Abstract Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.
Abstract Motivated by recent advances in fabricating artificial lattices in semiconductors and their promise for quantum simulation of topological materials, we study the one-dimensional dimerized Fermi–Hubbard model. We show how the topological phases at half-filling can be characterized by a reduced Zak phase defined based on the reduced density matrix of each spin subsystem. Signatures of bulk–boundary correspondence are observed in the triplon excitation of the bulk and the edge states of uncoupled spins at the boundaries. At quarter-filling, we show that owing to the presence of the Hubbard interaction the system can undergo a transition to the topological ground state of the non-interacting Su–Schrieffer–Heeger model with the application of a moderate-strength external magnetic field. We propose a robust experimental realization with a chain of dopant atoms in silicon or gate-defined quantum dots in GaAs where the transition can be probed by measuring the tunneling current through the many-body state of the chain.
The interplay and competition of topology and electron--electron interactions have fascinated researchers since the discovery of topological insulators. The Su--Schrieffer--Heeger--Hubbard (SSH-Hubbard) model is a prototypical model which includes both nontrivial topology and interactions. Due to its simplicity, there are several artificial quantum systems which can realize such a model to a good approximation. Here we focus on the quarter-filled case, where interactions and dimerization open a charge gap. In particular, we study the single-particle spectral function for the extended SSH-Hubbard model with magnetic field and explore several parameter limits where effective model descriptions arise. In the strongly dimerized limit, we show that the low-energy excitations of the spectral function resemble a half-filled Hubbard model with effective dimer sites and renormalized couplings. For strong magnetic field and interactions, we find physics akin to the spinless Su--Schrieffer--Heeger model at half filling, featuring a noninteracting topological phase transition. Moreover, in light of the recent realization of this model in quantum dot simulation, we provide evidence for the stability of the topological phase towards moderate nonlocal interactions in the experimentally expected parameter range.
We study the effects of electron-electron interactions on the charge excitation spectrum of the spinful Su-Schrieffer-Heeger (SSH) model, a prototype of a one-dimensional bulk obstructed topological insulator. In view of recent progress in the fabrication of dopant-based quantum simulators we focus on experimentally detectable signatures of interacting topology in finite lattices. To this end we use Lanczos-based exact diagonalization to calculate the single-particle spectral function in real space which generalizes the local density of states to interacting systems. Its spatial and spectral resolution allows for the direct investigation and identification of edge states. By studying the noninteracting limit, we demonstrate that the topological in-gap states on the boundary are robust against both finite-size effects as well as random bond and onsite disorder which suggests the feasibility of simulating the SSH model in engineered dopant arrays in silicon. While edge excitations become zero-energy spinlike for any finite interaction strength, our analysis of the spectral function shows that the single-particle charge excitations are gapped out on the boundary. Despite the loss of topological protection, we find that these edge excitations are quasiparticlelike as long as they remain within the bulk gap. Above a critical interaction strength of ${U}_{c}\ensuremath{\approx}5t$ these quasiparticles on the boundary lose their coherence which is explained by the merging of edge and bulk states. This is in contrast to the many-body edge excitations which survive the limit of strong coupling, as established in the literature. Our findings show that for moderate repulsive interactions the nontrivial phase of the interacting SSH model can be detected through remnant signatures of topological single-particle states using single-particle local measurement techniques such as scanning tunneling spectroscopy.
Despite extensive studies on the one-dimensional Su-Schrieffer-Heeger-Hubbard (SSHH) model, the variant incorporating second-nearest neighbor hopping remains largely unexplored. Here, the topological classification of the extended SSH model is analyzed within the framework of the BDI symmetry class, using the winding number as the corresponding topological invariant. We investigate the ground-state properties of this extended SSHH model using the constrained-path auxiliary-field quantum Monte Carlo (CP-AFQMC) method. We show that this model exhibits rich topological phases, characterized by robust edge states against interaction. We quantify the properties of these edge states by analyzing spin correlation and second-order Rényi entanglement entropy. The system exhibits long-range spin correlation and near-zero Rényi entropy at half-filling. Besides, there is an anti-ferromagnetic order at quarter-filling. Interestingly, an external magnetic field disrupts this anti-ferromagnetic order, restoring long-range spin correlation and near-zero Rényi entropy. Furthermore, our work provides a paradigm for studying topological properties in large interacting systems via the CP-AFQMC algorithm.
Abstract Topology in quantum many-body systems has profoundly changed our understanding of quantum phases of matter. The model that has played an instrumental role in elucidating these effects is the antiferromagnetic spin-1 Haldane chain 1,2 . Its ground state is a disordered state, with symmetry-protected fourfold-degenerate edge states due to fractional spin excitations. In the bulk, it is characterized by vanishing two-point spin correlations, gapped excitations and a characteristic non-local order parameter 3,4 . More recently it has been understood that the Haldane chain forms a specific example of a more general classification scheme of symmetry-protected topological phases of matter, which is based on ideas connected to quantum information and entanglement 5–7 . Here, we realize a finite-temperature version of such a topological Haldane phase with Fermi–Hubbard ladders in an ultracold-atom quantum simulator. We directly reveal both edge and bulk properties of the system through the use of single-site and particle-resolved measurements, as well as non-local correlation functions. Continuously changing the Hubbard interaction strength of the system enables us to investigate the robustness of the phase to charge (density) fluctuations far from the regime of the Heisenberg model, using a novel correlator.
We investigate theoretically the Bose-Hubbard version of the celebrated Su-Schrieffer-Heeger topological model, which essentially describes a one-dimensional dimerized array of coupled oscillators with on-site interactions. We study the physics arising from the whole gamut of possible dimerizations of the chain, including both the weakly and the strongly dimerized limiting cases. Focusing on two-excitation subspace, we systematically uncover and characterize the different types of states which may emerge due to the competition between the inter-oscillator couplings, the intrinsic topology of the lattice, and the strength of the on-site interactions. In particular, we discuss the formation of scattering bands full of extended states, bound bands full of two-particle pairs (including so-called 'doublons', when the pair occupies the same lattice site), and different flavors of topological edge states. The features we describe may be realized in a plethora of systems, including nanoscale architectures such as photonic cavities, optical lattices and qubits, and provide perspectives for topological two-particle and many-body physics.
We analyze interacting ultracold bosonic atoms in a one-dimensional superlattice potential with alternating tunneling rates t1 and t2 and inversion symmetry, which is the bosonic analogue of the Su-Schrieffer-Heeger model. A Z2 topological order parameter is introduced which is quantized for the Mott insulating (MI) phases. Depending on the ratio t1/t2 the n=1/2 MI phase is topologically nontrivial, which results in many-body edge states at open boundaries. In contrast to the Su-Schrieffer-Heeger model the bosonic counterpart lacks chiral symmetry and the edge states are no longer midgap. This leads to a generalization of the bulk-edge correspondence, which we discuss in detail. The edge states can be observed in cold atom experiments by creating a step in the effective confining potential, e.g., by a second heavy atom species, which leads to an interface between two MI regions with filling n=1 and n=1/2. The shape and energy of the edge states as well as the conditions for their occupation are determined analytically in the strong coupling limit and in general by density-matrix renormalization group simulations.