremath{\tau}$ and has a turning point at a characteristic time scale $\ensuremath{\tau}={\ensuremath{\tau}}_{0}$. For small $\ensuremath{\tau}$, the excited states lead to a huge unidirectional surge in the edge current of both edges. On the other hand, in the limit of large $\ensuremath{\tau}$, the edge current saturates to its expected equilibrium ground-state value. This competition between the two limits lead to the observed nonmonotonic behavior. Interestingly, ${\ensuremath{\tau}}_{0}$ seems to depend only on the Semenoff mass and the Haldane flux. A similar dynamics for the edge current is also expected in other systems with topological phases.
Topological insulators are materials that behave like an insulator in the bulk but have conducting edge states. These edge states are topologically protected and exhibit unique properties. Studying the dynamics of these systems far-from equilibrium can provide information on the stability of these edge states and provide insight on the propagation of entanglement which is of interest in quantum information. In this thesis, I study the far-from-equilibrium dynamics of the Haldane model. Various quenches between different topological phases are performed, and the dynamics of both the entanglement and particle numbers are analyzed. Using a correlation matrix, the time evolution of the entanglement and charge fluctuations are calculated. The dynamics of the entanglement and charge fluctuations provides insight on the evolution of this system following a quench. The charge fluctuations allow us to probe the entanglement of these systems using a quantity that can be measured experimentally. I showed that for the various quenches, the charge fluctuations mirrors the entanglement entropy providing examples for which the second moment provides the majority of the weight. Additionally, I showed that the entanglement entropy drastically increases immediately following a quench until the system reaches a steady state. By analyzing the entanglement spectrum I showed that the bulk states contribute to the entanglement following a quench. This thesis establishes a framework that can be applied to other topological systems.
A characteristic feature of topological systems is the presence of robust gapless edge states. In this work the effect of time-dependent perturbations on the edge states is considered. Specifically we consider perturbations that can be understood as changes of the parameters of the Hamiltonian. These changes may be sudden or carried out at a fixed rate. In general, the edge modes decay in the thermodynamic limit, but for finite systems a revival time is found that scales with the system size. The dynamics of fermionic edge modes and Majorana modes are compared. The effect of periodic perturbations is also referred allowing the appearance of edge modes out of a topologically trivial phase.