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

Topological magnon bound-states in quantum Heisenberg chains

Xizhou Qin, Feng Mei, Yongguan Ke, Li Zhang, Chaohong Lee

Published Feb 9, 2016• 1 citation
OpenAlex

Abstract

It is still an outstanding challenge to characterize and understand the topological features of strongly correlated states such as bound-states in interacting multi-particle quantum systems. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore an unprecedented topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry allows us to formulate a direct topological invariant for the multi-particle quantum states, which can be used to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and topological invariants of the two-magnon bound-states and show the existence of topological magnon bound-states. Our study not only opens a new prospect to pursue topological bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.

Related papers

Topological magnon bound states in periodically modulated Heisenberg XXZ chains

Xizhou Qin, Feng Mei, Yongguan Ke +2 more

Strongly interacting topological states in multiparticle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multiparticle quantum states, which enables us to characterize the topological features of multimagnon excitations. We calculate energy spectra, density distributions, correlations, and Chern numbers of the two-magnon bound states and show the existence of topological protected edge bound states. Our study not only opens a prospect to pursue topological magnon bound states, but also gives insights into the characterization and understanding of strongly interacting topological states.

arXiv:1602.03217•Physical review. B./Physical review. B•Nov 15, 2017•35 citations

Topological invariant and cotranslational symmetry in strongly interacting multi-magnon systems

Xizhou Qin, Feng Mei, Yongguan Ke +2 more

It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless–Kohmoto–Nightingale–den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms (Aidelsburger et al 2013 Phys. Rev. Lett. 111 , 185301; Miyake et al 2013 Phys. Rev. Lett. 111 , 185302). Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.

arXiv:1611.00205•New Journal of Physics•Oct 23, 2017•21 citations

Topological incommensurate magnetization plateaus in quasi-periodic quantum spin chains

Haiping Hu, Chen Cheng, Hong‐Gang Luo +1 more

Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.

arXiv:1409.3895•Scientific Reports•Feb 13, 2015•16 citations

Symmetry-protected topological phase for spin-tensor-momentum-coupled ultracold atoms

Zhoutao Lei, Yuangang Deng, Chaohong Lee

We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer classification, we show that our system hosts a symmetry-protected phase protected by a magnetic group symmetry ($\mathcal{M}$) and characterized by a ${Z}_{2}$ topological invariant. In single-particle spectra, we show that the topological nontrivial phase supports two kinds of edge states, which include two (four) zero-energy edge modes in the absence (presence) of two-photon detuning. We further study the bulk-edge correspondence in a non-Hermitian model by taking into account the particle dissipation. It is shown that the non-Hermitian system preserves the bulk-edge correspondence under the $\mathcal{M}$ symmetry but exhibits the non-Hermitian skin effect with breaking the $\mathcal{M}$ symmetry at nonzero magnetic flux. This work provides insights in understanding the exotic topological quantum states of high-spin systems and facilitating their experimental explorations.

arXiv:1912.06323•Physical Review A•Jul 2, 2020•10 citations

Multi-magnon excitations in Heisenberg spin-Schains with next-nearest-neighbour interactions

S L M Cyr, B. W. Southern, David A. Lavis

The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.

Journal of Physics Condensed Matter•Jun 24, 1996•4 citations

Interaction-induced topological bound states and Thouless pumping in a one-dimensional optical lattice

Ling Lin, Yongguan Ke, Chaohong Lee

We study topological features of interacting spin-$\frac{1}{2}$ particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.

