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:1802.05689 · Physical Review Letters

Strongly Correlated Bosons on a Dynamical Lattice

Daniel González-Cuadra, Przemysław R. Grzybowski, Alexandre Dauphin, Maciej Lewenstein

Published Aug 30, 2018• 55 citations
arXivHTMLPDF

Abstract

We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.

DOI
10.1103/physrevlett.121.090402

Related papers

Symmetry-breaking topological insulators in the Z2 Bose-Hubbard model

Daniel González-Cuadra, Alexandre Dauphin, Przemysław R. Grzybowski +3 more

We study a one-dimensional model of interacting bosons coupled to a dynamical ${\mathbb{Z}}_{2}$ field, the ${\mathbb{Z}}_{2}$ Bose-Hubbard model, and analyze the interplay between spontaneous symmetry breaking and topological symmetry protection. In a previous work, we showed how this model exhibits a spontaneous breaking of the translational symmetry through a bosonic Peierls transition. Here we find how, at half filling, the resulting phase also displays topological features that coexist with the presence of long-range order and yields a topological bond order wave. Using both analytical and numerical methods, we describe the properties of this phase, showing that it cannot be adiabatically connected to a topological phase of noninteracting bosons, and thus constitutes an instance of an interaction-induced symmetry-breaking topological insulator.

arXiv:1811.08392•Physical review. B./Physical review. B•Jan 24, 2019•61 citations

Devil's staircase of topological Peierls insulators and Peierls supersolids

Titas Chanda, Daniel González-Cuadra, Maciej Lewenstein +2 more

We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.

arXiv:2011.09228•SciPost Physics•Feb 25, 2022•12 citations

Phase transitions in strongly interacting quantum systems

Christopher N. Varney

Strongly correlated materials exhibit some of the most complex and technologically useful phenomena in condensed matter. We use the world line and determinant quantum Monte Carlo techniques to explore the phases of the Hubbard Hamiltonian, a model describing strong interactions, in a number of different contexts. We first consider the spin, charge, and bond order correlations of the one-dimensional extended fermion Hubbard model in the presence of a coupling to the lattice. A static alternating lattice distortion leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic, we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases. Second, we examine mixtures of bosons and fermions in one-dimensional optical lattices. We evaluate the density profiles and bosonic visibility [special characters omitted] resolving the discrepancy between theory and experiment by identifying parameter regimes where [special characters omitted] is reduced and increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that [special characters omitted] exhibits kinks which are tied to the domain evolution present in the pure bosonic case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments. Third, we report large scale calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the momentum distribution, allowing a more quantitative comparison with time-of-flight optical lattice experiments.

•Jan 1, 2009•0 citations

Higher-Order Topological Peierls Insulator in a Two-Dimensional Atom-Cavity System

Joana Fraxanet, Alexandre Dauphin, Maciej Lewenstein +2 more

In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.

arXiv:2305.03409•Physical Review Letters•Dec 27, 2023•16 citations

Bond-order density wave phases in dimerized extended Bose-Hubbard models

Zeki Zeybek, Peter Schmelcher, Rick Mukherjee

The Bose-Hubbard model (BHM) has been widely explored to develop a profound understanding of the strongly correlated behavior of interacting bosons. Quantum simulators not only allow the exploration of the BHM but also extend it to models with interesting phenomena such as gapped phases with multiple orders and topological phases. In this work, an extended Bose-Hubbard model involving a dimerized one-dimensional model of long-range interacting hard-core bosons is studied. Bond-order density wave phases (BODW) are characterized in terms of their symmetry breaking and topological properties. At certain fillings, interactions combined with dimerized hoppings give rise to an emergent symmetry-breaking leading to BODW phases, which differs from the case of non-interacting models that require an explicit breaking of the symmetry. Specifically, the BODW phase at filling $\ensuremath{\rho}=1/3$ possesses no analog in the noninteracting model in terms of its symmetry-breaking properties and the unit cell structure. Upon changing the dimerization pattern, the system realizes topologically trivial BODW phases. At filling $\ensuremath{\rho}=1/4$, on-site density modulations are shown to stabilize the topological BODW phase. Our work provides the bridge between interacting and noninteracting BODW phases and highlights the significance of long-range interactions in a dimerized lattice by showing unique BODW phases that do not exist in the noninteracting model.

