Quantum Many-Body Pumps

• Quantum many-body pumps are paradigmatic protocols that use cyclic adiabatic driving to transport conserved quantities quantized by many-body Chern invariants.
• They generalize the Thouless pump by incorporating strong correlations, fractional pumping, and novel mechanisms of adiabatic breakdown, reshaping topological classifications.
• Recent experiments in ultracold atoms, superconducting arrays, and quantum-dot systems demonstrate these pumps, highlighting practical applications in quantized quantum transport.

Quantum many-body pumps are paradigmatic out-of-equilibrium protocols in which adiabatic, cyclic driving leads to quantized or geometric transport of conserved quantities—charge, spin, energy—in systems with many-body interactions, nontrivial topology, or approximate integrability. They generalize the seminal Thouless pump by incorporating strong correlations, emergent scattering, and unconventional mechanisms of adiabatic breakdown and fluctuation. Recent theoretical and experimental advances have clarified their classification in terms of many-body Chern invariants, the crucial role of adiabaticity versus orthogonality catastrophe, fractional/quasiparticle pumping, as well as novel forms of pumping in approximately integrable and open quantum systems.

1. Fundamental Principles and Classification

Quantum many-body pumps operate under Hamiltonians $H(\lambda)$ with periodically and adiabatically modulated parameters $\lambda(t)$ over $t\in[0,T]$, such that the initial and final many-body ground states are related up to a geometric (Berry) phase. For strictly adiabatic, gapped systems, the charge pumped per cycle is given by a many-body Chern number: $$Q = \oint F_{\lambda\kappa}d\lambda\,d\kappa \in \mathbb{Z}$$ where $$F_{\lambda\kappa} = i(\langle \partial_\lambda \Phi | \partial_\kappa \Phi \rangle - c.c.)$$ is the many-body Berry curvature and $\kappa$ an auxiliary flux or twist variable. This framework encompasses standard topological Thouless pumps, fractionally quantized pumps in systems with degenerate ground state manifolds, and pumps protected by generalized symmetry or integrability (Lychkovskiy et al., 2017, Taddia et al., 2016, Friedman et al., 2019).

The dynamical realization of this quantization is predicated on (i) the closure of the many-body gap throughout the cycle and (ii) the maintenance of adiabaticity, i.e., the evolving state $|\Psi_\lambda\rangle$ co-moving with $|\Phi_\lambda\rangle$. Many-body interactions can challenge both requirements by generating large orthogonality catastrophes, closing spectral gaps, or inducing new dynamical constraints.

Pumps fall into several types:

• Standard topological pumps: transport is characterized by integer (or, in certain cases, fractional) many-body Chern numbers, often realized in band-insulating or Mott states with periodic modulation (Lychkovskiy et al., 2017, Taddia et al., 2016).
• Fractional pumps: quantized transport in units of $p/q$ per cycle, due to $q$-fold ground-state degeneracy and non-Abelian Wilczek-Zee curvature (Taddia et al., 2016).
• Integrable and Floquet pumps: exact solvability enables precise control of quantized pumping even in the presence of strong interactions and time-periodic driving (Friedman et al., 2019).
• Peristaltic (resonant) pumps: particle transfer arises from a sliding finite-size potential, without a bulk topological invariant (Romeo et al., 2017).

2. Adiabatic Limits, Orthogonality, and Scaling Laws

In large, interacting systems, the adiabatic theorem requires careful re-examination due to the non-commutativity of the limits $\Gamma\to 0$ (driving rate) and $N\to\infty$ (system size). Lychkovskiy et al. (Lychkovskiy et al., 2017) establish a quantitative connection between adiabaticity, many-body orthogonality catastrophe, and quantized pumping: $$|F(\lambda)-C(\lambda)| \leq \frac{\lambda^2 \delta V_N}{2\Gamma}$$ where $$F(\lambda)=|\langle\Phi_\lambda|\Psi_\lambda\rangle|^2$$ is the adiabatic fidelity, $$C(\lambda)=|\langle\Phi_\lambda|\Phi_0\rangle|^2\approx e^{-C_N\lambda^2}$$ (orthogonality overlap), and $\delta V_N$ is the ground-state fluctuation of the drive-induced perturbation $V$.

In paradigmatic models such as the Rice–Mele pump, the orthogonality exponent grows extensively, $C_N\sim N$, and $\delta V_N\sim\sqrt{N}$. The adiabatic “mean-free-path” $\lambda^*$—the maximal parameter range over which adiabaticity is maintained—scales as

$\lambda^* = C_N^{-1/2} \sim N^{-1/2}$

implying that the driving rate $\Gamma$ must be reduced as $1/\sqrt{N}$ to reach the adiabatic limit in the thermodynamic limit. This scaling is even more restrictive in models such as the impurity-in-fluid McGuire model, where $C_N\sim \log N$ and $\lambda^*\sim (\log N)^{-1/2}$ (Lychkovskiy et al., 2017).

This interplay dictates that quantized pumping is guaranteed only if the adiabatic limit is taken before the thermodynamic limit; otherwise, pumped charge loses quantization as fidelity collapses.

