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arXiv:2405.10291

Interaction induced splitting of Dirac monopoles in the topological Thouless pumping of strongly interacting Bosons and SU($N$) Fermions

Hei Lam, Yangqian Yan

Published May 16, 2024• 0 citations
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Abstract

Motivated by the observation of the breakdown of quantization for the Thouless pump in the presence of strong interaction by ETH [Walter et. al. Nat. Phys. 19, 1471 (2023), Viebahn et. al. arXiv:2308.03756], we study the interplay of strong interaction and topology in the (1+1)-dimensional interacting Rice-Mele model. We point out that the quantization of the interacting Thouless pump is dictated by the Chern number, i.e., the Dirac monopoles enclosed by the generalized Brillouin zone of the many-body wave function. By analyzing the change of location monopoles due to interaction, we predict the Thouless charge pump for strongly interacting Bose and SU($N$) Fermi gases in optical lattices and explain the ETH experiment.

DOI
10.48550/arxiv.2405.10291

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Interaction induced splitting of Dirac monopoles in the topological Thouless pumping of strongly interacting Bosons and SU(NNN) Fermions
Motivated by the observation of the breakdown of quantization for the Thouless pump in the presence of strong interaction by ETH [Walter et. al. Nat. Phys. 19, 1471 (2023), Viebahn et. al. arXiv:2308.03756], we study the interplay of strong interaction and topology in the (1+1)-dimensional interacting Rice-Mele model. We point out that the quantization of the interacting Thouless pump is dictated by the Chern number, i.e., the Dirac monopoles enclosed by the generalized Brillouin zone of the many-body wave function. By analyzing the change of location monopoles due to interaction, we predict the Thouless charge pump for strongly interacting Bose and SU(NNN) Fermi gases in optical lattices and explain the ETH experiment.
Abstract Geometric properties of wave functions can explain the appearance of topological invariants in many condensed-matter and quantum systems 1 . For example, topological invariants describe the plateaux observed in the quantized Hall effect and the pumped charge in its dynamic analogue—the Thouless pump 2–4 . However, the presence of interparticle interactions can affect the topology of a material, invalidating the idealized formulation in terms of Bloch waves. Despite pioneering experiments in different platforms 5–9 , the study of topological matter under variations in interparticle interactions has proven challenging 10 . Here we experimentally realize a topological Thouless pump with fully tuneable Hubbard interactions in an optical lattice and observe regimes with robust pumping, as well as an interaction-induced breakdown. We confirm the pump’s robustness against interactions that are smaller than the protecting gap for both repulsive and attractive interactions. Furthermore, we identify that bound pairs of fermions are responsible for quantized transport at strongly attractive interactions. However, for strong repulsive interactions, topological pumping breaks down, but we show how to reinstate it by modifying the pump trajectory. Our results will prove useful for further investigations of interacting topological matter 10 , including edge effects 11 and interaction-induced topological phases 12–15 .
We investigate topological charge pumping in a system of interacting bosons in the tight-binding limit, described by the Rice-Mele model. An appropriate topological invariant for the many-body case is the change of polarization per pump cycle, which we compute for various interaction strengths from infinite-size matrix-product-state simulations. We verify that the charge pumping remains quantized as long as the pump cycle avoids the superfluid phase. In the limit of hardcore bosons, the quantized pumped charge can be understood from single-particle properties such as the integrated Berry curvature constructed from Bloch states, while this picture breaks down at finite interaction strengths. These two properties---robust quantized charge transport in an interacting system of bosons and the breakdown of a single-particle invariant---could both be measured with ultracold quantum gases extending a previous experiment [Lohse et al., Nat. Phys. 12, 350 (2016)]. Furthermore, we investigate the entanglement spectrum of the Rice-Mele model and argue that the quantized charge pumping is encoded in a winding of the spectral flow in the entanglement spectrum over a pump cycle.
Thouless pumping represents a powerful concept to probe quantized topological invariants in quantum systems. We explore this mechanism in a generalized Rice-Mele Fermi-Hubbard model characterized by the presence of competing onsite and intersite interactions. Contrary to recent experimental and theoretical results, showing a breakdown of quantized pumping induced by the onsite repulsion, we prove that sufficiently large intersite interactions allow for an interaction-induced recovery of Thouless pumps. Our analysis further reveals that the occurrence of stable topological transport at large interactions is connected to the presence of a spontaneous bond-order-wave in the ground-state phase diagram of the model. Finally, we discuss a concrete experimental setup based on ultracold magnetic atoms in an optical lattice to realize the newly introduced Thouless pump. Our results provide a new mechanism to stabilize Thouless pumps in interacting quantum systems.
