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

arXiv:1603.06495 · Canadian Journal of Physics

Topological hardcore bosons on the honeycomb lattice

S. A. Owerre

Published Jun 17, 2016• 0 citations
arXivHTMLPDF

Abstract

This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.

DOI
10.1139/cjp-2016-0235

Related papers

Magnon edge states in the hardcore- Bose–Hubbard model

S. A. Owerre

Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.

arXiv:1603.07989•Journal of Physics Condensed Matter•Sep 7, 2016•8 citations

Topological bosonic states on ribbons of a honeycomb lattice

Yi‐Ping Wang, Xingchuan Zhu, Kefei Zou +2 more

The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.

arXiv:1808.03025•Physical Review A•Oct 15, 2018•3 citations

A semiclassical study of the topological Bose-Hubbard model

S. A. Owerre

We present a semiclassical perspective of the topological Bose-Hubbard model recently studied by quantum Monte Carlo (QMC) simulation on the honeycomb lattice [Phys. Rev. B 93, 121401(R) (2016)]. The three insulating phases uncovered by QMC are as follows: a superfluid, a Mott phase, and a charge-density-wave insulating phase. We show that this model maps to a spin-$1/2$ quantum XY model with competing magnetic fields on the two honeycomb sublattices. We give an explicit analytical origin of the quantum phase diagram using mean-field theory. Basically, the competition between the sublattice magnetic fields leads to three distinct phases uncovered by QMC. We find that the mean-field phase diagram captures a large regime of the quantum phase diagram. Furthermore, due to the mapping from bosons to spin variables and vice versa, the bosonic excitations of the Bose-Hubbard model correspond to the magnon excitations of the quantum spin system. We corroborate this assertion by computing the magnon bulk bands and the Berry curvatures and we find that the Berry curvatures have the same trends as the QMC result.

•Mar 25, 2016•0 citations

Topological excitations in quasi two-dimensional quantum magnets with weak interlayer interactions

Dhiman Bhowmick

The study of topological magnetic excitations have attracted widespread attention in the past few years.The wide variety of ground state phases realized in different two-dimensional magnets have emerged as versatile platforms for realizing magnetic analogues of topological phases uncovered in electronic systems over the past two decades.Dzyaloshinskii-Moriya(DM) interactions, that are ubiquitous in many quantum magnets, and has been demonstrated to induce a non-trivial topology in the magnetic excitations in many quantum magnets.In particular, signatures of DM-interaction induced topological features observed in the dispersion of magnetic excitations in the geometrically frustrated Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 and honeycomb ferromagnet CrI 3 have provided the motivation behind the bulk of the research presented in this thesis.In the first chapter we introduce the background and motivation of our study.We showed that the vastly available materials with a possibility of nonzero symmetry allowed DM-interaction motivate us to study the minimal models of interacting spins related to the materials.In the second chapter we have described the methods that is used to study the spin systems.To describe the spin excitations in the long-range ordered system and dimerized system, we use Holstein-Primakoff transformation and bond-operator formalism respectively.The Schwinger Boson mean field theory is applicable for any generic magnetic ground state and useful to study the system at high temperatures compared with Holstein-Primakoff transformation.After transforming the Hamiltonian into a quadratic bosonic Hamiltonian, it is diagonalized by using Bogoliubov-Valatin transformation.Different observables like Berry-curvature, Chern-number, Dynamical Spin structure factor etc. are cal-vii culated by using the single particle wave-function obtained from Bogoliubov-Valatin transformation.A non-zero Berry curvature is a signature of topologically protected edge states in a stripe geometry of a lattice and a systematic way of calculating edge states is also explained in the second chapter.Moreover in the second chapter the usefulness of symmetry in obtaining band degeneracies and the allowed spin-spin interaction terms are also described.The past theoretical studies show the presence of topological magnons in honeycomb ferromagnetic models due to presence of DM-interaction on a next-nearest neighbour bonds.Recently this kind of DM-interaction is detected in the honeycomb ferromagnet CrI 3 .This type of DM-interaction induces chiral edge states of magnon in the system and so we named it as chiral DM-interaction.In the third chapter we show that breaking of inversion symmetry at the center of honeycomb structure gives rise to a extra DM-interaction which we named as anti-chiral DM-interaction.We studied the system by using Schwinger Boson mean field theory and Holstein-Primakoff transformation and show that when the antichiral DM-interaction dominates over the chiral DM-interaction, the direction of velocity of the edge states become in the same direction (antichiral edge states).Due to conservation of total number of spins in the system a bulk current flows in the opposite direction relative to the antichiral edge current.In this study we suggested the way to break the inversion symmetries in the materials CrSrTe 3 , CrGrTe 3 , AFe 2 (PO 4 ) 2 (A=Ba, Cs, K, La) to achieve antichiral DM-interaction.The presence of antichiral edge states can be detected by using inelastic neutron scattering by detecting the band tilting at K and K points of magnon bands.Moreover we showed that spin noise spectroscopy at the edges is useful measurements to detect the presence of antichiral edge modes.Magnetic force microscopy is also a promising tool to detect the antichiral magnons at edges.The underlying spin-Hamiltonian of the antiferromagnetic systems in the materials like rare-earth tetraborides(RB 4 , R=Er,Tm) and U 2 Pd 2 In can be described by using extended Shastry-Sutherland models.In previous theoretical studies it is shown that there is a non-collinear spin-state known as flux state exists in the Shastry-Sutherland model in presence of out of plane DM-interaction.Although the presence of perpendicular component of DM-interactions in the rare-earth materials are not known, it can be induced artificially by using circularly polarized light or using heavy-metal alloys.In the fourth chapter, we studied the magnetic excitations in the flux state on Shastry-Sutherland lattice in-First of all, I would like to thank my research supervisor Prof. Pinaki Sengupta for his continuous support and guidance throughout my Ph.D. study on and off the field.whenever I went to his office with a problem he always welcomed me and assisted me.He has encouraged and inspired me to become an independent researcher and developed my critical thinking.I am really grateful to him as a person who introduced me the field of research.Moreover my scientific writing and presentation skills also improved due to his suggestions.I am really very thankful for being so flexible and allowing me to choose the work and project which interests me most.