arXiv:2403.06649•Physical review. B./Physical review. B•Aug 6, 2024•8 citations

Self-organized topological insulator due to cavity-mediated correlated tunneling

Titas Chanda, Rebecca Kraus, Giovanna Morigi +1 more

Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings. Originating from quantum interference, this topological phase is found in "exact" density-matrix renormalization group calculations and is entirely absent in the mean-field approach. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.

arXiv:2011.01687•Quantum•Jul 13, 2021•31 citations
We study a one-dimensional system of strongly correlated bosons on a dynamical lattice. To this end, we extend the standard Bose-Hubbard Hamiltonian to include extra degrees of freedom on the bonds of the lattice. We show that this minimal model exhibits phenomena reminiscent of fermion-phonon models. In particular, we discover a bosonic analog of the Peierls transition, where the translational symmetry of the underlying lattice is spontaneously broken. This provides a dynamical mechanism to obtain a topological insulator in the presence of interactions, analogous to the Su-Schrieffer-Heeger model for electrons. We characterize the phase diagram numerically, showing different types of bond order waves and topological solitons. Finally, we study the possibility of implementing the model using atomic systems.
We study a one-dimensional model of interacting bosons coupled to a dynamical Z2{\mathbb{Z}}_{2}Z2​ field, the Z2{\mathbb{Z}}_{2}Z2​ Bose-Hubbard model, and analyze the interplay between spontaneous symmetry breaking and topological symmetry protection. In a previous work, we showed how this model exhibits a spontaneous breaking of the translational symmetry through a bosonic Peierls transition. Here we find how, at half filling, the resulting phase also displays topological features that coexist with the presence of long-range order and yields a topological bond order wave. Using both analytical and numerical methods, we describe the properties of this phase, showing that it cannot be adiabatically connected to a topological phase of noninteracting bosons, and thus constitutes an instance of an interaction-induced symmetry-breaking topological insulator.
We consider a mixture of ultracold bosonic atoms on a one-dimensional lattice described by the XXZ-Bose-Hubbard model, where the tunneling of one species depends on the spin state of a second deeply trapped species. We show how the inclusion of antiferromagnetic interactions among the spin degrees of freedom generates a Devil's staircase of symmetry-protected topological phases for a wide parameter regime via a bosonic analog of the Peierls mechanism in electron-phonon systems. These topological Peierls insulators are examples of symmetry-breaking topological phases, where long-range order due to spontaneous symmetry breaking coexists with topological properties such as fractionalized edge states. Moreover, we identify a region of supersolid phases that do not require long-range interactions. They appear instead due to a Peierls incommensurability mechanism, where competing orders modify the underlying crystalline structure of Peierls insulators, becoming superfluid. Our work show the possibilities that ultracold atomic systems offer to investigate strongly-correlated topological phenomena beyond those found in natural materials.
Strongly correlated materials exhibit some of the most complex and technologically useful phenomena in condensed matter. We use the world line and determinant quantum Monte Carlo techniques to explore the phases of the Hubbard Hamiltonian, a model describing strong interactions, in a number of different contexts. We first consider the spin, charge, and bond order correlations of the one-dimensional extended fermion Hubbard model in the presence of a coupling to the lattice. A static alternating lattice distortion leads to enhanced charge density wave correlations at the expense of antiferromagnetic order. When the lattice degrees of freedom are dynamic, we show that a similar effect occurs even though the charge asymmetry must arise spontaneously. Although the evolution of the total energy with lattice coupling is smooth, the individual components exhibit sharp crossovers at the phase boundaries. Finally, we observe a tendency for bond order in the region between the charge and spin density wave phases. Second, we examine mixtures of bosons and fermions in one-dimensional optical lattices. We evaluate the density profiles and bosonic visibility [special characters omitted] resolving the discrepancy between theory and experiment by identifying parameter regimes where [special characters omitted] is reduced and increased. We present a simple qualitative picture of the different response to the fermion admixture in terms of the superfluid and Mott-insulating domains before and after the fermions are included. Finally, we show