3. Many-Body Topological and Fractional Pumps

Strongly correlated systems can exhibit topological quantized or fractional pumping, depending on their symmetry, ground-state degeneracy, and interaction structure. In interacting alkaline-earth(-like) atomic ladders, fractional filling ($\nu=p/q$) produces a $q$-fold ground-state manifold, and the pumped charge per cycle after averaging is (Taddia et al., 2016): $\overline{Q}_R = \frac{\mathcal{C}_1}{q}$ where $\mathcal{C}_1$ is the first Chern number of the Wilczek-Zee non-Abelian curvature, and thus the transport can realize fractional quantization $p/q$ exactly for hard-core interaction constraints.

Many-body adiabatic expansions and matrix-product state simulations confirm the robustness and quantized nature of fractional pumping under realistic finite-size and nonadiabatic corrections, controlled by the ratio $1/(\Delta T)$ where $\Delta$ is the gap and $T$ the cycle period. In the exactly solvable U→∞ (“hard-core”) models, flux-attachment mappings and composite-fermion constructions confirm $p/q$ quantization nonperturbatively (Taddia et al., 2016).

Numerical evidence supports that adiabatic corrections vanish in the joint limits $T\to\infty$, $L\to\infty$, while spatial averaging over a crystal unit cell restores quantization even in moderately finite systems.

4. Strong Correlations and Novel Pumping Phenomena

Quantum many-body pumps in strongly correlated settings reveal phenomena absent in single-particle or weakly interacting systems:

• In coupled chains of strongly interacting fermions, the many-body spectrum splits into sectors supporting bound pairs and single particles. Adiabatic parameter cycles give rise to opposite-direction pumps for these two sectors, with pumped charge per cycle set by many-body Chern numbers ($C_{\text{pair}}=+1$, $C_{\text{single}}=-2$ in certain models) (Voorden et al., 2018).
• In a solid-state 36-qubit array with attractive Hubbard interactions, bound-state and resonant tunneling pumps appear. When the interaction $U$ exceeds the dimerization, pairs are pumped as composite objects with center-of-mass shift per cycle quantized by the many-body Chern number. For $2|\Delta_0|>|U|$, topological resonant tunneling enables single-fermion steps across barriers, and edge asymmetry emerges due to nontrivial pair band structures near open-system boundaries (Tao et al., 2023).
• Floquet integrable models (“DFFA” model) exhibit exactly solvable, interacting many-body pumps with chiral, topologically nontrivial band structure, quantized pumping per cycle, and yet preserve a remarkable absence of operator scrambling (“no butterfly effect”) due to hard-rod scattering structure (Friedman et al., 2019).

5. Non-Topological and Approximately Integrable Quantum Pumps

Not all quantum many-body pumps rely on global topology. Peristaltic pumps based on a sliding, finite-size microlattice transfer particles between reservoirs by local resonant tunneling. Their efficiency is set by resonance between discrete barrier levels and the Fermi energy, barrier width, pumping frequency, and coherence length; quantization is not ensured but strong many-body coherence is still essential for efficient operation (Romeo et al., 2017).

In weakly perturbed integrable systems (e.g., the XXZ chain), periodic pumping can transfer large spin or heat currents into approximately conserved quasi-local charges. The resulting non-equilibrium steady state is captured by a truncated generalized Gibbs ensemble whose Lagrange multipliers encode the structure (but not amplitude) of the perturbation. These currents are typically quadratic in drive amplitude and inversely proportional to relaxation rates due to integrability-breaking processes (Lange et al., 2016).

6. Fluctuation Relations and Many-Body Interaction Effects

Quantum many-body pumps driven by slow, time-periodic bias in open systems reveal fundamental modifications of non-equilibrium fluctuation relations. In the presence of many-body interactions, geometric corrections to the pumping current lead to a violation of the standard fluctuation-dissipation theorem (FDT) for the pumping contributions. The deviation is governed by the energy current pumped into the system, which for noninteracting cases vanishes for cross-derivatives but remains finite and interaction-induced when many-body Coulomb terms are present (Riwar et al., 2020): $$S_{LR}^{(1)} - k_B T \left( \frac{\partial I_L^{(1)}}{\partial \mu_R} + \frac{\partial I_R^{(1)}}{\partial \mu_L} \right) = - k_B T \frac{\partial^2 I_{PE}}{\partial \mu_L \partial \mu_R}$$ where $I_{PE}$ is the pumped energy current per cycle. Measurement of these deviations in charge and energy current-noise correlations thus constitutes a sensitive probe of interaction-induced many-body correlations in quantum pumps.

7. Experimental Realizations and Outlook

Quantum many-body pumps have been realized or proposed in a range of platforms:

• Ultracold alkaline-earth(-like) atomic ladders, validating fractional pumping and topological protection through real-space imaging and time-of-flight reconstruction (Taddia et al., 2016).
• Superconducting transmon qubit arrays, enabling direct site- and state-resolved observation of single-particle and pair pumping, resonant tunneling, and edge-modulated topological transport (Tao et al., 2023).
• Quasi-1D spin-chain materials under terahertz drive, evidencing integrability-protected many-body pumping of spin and energy (Lange et al., 2016).
• Nanostructured quantum-dot systems, with predictions for modified fluctuation-response protocols to detect strong correlations via noise and energy current readout (Riwar et al., 2020).

The interplay of adiabaticity, many-body orthogonality, ground state degeneracy, integrability, and local versus global dynamical mechanisms continues to drive theoretical and experimental advances, with implications for topological quantum information transfer, exotic emergent phases, and fundamental non-equilibrium phenomena in quantum matter.