arXiv:2103.00401•Jan 1, 2020•0 citations

Occupancy oscillation of honeycomb-lattice hard-core bosons under a pseudo-magnetic-field

Jiaojiao Guo, Huaiming Guo

We investigate the hardcore Bose-Hubbard model on a honeycomb lattice under a pseudo-magnetic field generated by triaxial strain using the quantum Monte Carlo (QMC) method. In the presence of strain, we construct a phase diagram that encompasses superfluid and solid phases at different fillings. Interestingly, we observe intriguing phenomena related to filling factors, including a solid phase with a filling of $\ensuremath{\rho}=0.4912$. This solid phase is characterized by distinct sublattice occupancies separated by large domain walls. Additionally, within the superfluid region, we observe stripe phases where the occupancy of hardcore bosons exhibits oscillatory behavior. Finally, we employ linear spin-wave theory and derive the pseudo-Landau levels present in the excitation spectrum. Our findings not only provide valuable insights into the behavior of hardcore bosons in the presence of pseudo-magnetic fields, but they can also be experimentally realized using ultracold bosonic atoms confined in optical lattices.

Physical Review A•Dec 19, 2023•0 citations

Bosonic edge states in gapped honeycomb lattices

Huaiming Guo, Yuekun Niu, Shu Chen +1 more

By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we show the existence of bosonic edge states. For a single layer honeycomb lattice, bosonic edge states can be controlled to appear, cross the gap, and merge into bulk states by an on-site potential applied on the outermost sites of the boundary. On a bilayer honeycomb lattice, A bosonic edge state traversing the gap at half filling is demonstrated. The topological origin of the bosonic edge states is discussed with pseudo Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states with ultracold bosons trapped in honeycomb optical lattices.

