[challenge]: Many-body dissipative Floquet system beyond the markovian model

Released by

Zhuocheng Ma, Peking University

Contact email

mzhch3@stu.pku.edu.cn

Method

uniTEMPO

Challenge issue

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挑战提案：Many-body dissipative Floquet system beyond the markovian model

标签： uniTEMPO, open-quantum-systems, floquet, many-body, non-markovian

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What is the issue?

The exact Floquet influence functional (Floquet-IF) framework introduced by Mickiewicz, Link & Strunz (PRL 136, 200201 (2026)) provides a numerically exact route to the dynamics of strongly damped, periodically driven quantum systems. In their paradigmatic single-spin-boson example, the authors reveal that the frequency-resolved heat current density $\bar{j}(\omega)$ exhibits:

• Longitudinal driving: resonant peaks at $n\omega_d \pm \Omega$;
• Transversal driving: a Mollow-triplet-like structure with $\delta$-peaks at odd multiples of $\omega_d$ and sidebands shifted by the Rabi frequency $\epsilon_d$.

However, all of this is single-impurity physics. The crucial open question is:

What happens to $\bar{j}(\omega)$ when the "system" is a many-body interacting spin chain (or a few coupled qubits) jointly coupled to a common non-Markovian bosonic bath?

In a many-body setting, the bath couples to a collective operator $S = \sum_i \sigma_z^{(i)}$, and the internal Hamiltonian $H_{\mathrm{sys}}$ contains interactions, e.g. an Ising term:

$$
H_{\mathrm{sys}}(t) = -J\sum_{\langle i,j\rangle}\sigma_z^{(i)}\sigma_z^{(j)} + \frac{\Omega}{2}\sum_i \sigma_x^{(i)} + H_{\mathrm{drive}}(t).
$$

The single-spin Rabi frequency $\Omega$ is replaced by a spectrum of collective excitations (magnons, domain walls, or Majorana modes depending on the phase). The bath-induced correlations between spins mediate effective long-range interactions that compete with the drive and the internal Hamiltonian. Existing master-equation approaches (Floquet-Lindblad, Redfield-Magnus) fail in this regime because:

1. Strong system-bath coupling violates Born-Markov approximations;
2. Non-commuting drive and interaction invalidate the Magnus expansion;
3. Non-Markovian memory from the common bath creates temporal entanglement that cannot be captured by local generators.

Consequently, we have no exact theoretical prediction for how many-body Floquet heating manifests in the frequency domain. Do the Mollow sidebands split into a spin-wave continuum? Does the heat current near a quantum critical point develop a power-law singularity? Can many-body entanglement open "dark channels" that suppress heating at specific frequencies?

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Why might it lead to research output?

This challenge sits at the intersection of three rapidly evolving frontiers: Floquet engineering, non-Markovian open quantum systems, and quantum many-body physics. A successful attack is likely to yield tangible research output for several reasons:

1. Discovery of new spectral signatures of many-body phases in heat transport
   The heat current density $\bar{j}(\omega)$ is an experimentally accessible probe (via calorimetry or noise spectroscopy in superconducting circuits). If the Floquet-IF calculation reveals that $\bar{j}(\omega)$ develops, say, a spin-wave sideband structure or a critical divergence as $J/\Omega$ approaches a quantum phase transition point, this would constitute a first-principles prediction of a new nonequilibrium spectroscopic tool.

2. Quantifying the breakdown of single-picture approximations
   By comparing the exact Floquet-IF results against Floquet-Lindblad and Redfield-Magnus predictions for the same many-body model, one can map out the precise parameter regime where many-body master equations fail. This is valuable methodological knowledge for the broader community working on driven-dissipative many-body systems.

3. Entanglement-assisted heat transport
   In the single-spin case, the bath only sees one qubit. In the many-body case, the collective coupling means the bath "measures" the total magnetization. If the drive stabilizes a highly entangled state (e.g., a singlet or symmetry-protected topological state), the variance of $S$ may be suppressed, leading to a quantum-interference-induced suppression of heating—a genuinely collective effect with no single-spin analog.

4. Scalability and method development
   The challenge naturally forces the development of computational techniques to combine Floquet-IF with matrix-product-state (MPS) representations of the system density matrix, while the bath is handled by the MPO influence functional. This hybrid "IF-MPS" approach, hinted at in the original paper's outlook, would be a methodological advance with applications beyond this specific model (e.g., DMFT impurity solvers).

