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

Detecting topology through dynamics in interacting fermionic wires

Andreas Haller, Pietro Massignan, Matteo Rizzi

Published Jan 1, 2020• 10 citations
OpenAlex

Abstract

Probing the topological invariants of interacting systems stands as a grand and open challenge. Here we describe a dynamical method to characterize 1D chiral models, based on the direct observation of time-evolving bulk excitations. We present analytical and state-of-the-art numerical calculations on various flavors of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how measuring the mean chiral displacement allows us to distinguish between topological insulator, trivial insulator, and symmetry-broken phases. Finally, we provide a readily-feasible experimental blueprint for a model displaying these three phases and we describe how to detect those.

Related papers

Detecting topology through dynamics in interacting fermionic wires

Andreas Haller, Pietro Massignan, Matteo Rizzi

This work describe a dynamical method to characterize one dimensional chiral models, based on the direct observation of time-evolving bulk excitations. The protocol is tested on top of a readily-feasible experimental set-up of an interacting Su-Schrieffer-Heeger (SSH) chain which realizes both topological and symmetry-broken phases.

arXiv:2001.09074•Physical Review Research•Aug 5, 2020•11 citations

Charge waves and dynamical signatures of topological phases in Su-Schrieffer-Heeger chains

T. Kwapiński, Marcin Kurzyna, Luis E. F. Foa Torres

We investigate the emergence of charge waves and their temporal dynamics in one-dimensional Su-Schrieffer-Heeger (SSH) topological chains. Contrary to the conventional view that charge oscillations are suppressed in gapped topological systems with preserved chiral symmetry, we show that such oscillations can indeed occur. The general condition for an arbitrary oscillation period is analysed, and we find that the charge waves propagating along the chain do not depend on its topology, except at the edges, where both topological phases exhibit essential differences. In chains with inequivalent atoms within the SSH unit cell, we observe regular long-period sublattice oscillations that appear simultaneously with even-odd charge oscillations. Furthermore, we study the nonequilibrium dynamics in SSH chains. After a quench, the time evolution of the local density of states and charge occupancies exhibits clear dynamical fingerprints that distinguish topologically trivial and nontrivial phases. Our results establish that transient charge dynamics can distinguish topologically trivial and nontrivial phases in real time by detecting the presence of topologically-protected edge states.

arXiv:2604.13682•Physical review. B./Physical review. B•Apr 14, 2026•0 citations

Multiparticle quantum walk: A dynamical probe of topological many-body excitations

B. Ostahie, Doru Sticlet, Cătălin Paşcu Moca +4 more

Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting $N$ particles with multiple flavors in the interacting $\text{SU}(N)$ Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the $N$-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.

arXiv:2209.03569•Physical review. B./Physical review. B•Jul 13, 2023•4 citations

Topological phases and spontaneous symmetry breaking: the revenge of the original Su-Schrieffer-Heeger model

Polina Matveeva, Dmitri B. Gutman, Sam T. Carr

We study the interplay of spontaneous symmetry breaking and topological properties in interacting one-dimensional models. We solve these models using bozonization and identify topologically non-trivial phases by counting the additional degeneracy (affiliated with the edge modes) of a finite-size system relative to the infinite one. We find even if the mean-field solution is topological, this may not be true when it arises from spontaneous symmetry breaking, including in the Su-Schrieffer-Heeger (SSH) model. This implies that the original SSH model, as presented by Su, Schrieffer, and Heeger, is topologically trivial, as opposed to its mean-field version. A spinful version, on the other hand, does exhibit a topologically non-trivial phase. In that state, both mean-field solutions are topologically non-trivial and correspond to non-interacting SSH chains in the opposite phases with the winding number $ν=1$. We show that this phase is protected by a chiral symmetry, similar to the non-interacting phases.

arXiv:2508.01985•Aug 4, 2025•0 citations

Detection of Zak phases and topological invariants in a chiral photonic quantum walk

Filippo Cardano, Alessio D’Errico, Alexandre Dauphin +9 more

Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.