arXiv:1512.01340•Physical review. B./Physical review. B•Mar 1, 2016•9 citations
This paper presents a connection between the topological properties of hardcore bosons and that of magnons in quantum spin magnets. We utilize the Haldane-like hardcore bosons on the honeycomb lattice as an example. We show that this system maps to a spin-1/2 quantum XY model with a next-nearest-neighbour Dzyaloshinsky–Moriya interaction. We obtain the magnon excitations of the quantum spin model and compute the edge states, Berry curvature, and thermal and spin Nernst conductivities. Because of the mapping from spin variables to bosons, the hardcore bosons possess the same nontrivial topological properties as those in quantum spin systems. These results are important in the study of magnetic excitations in quantum magnets and they are also useful for understanding the control of ultracold bosonic quantum gases in honeycomb optical lattices, which is experimentally accessible.
Quantum Monte Carlo (QMC) simulation has uncovered nonzero Berry curvature and bosonic edge states in the hardcore-Bose-Hubbard model on the gapped honeycomb lattice. The competition between the chemical potential and staggered onsite potential leads to an interesting quantum phase diagram comprising the superfluid phase, Mott insulator, and charge density wave insulator. In this paper, we present a semiclassical perspective of this system by mapping to a spin-1/2 quantum XY model. We give an explicit analytical origin of the quantum phase diagram, the Berry curvatures, and the edge states using semiclassical approximations. We find very good agreement between the semiclassical analyses and the QMC results. Our results show that the topological properties of the hardcore-Bose-Hubbard model are the same as those of magnon in the corresponding quantum spin system. Our results are applicable to systems of ultracold bosonic atoms trapped in honeycomb optical lattices.
The topological properties of hardcore bosons on ribbons of honeycomb lattice are studied using quantum Monte Carlo simulations. We map out a rich phase diagram with the superfluid and insulator phases at various fillings. Particularly, it is revealed that the insulator state at half filling is a topological bosonic state, which is characterized by a nontrivial Berry phase and a pair of end states. We provide an intuitive picture to understand this topological bosonic insulator state by showing that it can be adiabatically mapped to a topological fermionic model. It is also shown that the topological end states are robust against weak interactions beyond the hardcore repulsion. Our results can be simulated by using bosonic cold atoms trapped in designed optical lattices.
We present a semiclassical perspective of the topological Bose-Hubbard model recently studied by quantum Monte Carlo (QMC) simulation on the honeycomb lattice [Phys. Rev. B 93, 121401(R) (2016)]. The three insulating phases uncovered by QMC are as follows: a superfluid, a Mott phase, and a charge-density-wave insulating phase. We show that this model maps to a spin-1/21/21/2 quantum XY model with competing magnetic fields on the two honeycomb sublattices. We give an explicit analytical origin of the quantum phase diagram using mean-field theory. Basically, the competition between the sublattice magnetic fields leads to three distinct phases uncovered by QMC. We find that the mean-field phase diagram captures a large regime of the quantum phase diagram. Furthermore, due to the mapping from bosons to spin variables and vice versa, the bosonic excitations of the Bose-Hubbard model correspond to the magnon excitations of the quantum spin system. We corroborate this assertion by computing the magnon bulk bands and the Berry curvatures and we find that the Berry curvatures have the same trends as the QMC result.
The study of topological magnetic excitations have attracted widespread attention in the past few years.The wide variety of ground state phases realized in different two-dimensional magnets have emerged as versatile platforms for realizing magnetic analogues of topological phases uncovered in electronic systems over the past two decades.Dzyaloshinskii-Moriya(DM) interactions, that are ubiquitous in many quantum magnets, and has been demonstrated to induce a non-trivial topology in the magnetic excitations in many quantum magnets.In particular, signatures of DM-interaction induced topological features observed in the dispersion of magnetic excitations in the geometrically frustrated Shastry-Sutherland compound SrCu 2 (BO 3 ) 2 and honeycomb ferromagnet CrI 3 have provided the motivation behind the bulk of the research presented in this thesis.In the first chapter we introduce the background and motivation of our study.We showed that the vastly available materials with a possibility of nonzero symmetry allowed DM-interaction motivate us to study the minimal models of interacting spins related to the materials.In the second chapter we have described the methods that is used to study the spin systems.To describe the spin excitations in the long-range ordered system and dimerized system, we use Holstein-Primakoff transformation and bond-operator formalism respectively.The Schwinger Boson mean field theory is applicable for any generic magnetic ground state and useful to study the system at high