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Proposed roadmap

To keep the challenge tractable within a summer-school timeframe, we suggest a tiered approach:

Tier 1 – Reproduce the single-spin Floquet heating (code validation)
Start by reproducing the transversal-driving heat-current density $\bar{j}(\omega)$ shown in Fig. 3 (bottom panel) of Mickiewicz et al. for the single driven spin-boson model. The goal is to validate your Floquet-IF / uniTEMPO implementation and familiarize yourself with the heat-current formula (Eq. B2 in the End Matter). If you can recover the Mollow-triplet-like structure with $\delta$-peaks at $\omega_d$ and sidebands near $\omega_d \pm \epsilon_d$, your machinery is ready.

Tier 2 – Small chains ($N=3,4$) and the onset of collective modes
Increase $N$ and add an Ising interaction $J$. Identify whether the heat-current peaks track the single-qubit Rabi frequency $\Omega$ or the collective gap $\Delta(J,\Omega)$. Search for signatures of quantum synchronization in the heat current.

Tier 3 – Benchmark against master equations (the payoff)
For the same spin chain model and parameters, implement a Floquet-Lindblad (or Redfield-Magnus) master equation. Compute its prediction for the heat current or the reduced density matrix, and compare it quantitatively to your exact Tier-2 Floquet-IF results. The deliverable is a phase diagram or error map showing where the master equation breaks down as a function of, e.g., system-bath coupling strength $\alpha$ and driving frequency $\omega_d$. This directly addresses the methodological gap highlighted in the original paper and provides an immediately useful benchmark for the community.

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References, code, data, or context

Core methodology:

• K. Mickiewicz, V. Link, W. T. Strunz, Exact Floquet Dynamics of Strongly Damped Driven Quantum Systems, Phys. Rev. Lett. 136, 200201 (2026).
  [The Floquet-IF framework; Fig. 3 shows the single-spin heat current density.]
• V. Link, H.-H. Tu, W. T. Strunz, Open quantum system dynamics from infinite tensor network contraction, Phys. Rev. Lett. 132, 200403 (2024).
  [Introduction of the uniTEMPO algorithm for uniform MPO influence functionals.]
• M. Sonner, V. Link, D. A. Abanin, Semigroup influence matrices for nonequilibrium quantum impurity models, Phys. Rev. Lett. 135, 170402 (2025).
  [Semigroup structure of influence functionals and spectral analysis of transient dynamics.]

Many-body open systems & heat transport:

• D. Gribben et al., Exact dynamics of nonadditive environments in non-markovian open quantum systems, PRX Quantum 3, 010321 (2022).
  [TEMPO for multiple qubits in non-additive baths.]
• G. E. Fux et al., Tensor network simulation of chains of non-Markovian open quantum systems, Phys. Rev. Res. 5, 033078 (2023).
  [MPS chains with local non-Markovian baths.]
• A. Kato and Y. Tanimura, Quantum heat current under nonperturbative and non-Markovian conditions, J. Chem. Phys. 145, 224105 (2016).
  [Heat current formulas for strongly coupled Gaussian baths.]
• F. Albarelli, B. Vacchini, A. Smirne, Pseudomode treatment of strong-coupling quantum thermodynamics, Quantum Sci. Technol. 10, 015041 (2025).
  [Strong-coupling thermodynamics and heat-current definitions.]

Reaction-coordinate mapping (for time-dependent coupling):

• A. Nazir and G. Schaller, The reaction coordinate mapping in quantum thermodynamics, in Thermodynamics in the Quantum Regime (Springer, 2019), pp. 551–577.
• M. Shubrook, J. Iles-Smith, A. Nazir, Non-Markovian quantum heat statistics with the reaction coordinate mapping, Quantum Sci. Technol. 10, 025063 (2025).

Data & code context:

• The authors of the original paper provide open data at Zenodo: https://zenodo.org/records/19593671.
• The uniTEMPO algorithm is conceptually related to the open-source PT-TEMPO and OQuPy (formerly TEMPO) libraries, though a Floquet-IF extension does not yet exist in public code. Participants would likely need to extend a TEMPO-like implementation to support periodic MPO tensors.

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Contact

If you are interested in mentoring or discussing this challenge, please join us.

Start by locating the uniTEMPO implementation and determine whether it supports periodic Floquet influence-functional tensors. Reproduce the single-spin heat-current density from Fig. 3 and Eq. B2 before extending to N=3 or 4 chains. Done means documented results for the many-body calculation and a quantitative comparison with Floquet-Lindblad or Redfield-Magnus predictions.