•Oct 20, 2016•4 citations

Topological characterizations of an extended Su–Schrieffer–Heeger model

Dizhou Xie, Wei Gou, Teng Xiao +2 more

Abstract The Su–Schrieffer–Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higher-dimensional extension of the mean chiral displacement measurement, however, this has not yet been verified in experiment. Here, we report the realization of this model with ultracold atoms in a momentum lattice. We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary.

arXiv:1906.12019•npj Quantum Information•May 30, 2019•177 citations
Probing the topological invariants of interacting systems stands as a grand and open challenge. Here we describe a dynamical method to characterize 1D chiral models, based on the direct observation of time-evolving bulk excitations. We present analytical and state-of-the-art numerical calculations on various flavors of interacting Su-Schrieffer-Heeger (SSH) chains, demonstrating how measuring the mean chiral displacement allows us to distinguish between topological insulator, trivial insulator, and symmetry-broken phases. Finally, we provide a readily-feasible experimental blueprint for a model displaying these three phases and we describe how to detect those.
We investigate the emergence of charge waves and their temporal dynamics in one-dimensional Su-Schrieffer-Heeger (SSH) topological chains. Contrary to the conventional view that charge oscillations are suppressed in gapped topological systems with preserved chiral symmetry, we show that such oscillations can indeed occur. The general condition for an arbitrary oscillation period is analysed, and we find that the charge waves propagating along the chain do not depend on its topology, except at the edges, where both topological phases exhibit essential differences. In chains with inequivalent atoms within the SSH unit cell, we observe regular long-period sublattice oscillations that appear simultaneously with even-odd charge oscillations. Furthermore, we study the nonequilibrium dynamics in SSH chains. After a quench, the time evolution of the local density of states and charge occupancies exhibits clear dynamical fingerprints that distinguish topologically trivial and nontrivial phases. Our results establish that transient charge dynamics can distinguish topologically trivial and nontrivial phases in real time by detecting the presence of topologically-protected edge states.
Recent experiments demonstrated that single-particle quantum walks can reveal the topological properties of single-particle states. Here, we generalize this picture to the many-body realm by focusing on multiparticle quantum walks of strongly interacting fermions. After injecting NNN particles with multiple flavors in the interacting SU(N)\text{SU}(N)SU(N) Su-Schrieffer-Heeger chain, their multiparticle continuous-time quantum walk is monitored by a variety of methods. We find that the many-body Berry phase in the NNN-body part of the spectrum signals a topological transition upon varying the dimerization, similarly to the single-particle case. This topological transition is captured by the single- and many-body mean chiral displacement during the quantum walk and remains present for strong interaction as well as for moderate disorder. Our predictions are well within experimental reach for cold atomic gases and can be used to detect the topological properties of many-body excitations through dynamical probes.
We study the interplay of spontaneous symmetry breaking and topological properties in interacting one-dimensional models. We solve these models using bozonization and identify topologically non-trivial phases by counting the additional degeneracy (affiliated with the edge modes) of a finite-size system relative to the infinite one. We find even if the mean-field solution is topological, this may not be true when it arises from spontaneous symmetry breaking, including in the Su-Schrieffer-Heeger (SSH) model. This implies that the original SSH model, as presented by Su, Schrieffer, and Heeger, is topologically trivial, as opposed to its mean-field version. A spinful version, on the other hand, does exhibit a topologically non-trivial phase. In that state, both mean-field solutions are topologically non-trivial and correspond to non-interacting SSH chains in the opposite phases with the winding number ν=1ν=1ν=1. We show that this phase is protected by a chiral symmetry, similar to the non-interacting phases.
Topological insulators are fascinating states of matter exhibiting protected edge states and robust quantized features in their bulk. Here, we propose and validate experimentally a method to detect topological properties in the bulk of one-dimensional chiral systems. We first introduce the mean chiral displacement, and we show that it rapidly approaches a multiple of the Zak phase in the long time limit. Then we measure the Zak phase in a photonic quantum walk, by direct observation of the mean chiral displacement in its bulk. Next, we measure the Zak phase in an alternative, inequivalent timeframe, and combine the two windings to characterize the full phase diagram of this Floquet system. Finally, we prove the robustness of the measure by introducing dynamical disorder in the system. This detection method is extremely general, as it can be applied to all one-dimensional platforms simulating static or Floquet chiral systems.
Abstract The Su–Schrieffer–Heeger (SSH) model perhaps is the easiest and the most basic model for topological excitations. Many variations and extensions of the SSH model have been proposed and explored to better understand both fundamental and novel aspects of topological physics. The SSH4 model has been proposed theoretically as an extended SSH model with higher dimension (the internal dimension changes from two to four). It has been proposed that the winding number in this system can be determined through a higher-dimensional extension of the mean chiral displacement measurement, however, this has not yet been verified in experiment. Here, we report the realization of this model with ultracold atoms in a momentum lattice. We verify the winding number through measurement of the mean chiral displacement in a system with higher internal dimension, we map out the topological phase transition in this system, and we confirm the topological edge state by observation of the quench dynamics when atoms are initially prepared at the system boundary.