arXiv:1910.09948•Physical Review A•Feb 27, 2020•60 citations
It is still an outstanding challenge to characterize and understand the topological features of strongly correlated states such as bound-states in interacting multi-particle quantum systems. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore an unprecedented topological state called topological magnon bound-state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry allows us to formulate a direct topological invariant for the multi-particle quantum states, which can be used to characterize the topological features of multi-magnon excitations. We calculate energy spectra, density distributions, correlations and topological invariants of the two-magnon bound-states and show the existence of topological magnon bound-states. Our study not only opens a new prospect to pursue topological bound-states, but also gives insights into the characterization and understanding of strongly interacting topological states.
Strongly interacting topological states in multiparticle quantum systems pose great challenges to both theory and experiment. Recently, bound states of elementary spin waves (magnons) in quantum magnets have been experimentally observed in quantum Heisenberg chains comprising ultracold Bose atoms in optical lattices. Here, we explore a strongly interacting topological state called topological magnon bound state in the quantum Heisenberg chain under cotranslational symmetry. We find that the cotranslational symmetry is the key to the definition of a topological invariant for multiparticle quantum states, which enables us to characterize the topological features of multimagnon excitations. We calculate energy spectra, density distributions, correlations, and Chern numbers of the two-magnon bound states and show the existence of topological protected edge bound states. Our study not only opens a prospect to pursue topological magnon bound states, but also gives insights into the characterization and understanding of strongly interacting topological states.
It is still an outstanding challenge to characterize and understand the topological features of strongly interacting states such as bound states in interacting quantum systems. Here, by introducing a cotranslational symmetry in an interacting multi-particle quantum system, we systematically develop a method to define a Chern invariant, which is a generalization of the well-known Thouless–Kohmoto–Nightingale–den Nijs invariant, for identifying strongly interacting topological states. As an example, we study the topological multi-magnon states in a generalized Heisenberg XXZ model, which can be realized by the currently available experiment techniques of cold atoms (Aidelsburger et al 2013 Phys. Rev. Lett. 111 , 185301; Miyake et al 2013 Phys. Rev. Lett. 111 , 185302). Through calculating the two-magnon excitation spectrum and the defined Chern number, we explore the emergence of topological edge bound states and give their topological phase diagram. We also analytically derive an effective single-particle Hofstadter superlattice model for a better understanding of the topological bound states. Our results not only provide a new approach to defining a topological invariant for interacting multi-particle systems, but also give insights into the characterization and understanding of strongly interacting topological states.
Uncovering topologically nontrivial states in nature is an intriguing and important issue in recent years. While most studies are based on the topological band insulators, the topological state in strongly correlated low-dimensional systems has not been extensively explored due to the failure of direct explanation from the topological band insulator theory on such systems and the origin of the topological property is unclear. Here we report the theoretical discovery of strongly correlated topological states in quasi-periodic Heisenberg spin chain systems corresponding to a series of incommensurate magnetization plateaus under the presence of the magnetic field, which are uniquely determined by the quasi-periodic structure of exchange couplings. The topological features of plateau states are demonstrated by the existence of non-trivial spin-flip edge excitations, which can be well characterized by nonzero topological invariants defined in a two-dimensional parameter space. Furthermore, we demonstrate that the topological invariant of the plateau state can be read out from a generalized Streda formula and the spin-flip excitation spectrum exhibits a similar structure of the Hofstadter's butterfly spectrum for the two-dimensional quantum Hall system on a lattice.
We propose a realizable experiment scheme to construct a one-dimensional synthetic magnetic flux lattice with spin-tensor-momentum coupled spin-1 atoms and explore its exotic topological states. Different from the Altland-Zirnbauer classification, we show that our system hosts a symmetry-protected phase protected by a magnetic group symmetry (M\mathcal{M}M) and characterized by a Z2{Z}_{2}Z2​ topological invariant. In single-particle spectra, we show that the topological nontrivial phase supports two kinds of edge states, which include two (four) zero-energy edge modes in the absence (presence) of two-photon detuning. We further study the bulk-edge correspondence in a non-Hermitian model by taking into account the particle dissipation. It is shown that the non-Hermitian system preserves the bulk-edge correspondence under the M\mathcal{M}M symmetry but exhibits the non-Hermitian skin effect with breaking the M\mathcal{M}M symmetry at nonzero magnetic flux. This work provides insights in understanding the exotic topological quantum states of high-spin systems and facilitating their experimental explorations.
The spectra of both two- and three-magnon excitations in Heisenberg spin chains with next-nearest-neighbour (NNN) interactions are studied using scaling methods and the recursion method respectively. Both two-spin and three-spin couplings are considered for general spin S. In the three-magnon case, the asymptotic behaviour of the recursion coefficients can be used to directly identify the presence of bound states in the spectrum. Both integrable and non-integrable models can be studied, and the integrable models display special features in the bound-state spectra. Our results for the three-magnon bound states of S = 1 chains differ appreciably from those obtained in previous studies based upon an integral equation approach.
We study topological features of interacting spin-12\frac{1}{2}21​ particles in one-dimensional state-dependent optical lattices. Due to the cotranslational symmetry, we introduce the center-of-mass Zak phase with the help of center-of-mass momentum. There appear topological bound states composed by two particles in different spin states via tuning hopping and interaction strengths. Under symmetric open boundary conditions, topological edge bound states appear as a result of the nontrivial center-of-mass Zak phase of bound-state band, which is protected by the center-of-mass inversion symmetry. The interaction plays a crucial role in the appearance of topological bound states and the system becomes completely trivial if the interaction is switched off. By periodically modulating the hopping and interaction strengths, we show how to implement topological Thouless pumping of bound states, in which the quantized shift of center of mass can be described by a nontrivial center-of-mass Chern number.