Spin-incoherent Mott-Thouless pumps

Technical Summary: Spin-incoherent Mott-Thouless pumps

Problem Statement
Thouless pumps are paradigmatic examples of topological transport, where adiabatic, periodic modulation of Hamiltonian parameters results in the quantized transfer of an integer amount of charge per cycle. Standard theory dictates that this quantization requires the system to remain in its ground state with vanishing thermodynamic entropy throughout the process. However, realizing such low-entropy states in fermionic ultracold atom experiments remains a significant challenge. This paper investigates whether quantized topological transport can survive in highly entropic, "spin-incoherent" Mott states, where the spin degrees of freedom are thermalized ($T \gg J$, where $J$ is the exchange coupling) while the charge sector remains gapped. The central question is whether the extensive entropy of the spin sector destroys the quantization of charge transport or if the two sectors can remain dynamically decoupled.

Methodology
The authors employ a combination of analytical scaling arguments, effective field theories, and numerically exact real-time simulations (Exact Diagonalization) to study two primary models:

1. Lattice Model: An interacting variant of the Rice-Mele model (Hubbard model with staggered hopping and potential) at quarter-filling and half-filling.
2. Continuum Model: A time-dependent potential acting on spinful fermions, analyzed via Galilean transformations and WKB approximations.

The analysis focuses on the strong-coupling limit ($U \to \infty$) where the system forms a Mott insulator. The authors derive effective Heisenberg models for the spin degrees of freedom and analyze the coupling between the spin and charge sectors. They specifically examine heating mechanisms, including:

• Spin-sector heating due to the breaking of integrability by time-dependent exchange couplings.
• Spin-to-charge energy transfer, which creates detrimental charge excitations (doublons/holes).
• Direct charge-sector heating via multi-photon absorption.

The study contrasts two filling factors: quarter-filling (one fermion per two-site unit cell) and half-filling (one fermion per site), the latter being relevant to recent experimental realizations.

Key Contributions and Results

1. Exponentially Protected Pumping at Quarter-Filling:
   The authors demonstrate that at quarter-filling, a "Mott-Thouless pump" can operate in a spin-incoherent regime with extensive entropy ($S \sim \ln 2$ per particle).

   • Mechanism: In the limit of large $U$, the charge dynamics decouples from the spin dynamics. The pumped charge resides in a gapped sector, while the spin sector is described by a Heisenberg model with time-dependent couplings.
   • Heating Rates: While the spin sector heats up due to the periodic drive, the transfer of energy from the hot spin sector to the charge sector is exponentially suppressed. The rate of creating charge excitations scales as $\Gamma_{cs} \sim e^{-\alpha N_{cs}}$, where $N_{cs} \sim \Delta_c / \bar{J}_1$ (the ratio of the charge gap to the average spin exchange energy).
   • Finite-Size Effects: Numerical simulations on finite systems ($L=16$) confirm that deviations from quantized transport are exponentially small for large $U$. Interestingly, the authors observe that higher-energy initial spin states (which are more "disordered") can sometimes exhibit better quantization than low-energy states, a phenomenon reminiscent of the Mpemba effect, though they attribute this to finite-size constraints (e.g., fully polarized states having no inelastic scattering).
   • Length Scale: The system maintains quantized transport up to a characteristic length scale $\ell_{h}^{charge} \sim \max(\ell_{h}^{spin}, \ell_{cs})$, which is parametrically large in the adiabatic limit.

2. Breakdown of Protection at Half-Filling:
   In contrast to the quarter-filled case, the authors show that the half-filled Mott-Thouless pump (relevant to recent experiments by the Esslinger group) lacks this exponential protection.

   • Mechanism: At half-filling, the pumping cycle necessarily crosses a point where the spin gap closes while the charge gap remains finite. Consequently, spin excitations are generated efficiently.
   • Spin-Charge Conversion: Crucially, in the half-filled case, these spin excitations are not decoupled from the charge sector. Using Abelian bosonization, the authors show that the perturbation gapping the charge sector explicitly depends on the spin field. A local spin excitation (a kink in the spin field) reverses the effective potential for the charge field, directly converting spin excitations into charge excitations (particle-hole pairs).
   • Result: The rate of creating charge defects from spin defects is of order $\Gamma_{cs} \sim \omega$ (linear in frequency), leading to a rapid breakdown of quantized transport after the first cycle. This aligns with experimental observations where quantization is lost in subsequent cycles unless a large spin gap is artificially opened.

3. Continuum Model Analysis:
   The authors extend their findings to a continuum model with a sliding potential. They confirm that while Galilean invariance can protect the system, breaking this symmetry (e.g., $V_0 \neq V_1$) leads to heating. However, similar to the lattice model, the heating timescales for the charge sector remain exponentially large in the strong-coupling limit, provided the system is not at half-filling where the specific spin-charge coupling mechanism dominates.

Significance and Claims
The paper claims to establish that exponentially protected topological transport is possible in highly entropic many-body states, challenging the traditional requirement of ground-state initialization for Thouless pumps.

• Robustness: The quantization survives not because the system is cold, but because the entropy resides in a sector (spins) that is dynamically decoupled from the transport sector (charge) by an energy gap and exponentially suppressed coupling.
• Experimental Relevance: This finding is significant for ultracold atom experiments, as it suggests that topological phenomena can be observed even when the system has not been cooled to the ground state, provided the system is in a suitable spin-incoherent Mott regime (specifically at quarter-filling).
• Limitations: The authors modestly note that this protection is not universal; it depends critically on the filling factor and the specific nature of the spin-charge coupling. The half-filled case serves as a counter-example where spin excitations efficiently destroy quantization, highlighting that "incoherent" does not automatically imply "robust."

The work connects the phenomenology of weakly broken conservation laws, prethermalization, and generalized Gibbs ensembles to topological transport, suggesting that robust topological phenomena may persist in high-entropy quantum matter whenever coherent transport sectors remain dynamically protected from incoherent degrees of freedom.