A Thouless pump transports an integer amount of charge when pumping adiabatically around a singularity. We study the splitting of such a critical point into two separate critical points by adding a Hubbard interaction. Furthermore, we consider extensions to a spinful Rice-Mele model, namely, a staggered magnetic field or an Ising-type spin coupling, further reducing the spin symmetry. The resulting models additionally allow for the transport of a single charge in a two-component system of spinful fermions, whereas in the absence of interactions, zero or two charges are pumped. In the SU(2)-symmetric case, the ionic Hubbard model is visited once along pump cycles that enclose a single singularity. Adding a staggered magnetic field additionally transports an integer amount of spin while the Ising term realizes a pure charge pump. We employ real-time simulations in finite and infinite systems to calculate the adiabatic charge and spin transport, complemented by the analysis of gaps and the many-body polarization to confirm the adiabatic nature of the pump. The resulting charge pumps are expected to be measurable in finite-pumping speed experiments in ultracold atomic gases for which the SU(2)\mathrm{SU}(2)SU(2) invariant version is the most promising path. We discuss the implications of our results for a related quantum-gas experiment by Walter et al. [arXiv:2204.06561].
Recent experiments with ultracold quantum gases have successfully realized integer-quantized topological charge pumping in optical lattices. Motivated by this progress, we study the effects of static disorder on topological Thouless charge pumping. We focus on the half-filled Rice-Mele model of free spinless fermions and consider random diagonal disorder. We use both static and time-dependent simulations to characterize the charge pump. The set of measures that we compute in the instantaneous basis include the polarization, the entanglement spectrum, and the space-integrated local Chern marker. As a first main result, we conclude that the space-integrated local Chern marker is best suited for a quantitative determination of topological transitions in a disordered system. In the time-dependent simulations we use the time-integrated current to obtain the pumped charge in slowly periodically driven systems. As a second main result, we observe and characterize a disorder-driven breakdown of the quantized charge pump. There is an excellent agreement between the static and the time-dependent ways of computing the pumped charge. The topological transition occurs well in the regime where all states are localized on the given system sizes. This observation is consistent with previous studies and the topological transition is therefore not tied to a delocalization-localization transition of Hamiltonian eigenstates. For individual disorder realizations, the breakdown of the quantized pumping occurs for parameters where the spectral bulk gap inherited from the band gap of the clean system closes, leading to a globally gapless spectrum. As a third main result and with respect to the analysis of finite-size systems, we show that the disorder average of the bulk gap severely overestimates the stability of quantized pumping. A much better estimate is the typical value of the distribution of energy gaps, also called mode of the distribution. We discuss our results in the context of recent quantum-gas experiments that realized charge pumps.
A topological “Thouless” pump represents the quantized motion of particles in response to a slow, cyclic modulation of external control parameters. The Thouless pump, like the quantum Hall effect, is of fundamental interest in physics, because it links physically measurable quantities, such as particle currents, to geometric properties of the experimental system, which can be robust against perturbations and, thus, technologically useful. So far, experiments probing the interplay between topology and interparticle interactions have remained relatively scarce. Here, we observe a Thouless-type charge pump in which the particle current and its directionality inherently rely on the presence of strong interactions. Experimentally, we utilize a two-component Fermi gas in a dynamical superlattice which does not exhibit a sliding motion and remains trivial in the single-particle regime. However, when tuning interparticle interactions from zero to positive values, the system undergoes a transition from being stationary to drifting in one direction, consistent with quantized pumping in the first cycle. Remarkably, the topology of the interacting pump trajectory cannot be adiabatically connected to a noninteracting limit, highlighted by the fact that only one atom is transferred per cycle. Our experiments suggest that Thouless charge pumps are promising platforms to gain insights into interaction-driven topological transitions and topological quantum matter. Published by the American Physical Society 2024