temperatures compared with Holstein-Primakoff transformation.After transforming the Hamiltonian into a quadratic bosonic Hamiltonian, it is diagonalized by using Bogoliubov-Valatin transformation.Different observables like Berry-curvature, Chern-number, Dynamical Spin structure factor etc. are cal-vii culated by using the single particle wave-function obtained from Bogoliubov-Valatin transformation.A non-zero Berry curvature is a signature of topologically protected edge states in a stripe geometry of a lattice and a systematic way of calculating edge states is also explained in the second chapter.Moreover in the second chapter the usefulness of symmetry in obtaining band degeneracies and the allowed spin-spin interaction terms are also described.The past theoretical studies show the presence of topological magnons in honeycomb ferromagnetic models due to presence of DM-interaction on a next-nearest neighbour bonds.Recently this kind of DM-interaction is detected in the honeycomb ferromagnet CrI 3 .This type of DM-interaction induces chiral edge states of magnon in the system and so we named it as chiral DM-interaction.In the third chapter we show that breaking of inversion symmetry at the center of honeycomb structure gives rise to a extra DM-interaction which we named as anti-chiral DM-interaction.We studied the system by using Schwinger Boson mean field theory and Holstein-Primakoff transformation and show that when the antichiral DM-interaction dominates over the chiral DM-interaction, the direction of velocity of the edge states become in the same direction (antichiral edge states).Due to conservation of total number of spins in the system a bulk current flows in the opposite direction relative to the antichiral edge current.In this study we suggested the way to break the inversion symmetries in the materials CrSrTe 3 , CrGrTe 3 , AFe 2 (PO 4 ) 2 (A=Ba, Cs, K, La) to achieve antichiral DM-interaction.The presence of antichiral edge states can be detected by using inelastic neutron scattering by detecting the band tilting at K and K points of magnon bands.Moreover we showed that spin noise spectroscopy at the edges is useful measurements to detect the presence of antichiral edge modes.Magnetic force microscopy is also a promising tool to detect the antichiral magnons at edges.The underlying spin-Hamiltonian of the antiferromagnetic systems in the materials like rare-earth tetraborides(RB 4 , R=Er,Tm) and U 2 Pd 2 In can be described by using extended Shastry-Sutherland models.In previous theoretical studies it is shown that there is a non-collinear spin-state known as flux state exists in the Shastry-Sutherland model in presence of out of plane DM-interaction.Although the presence of perpendicular component of DM-interactions in the rare-earth materials are not known, it can be induced artificially by using circularly polarized light or using heavy-metal alloys.In the fourth chapter, we studied the magnetic excitations in the flux state on Shastry-Sutherland lattice in-First of all, I would like to thank my research supervisor Prof. Pinaki Sengupta for his continuous support and guidance throughout my Ph.D. study on and off the field.whenever I went to his office with a problem he always welcomed me and assisted me.He has encouraged and inspired me to become an independent researcher and developed my critical thinking.I am really grateful to him as a person who introduced me the field of research.Moreover my scientific writing and presentation skills also improved due to his suggestions.I am really very thankful for being so flexible and allowing me to choose the work and project which interests me most.
We investigate the hardcore Bose-Hubbard model on a honeycomb lattice under a pseudo-magnetic field generated by triaxial strain using the quantum Monte Carlo (QMC) method. In the presence of strain, we construct a phase diagram that encompasses superfluid and solid phases at different fillings. Interestingly, we observe intriguing phenomena related to filling factors, including a solid phase with a filling of $\ensuremath{\rho}=0.4912$. This solid phase is characterized by distinct sublattice occupancies separated by large domain walls. Additionally, within the superfluid region, we observe stripe phases where the occupancy of hardcore bosons exhibits oscillatory behavior. Finally, we employ linear spin-wave theory and derive the pseudo-Landau levels present in the excitation spectrum. Our findings not only provide valuable insights into the behavior of hardcore bosons in the presence of pseudo-magnetic fields, but they can also be experimentally realized using ultracold bosonic atoms confined in optical lattices.
By quantum Monte Carlo simulations of bosons in gapped honeycomb lattices, we show the existence of bosonic edge states. For a single layer honeycomb lattice, bosonic edge states can be controlled to appear, cross the gap, and merge into bulk states by an on-site potential applied on the outermost sites of the boundary. On a bilayer honeycomb lattice, A bosonic edge state traversing the gap at half filling is demonstrated. The topological origin of the bosonic edge states is discussed with pseudo Berry curvature. The results will simulate experimental studies of these exotic bosonic edge states with ultracold bosons trapped in honeycomb optical lattices.