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

Physical Review A

Experimental observation of a quadrupolar phase via quench dynamics on a spin simulator

Dafa Zhao, Shunzhong Xue, Dong Ruan, Jun Li, Dawei Lu, Wen Huang, Tao Xin, Hang Li, Xinfang Nie, Guilu Long

Published Dec 29, 2021• 2 citations
Publisher

Abstract

Recently, higher-order topological insulators have drawn much attention from researchers. For chiral-symmetric one-dimensional systems, the mean chiral displacement, a bulk observable related to the topological invariant, can distinguish topological states from trivial phases. Naturally, there exists an analogous quality for the higher-order one. In a previous work [T. Mizoguchi, Y. Kuno, and Y. Hatsugai, Phys. Rev. Lett. 126, 016802 (2021)], the mean chiral quadrupole moment is introduced. Inspired by this work, we investigate the quadrupolar phase of a higher-order topological insulator on a spin quantum simulator. With focus on a two-particle noninteracting Benalcazar-Bernevig-Hughes model, by changing the amplitude of hopping interactions, we first observe quantum phase transitions from topological phase to trivial phase using a spin simulator experimentally. Since the mean chiral quadrupole moment has robustness against environmental noise, we also test its dependence on perturbations. As an exploration of the bulk observable of a higher-order topological insulator, it may provide one path to investigate arbitrary dimensional systems.

DOI
10.1103/physreva.104.062615

Related papers

Detecting Bulk Topology of Quadrupolar Phase from Quench Dynamics

Tomonari Mizoguchi, Yoshihito Kuno, Yasuhiro Hatsugai

Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.

arXiv:2008.01924•Physical Review Letters•Jan 8, 2021•15 citations

Quantum Phases of Three-Dimensional Chiral Topological Insulators on a Spin Quantum Simulator

Tao Xin, Yishan Li, Yu-ang Fan +6 more

The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.

arXiv:2001.05122•Physical Review Letters•Aug 27, 2020•44 citations

Many-body higher-order topological invariant for Cn -symmetric insulators

Ammar Jahin, Yuan-Ming Lu, Yuxuan Wang

Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa [arXiv:2302.00800], we propose a well-defined, many-body bulk invariant for ${C}_{n}$-symmetric higher-order topological insulators that is valid for both noninteracting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of ${C}_{n}$ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as $e/n$ with ${C}_{n}$ symmetry, leading to a ${\mathbb{Z}}_{n}$ classification for higher-order topological insulators in two dimensions.

Physical review. B./Physical review. B•May 8, 2024•6 citations

Quantum Monte Carlo study of topological phases on a spin analogue of Benalcazar–Bernevig–Hughes model

Jiaojiao Guo, Junsong Sun, Xingchuan Zhu +3 more

We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.

arXiv:2010.05402•Journal of Physics Condensed Matter•Oct 19, 2021•10 citations

Topological dipole conserving insulators and multipolar responses

Julian May-Mann, Taylor L. Hughes

Higher order topological insulators (HOTIs) are a novel form of insulating quantum matter, which are characterized by having gapped boundaries that are separated by gapless corner or hinge states. Recently, it has been proposed that the essential features of a large class of HOTIs are captured by topological multipolar response theories. In this paper, we show that these multipolar responses can be realized in interacting lattice models, which conserve both charge and dipole. In this paper we study several models in both the strongly interacting and mean field limits. In two dimensions we consider a ring-exchange model which exhibits a quadrupole response, and can be tuned to a ${C}_{4}$ symmetric higher order topological phase with half-integer quadrupole moment, as well as half-integer corner charges. We then extend this model to develop an analytic description of adiabatic dipole pumping in an interacting lattice model. The quadrupole moment changes during this pumping process, and if the process is periodic we show the total change in the quadrupole moment is quantized as an integer. We also consider two interacting three-dimensional ($3\mathrm{D}$) lattice models with chiral hinge modes. We show that the chiral hinge modes are heralds of a recently proposed ``dipolar Chern-Simons'' response, which is related to the quadrupole response by dimensional reduction. Interestingly, we find that in the mean field limit both the two-dimensional and $3\mathrm{D}$ interacting models we consider here are equivalent to known models of noninteracting HOTIs (or boundary obstructed versions). The self-consistent mean field theory treatment provides insight into the connection between free-fermion (mean field) theories having vanishing polarization and interacting models where dipole moments are microscopically conserved.