that [special characters omitted] exhibits kinks which are tied to the domain evolution present in the pure bosonic case, and also additional structure arising from the formation of boson-fermion molecules, a prediction for future experiments. Third, we report large scale calculations of the effective bandwidth, momentum distribution, and magnetic correlations of the square lattice fermion Hubbard Hamiltonian. The sharp Fermi surface of the non-interacting limit is significantly broadened by the electronic correlations, but retains signatures of the approach to the edges of the first Brillouin zone as the density increases. Finite size scaling of simulations on large lattices allows us to extract the interaction dependence of the antiferromagnetic order parameter, exhibiting its evolution from weak-coupling to the strong-coupling Heisenberg limit. Our lattices provide improved resolution of the momentum distribution, allowing a more quantitative comparison with time-of-flight optical lattice experiments.
In this work, we investigate a two-dimensional system of ultracold bosonic atoms inside an optical cavity, and show how photon-mediated interactions give rise to a plaquette-ordered bond pattern in the atomic ground state. The latter corresponds to a 2D Peierls transition, generalizing the spontaneous bond dimerization driven by phonon-electron interactions in the 1D Su-Schrieffer-Heeger (SSH) model. Here the bosonic nature of the atoms plays a crucial role to generate the phase, as similar generalizations with fermionic matter do not lead to a plaquette structure. Similar to the SSH model, we show how this pattern opens a nontrivial topological gap in 2D, resulting in a higher-order topological phase hosting corner states, that we characterize by means of a many-body topological invariant and through its entanglement structure. Finally, we demonstrate how this higher-order topological Peierls insulator can be readily prepared in atomic experiments through adiabatic protocols. Our work thus shows how atomic quantum simulators can be harnessed to investigate novel strongly correlated topological phenomena beyond those observed in natural materials.
The Bose-Hubbard model (BHM) has been widely explored to develop a profound understanding of the strongly correlated behavior of interacting bosons. Quantum simulators not only allow the exploration of the BHM but also extend it to models with interesting phenomena such as gapped phases with multiple orders and topological phases. In this work, an extended Bose-Hubbard model involving a dimerized one-dimensional model of long-range interacting hard-core bosons is studied. Bond-order density wave phases (BODW) are characterized in terms of their symmetry breaking and topological properties. At certain fillings, interactions combined with dimerized hoppings give rise to an emergent symmetry-breaking leading to BODW phases, which differs from the case of non-interacting models that require an explicit breaking of the symmetry. Specifically, the BODW phase at filling $\ensuremath{\rho}=1/3$ possesses no analog in the noninteracting model in terms of its symmetry-breaking properties and the unit cell structure. Upon changing the dimerization pattern, the system realizes topologically trivial BODW phases. At filling $\ensuremath{\rho}=1/4$, on-site density modulations are shown to stabilize the topological BODW phase. Our work provides the bridge between interacting and noninteracting BODW phases and highlights the significance of long-range interactions in a dimerized lattice by showing unique BODW phases that do not exist in the noninteracting model.
Topological materials have potential applications for quantum technologies. Non-interacting topological materials, such as e.g., topological insulators and superconductors, are classified by means of fundamental symmetry classes. It is instead only partially understood how interactions affect topological properties. Here, we discuss a model where topology emerges from the quantum interference between single-particle dynamics and global interactions. The system is composed by soft-core bosons that interact via global correlated hopping in a one-dimensional lattice. The onset of quantum interference leads to spontaneous breaking of the lattice translational symmetry, the corresponding phase resembles nontrivial states of the celebrated Su-Schriefer-Heeger model. Like the fermionic Peierls instability, the emerging quantum phase is a topological insulator and is found at half fillings. Originating from quantum interference, this topological phase is found in "exact" density-matrix renormalization group calculations and is entirely absent in the mean-field approach. We argue that these dynamics can be realized in existing experimental platforms, such as cavity quantum electrodynamics setups, where the topological features can be revealed in the light emitted by the resonator.