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arXiv:2112.08785 · Physical Review Research

Revealing the topological nature of the bond order wave in a strongly correlated quantum system

Sergi Julià-Farré, Daniel González-Cuadra, A. Patscheider, Manfred J. Mark, Francesca Ferlaino, Maciej Lewenstein, Luca Barbiero, Alexandre Dauphin

Published Jul 8, 2022• 2 citations
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Abstract

polyacetylene.There, a bond order wave (BOW) arises spontaneously from the coupling between electrons and phonons through a Peierls mechanism [19], which can also occur in spin-boson models [20][21][22].Interestingly, similar BOW phases also appear in interacting single-species systems, induced by frustration between competing orders , including strongly correlated electrons, quantum magnets, or ultracold atomic systems.Although the insulating nature and effective dimerization of these systems have been very carefully characterized, their topological nature still needs to be unveiled.The latter requires an accurate analysis of such many-body interacting systems, as the sole presence of a spontaneous dimerization, i.e., a local order parameter, does not directly translate into a nontrivial topology.In this Letter, we reveal and characterize the SPT nature of such BOW phases arising from frustration in the presence of chiral symmetry [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].Moreover, we propose a realistic implementation and detection scheme for the realization of the frustration-induced topological BOW phase with dipolar gases in optical lattices.Our proposal allows us to go beyond the experimental simulation of noninteracting SPT phases, promising to access both bulk and edge physics of a strongly correlated topological phase with richer phenomenology.More specifically, we focus our analysis on the onedimensional (1D) extended Fermi-Hubbard (EFH) model.We demonstrate that, in the case of an infinite chain, two exactly degenerate BOW ground states occur.These states are 2643-1564/2022/4(3)/L032005(7) L032005-1

DOI
10.1103/physrevresearch.4.l032005

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polyacetylene.There, a bond order wave (BOW) arises spontaneously from the coupling between electrons and phonons through a Peierls mechanism [19], which can also occur in spin-boson models [20][21][22].Interestingly, similar BOW phases also appear in interacting single-species systems, induced by frustration between competing orders , including strongly correlated electrons, quantum magnets, or ultracold atomic systems.Although the insulating nature and effective dimerization of these systems have been very carefully characterized, their topological nature still needs to be unveiled.The latter requires an accurate analysis of such many-body interacting systems, as the sole presence of a spontaneous dimerization, i.e., a local order parameter, does not directly translate into a nontrivial topology.In this Letter, we reveal and characterize the SPT nature of such BOW phases arising from frustration in the presence of chiral symmetry [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42][43].Moreover, we propose a realistic implementation and detection scheme for the realization of the frustration-induced topological BOW phase with dipolar gases in optical lattices.Our proposal allows us to go beyond the experimental simulation of noninteracting SPT phases, promising to access both bulk and edge physics of a strongly correlated topological phase with richer phenomenology.More specifically, we focus our analysis on the onedimensional (1D) extended Fermi-Hubbard (EFH) model.We demonstrate that, in the case of an infinite chain, two exactly degenerate BOW ground states occur.These states are 2643-1564/2022/4(3)/L032005(7) L032005-1
We investigate the topological properties of the bond order wave phase arising in the extended Fermi-Hubbard model. In particular, we uncover a topological sector, which remained elusive in previous finite-size numerical studies due to boundary effects. We first show that, for an infinite system, the bond order wave regime is characterized by two degenerate bulk states corresponding to the trivial and topological sectors. The latter turns out to be indeed characterized by an even degeneracy of the entanglement spectrum and longe-range order of a string correlation function. For finite size systems, we show that the topological sector can be stabilized by imposing a suitable border potential. This therefore provides a concrete protocol for the observation of topologically protected degenerate edge modes in finite-size systems. Furthermore, we show that the bulk of the system is characterized by exotic solitonic solutions interpolating between the trivial and topological sectors. Finally, we propose an implementation and detection scheme of this strongly-correlated topological phase in a quantum simulator based on dipolar Fermi gases in optical lattices.
We demonstrate that electronic correlations in low-dimensional systems can induce topological phases starting from a topologically trivial noninteracting band structure. Using an advanced cluster-diagrammatic many-body approach applied to the one-dimensional extended Hubbard model, we show that tuning the nonlocal Coulomb interaction drives the emergence of bond-order-wave (BOW) and charge-density-wave (CDW) phases. Despite being interaction-driven and symmetry-broken, these states admit an effective low-energy single-particle description. In particular, the BOW phase maps onto an effective Su-Schrieffer-Heeger model, while the CDW phase, with subleading bond-order correlations, corresponds to a Rice-Mele model. Both phases exhibit a nontrivial topological character, manifested by the presence of localized edge states. Our results establish a mechanism by which nonlocal electronic correlations generate emergent topology in correlated systems.
Quantum paramagnets are strongly correlated phases of matter where competing interactions frustrate magnetic order down to zero temperature. In certain cases, quantum fluctuations instead induce topological order, supporting fractionalized quasiparticles. In this Letter, we investigate paradigmatic spin models and show how magnetic frustration can also give rise to higher-order topological properties. We first study the frustrated Heisenberg model in a square lattice, where a plaquette valence bond solid appears through the spontaneous breaking of translational invariance. Despite the amount of effort that has been devoted to study this phase, its topological nature has so far been overlooked. By means of tensor network simulations, we establish how such a state belongs to a higher-order symmetry-protected topological phase, where long-range plaquette order and nontrivial topology coexist. Through this interplay, we uncover excitations that would be absent otherwise, such as cornerlike bulk states bound to dynamical topological defects. Finally, we demonstrate how this higher-order topological quantum paramagnet is also induced by dipolar interactions, indicating the possibility to directly observe this phase using atomic quantum simulators.
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.
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.