arXiv:2103.00008•Physical review. B./Physical review. B•Aug 18, 2021•11 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
Recently, higher-order topological insulators have drawn much attention from researchers. For chiral-symmetric one-dimensional systems, the mean chiral displacement, a bulk observable related to the topological invariant, can distinguish topological states from trivial phases. Naturally, there exists an analogous quality for the higher-order one. In a previous work [T. Mizoguchi, Y. Kuno, and Y. Hatsugai, Phys. Rev. Lett. 126, 016802 (2021)], the mean chiral quadrupole moment is introduced. Inspired by this work, we investigate the quadrupolar phase of a higher-order topological insulator on a spin quantum simulator. With focus on a two-particle noninteracting Benalcazar-Bernevig-Hughes model, by changing the amplitude of hopping interactions, we first observe quantum phase transitions from topological phase to trivial phase using a spin simulator experimentally. Since the mean chiral quadrupole moment has robustness against environmental noise, we also test its dependence on perturbations. As an exploration of the bulk observable of a higher-order topological insulator, it may provide one path to investigate arbitrary dimensional systems.
Direct measurement of a bulk topological observable in topological phase of matter has been a long-standing issue. Recently, detection of bulk topology through quench dynamics has attracted growing interests. Here, we propose that topological characters of a quantum quadrupole insulator can be read out by quench dynamics. Specifically, we introduce a quantity, a quadrupole moment weighted by the eigenvalues of the chiral operator, which takes zero for the trivial phase and finite for the quadrupolar topological phase. By utilizing an efficient numerical method to track the unitary time evolution, we elucidate that the quantity we propose indeed serves as an indicator of topological character for both noninteracting and interacting cases. The robustness against disorders is also demonstrated.
The detection of topological phases of matter has become a central issue in recent years. Conventionally, the realization of a specific topological phase in condensed matter physics relies on probing the underlying surface band dispersion or quantum transport signature of a real material, which may be imperfect or even absent. On the other hand, quantum simulation offers an alternative approach to directly measure the topological invariant on a universal quantum computer. However, experimentally demonstrating high-dimensional topological phases remains a challenge due to the technical limitations of current experimental platforms. Here, we investigate the three-dimensional topological insulators in the AIII (chiral unitary) symmetry class, which yet lack experimental realization. Using the nuclear magnetic resonance system, we experimentally demonstrate their topological properties, where a dynamical quenching approach is adopted and the dynamical bulk-boundary correspondence in the momentum space is observed. As a result, the topological invariants are measured with high precision on the band-inversion surface, exhibiting robustness to the decoherence effect. Our Letter paves the way toward the quantum simulation of topological phases of matter in higher dimensions and more complex systems through controllable quantum phases transitions.
Higher-order topological insulators in two spatial dimensions display fractional corner charges. While fractional charges in one dimension are known to be captured by a many-body bulk invariant, computed by the Resta formula, a many-body bulk invariant for higher-order topology and the corresponding fractional corner charges remains elusive despite several attempts. Inspired by recent work by Tada and Oshikawa [arXiv:2302.00800], we propose a well-defined, many-body bulk invariant for Cn{C}_{n}Cn​-symmetric higher-order topological insulators that is valid for both noninteracting and interacting systems. Instead of relating them to the bulk quadrupole moment as was previously done, we show that in the presence of Cn{C}_{n}Cn​ rotational symmetry, this bulk invariant can be directly identified with quantized fractional corner charges. In particular, we prove that the corner charge is quantized as e/ne/ne/n with Cn{C}_{n}Cn​ symmetry, leading to a Zn{\mathbb{Z}}_{n}Zn​ classification for higher-order topological insulators in two dimensions.
We study the higher-order topological spin phases based on a spin analogue of Benalcazar-Bernevig-Hughes model in two dimensions using large-scale quantum Monte Carlo simulations. A continuous Néel-valence bond solid quantum phase transition is revealed by tuning the ratio between dimerized spin couplings, namely, the weak and strong exchange couplings. Through the finite-size scaling analysis, we identify the phase critical points, and consequently, map out the full phase diagrams in related parameter spaces. Particularly, we find that the valence bond solid phase can be a higher-order topological spin phase, which has a gap for spin excitations in the bulk while demonstrates characteristic gapless spin modes at corners of open lattices. We further discuss the connection between the higher-order topological spin phases and the electronic correlated higher-order phases, and find both of them possess gapless spin corner modes that are protected by higher-order topology. Our result exemplifies higher-order physics in the correlated spin systems and will contribute to further understandings of the many-body higher-order topological phenomena.
Higher order topological insulators (HOTIs) are a novel form of insulating quantum matter, which are characterized by having gapped boundaries that are separated by gapless corner or hinge states. Recently, it has been proposed that the essential features of a large class of HOTIs are captured by topological multipolar response theories. In this paper, we show that these multipolar responses can be realized in interacting lattice models, which conserve both charge and dipole. In this paper we study several models in both the strongly interacting and mean field limits. In two dimensions we consider a ring-exchange model which exhibits a quadrupole response, and can be tuned to a C4{C}_{4}C4​ symmetric higher order topological phase with half-integer quadrupole moment, as well as half-integer corner charges. We then extend this model to develop an analytic description of adiabatic dipole pumping in an interacting lattice model. The quadrupole moment changes during this pumping process, and if the process is periodic we show the total change in the quadrupole moment is quantized as an integer. We also consider two interacting three-dimensional (3D3\mathrm{D}3D) lattice models with chiral hinge modes. We show that the chiral hinge modes are heralds of a recently proposed ``dipolar Chern-Simons'' response, which is related to the quadrupole response by dimensional reduction. Interestingly, we find that in the mean field limit both the two-dimensional and 3D3\mathrm{D}3D interacting models we consider here are equivalent to known models of noninteracting HOTIs (or boundary obstructed versions). The self-consistent mean field theory treatment provides insight into the connection between free-fermion (mean field) theories having vanishing polarization and interacting models where dipole moments are microscopically conserved.
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.