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arxiv: 2606.21813 · v1 · pith:6DZSEYFUnew · submitted 2026-06-20 · 🪐 quant-ph · cond-mat.quant-gas· cond-mat.str-el

Prethermal cooling with many-body quantum quenches

Jacob F. Steiner , Mohammad Hafezi , Stefan Kehrein , Gil Refael This is my paper

Pith reviewed 2026-06-26 12:19 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.quant-gascond-mat.str-el
keywords prethermalizationquantum quenchHubbard modeldoublonseffective temperaturefluctuation-dissipationcooling protocoladiabatic demagnetization
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The pith

A hopping quench in the Hubbard model creates a prethermal state whose effective temperature drops by the square of the final-to-initial hopping ratio.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Quantum quenches typically heat many-body systems, but this work shows that increasing the hopping amplitude in the strongly interacting half-filled Hubbard model can instead cool low-energy degrees of freedom. The energy supplied by the quench is absorbed into a non-equilibrium population of doublons whose density remains out of equilibrium for a time exponentially long in (U/t)^2. Within this prethermal window, operators that conserve doublon number obey an effective fluctuation-dissipation relation with a temperature reduced by (t_final/t_initial)^2 relative to the initial temperature. The Hubbard system can therefore act as a refrigerant for a target system whose coupling preserves doublon number. The protocol is presented as a many-body quantum-quench analogue of adiabatic demagnetization.

Core claim

In the half-filled fermionic Hubbard model with U ≫ t, a sudden quench of the hopping term from t_i to t_f deposits work into a long-lived non-equilibrium doublon density. This density persists for a time exponentially large in (U/t)^2. During the resulting prethermal regime, doublon-number-conserving operators experience an effective temperature T_pre = T_init × (t_f / t_i)^2 and satisfy a corresponding fluctuation-dissipation relation. The Hubbard lattice can therefore cool another system when the inter-system coupling conserves doublon number.

What carries the argument

The quench-induced non-equilibrium doublon density, which stores the work performed by the hopping increase and thereby lowers the effective temperature of doublon-conserving operators.

If this is right

  • The prethermal temperature is lowered by the square of the hopping ratio for all doublon-number-conserving operators.
  • An effective fluctuation-dissipation theorem holds inside the prethermal window for those operators.
  • The prethermal regime survives for a time exponentially large in (U/t)^2 before full thermalization.
  • The Hubbard system functions as a refrigerant for any target coupled through doublon-conserving interactions.
  • The cooling protocol extends the principle of adiabatic demagnetization to a many-body quantum quench setting.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • The same mechanism could be tested in optical-lattice experiments by preparing an initial thermal state, performing the hopping quench, and tracking correlation functions of spin or charge operators.
  • Analogous cooling may occur in other strongly interacting lattice models that possess a gapped, long-lived high-energy excitation whose number is approximately conserved.
  • Cooling efficiency would degrade if the coupling to the target system allows doublon creation or annihilation at appreciable rates.
  • The protocol suggests exploring whether periodic driving or other quench sequences can further extend the lifetime of the non-equilibrium doublon reservoir.

Load-bearing premise

The doublon density produced by the quench stays out of equilibrium for a time exponentially longer than the timescales on which the prethermal state would otherwise relax.

What would settle it

After the quench, measure the effective temperature of doublon-conserving operators through their fluctuation-dissipation ratio and check whether it equals the initial temperature multiplied by (t_f/t_i)^2; or directly measure whether the doublon lifetime is shorter than exponentially large in (U/t)^2.

Figures

Figures reproduced from arXiv: 2606.21813 by Gil Refael, Jacob F. Steiner, Mohammad Hafezi, Stefan Kehrein.

Figure 1
Figure 1. Figure 1: Prethermal cooling with quantum quenches. (a) Sketch of the setup. A Hubbard system, initialized in a thermal state [PITH_FULL_IMAGE:figures/full_fig_p002_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: Numerical extraction of effective temperature from fluctuation-dissipation relation (FDR) for a one-dimensional [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗
Figure 3
Figure 3. Figure 3: Asymptotic temperature after a quantum quench in the one-dimensional Hubbard model, obtained from the exact [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: shows data for very weak interactions, U = 0.1t. The behavior is essentially that of an overall quench of the Hamiltonian H → gfH, leading to a trivial linear temperature reduction regardless of coupling operator. Note that the lowest initial temperature is comparable to the finite size gap (black data points). We do not expect the approach to work well in this extreme limit [PITH_FULL_IMAGE:figures/full_… view at source ↗
Figure 5
Figure 5. Figure 5: Parameters: U/t = 3.3, N = 10 [PITH_FULL_IMAGE:figures/full_fig_p016_5.png] view at source ↗
Figure 6
Figure 6. Figure 6: Parameters: U/t = 10.0, N = 6. 3. Finite-size scaling Finally, we check convergence of the extracted temperature with system size, see Figs. 7 through 10. We note an even-odd effect in system size for the FDR violation, but not for the extracted temperatures which appear well￾converged. 0.64 0.66 0.68 0.70 Teff/Ti (a) O = nj,↑ − nj,↓ 5 10 (b) O = P σ c † j,σcj+1,σ + h.c. 3 4 5 6 7 8 9 10 L 1 2 3 4 FDR viol… view at source ↗
Figure 7
Figure 7. Figure 7: Parameters: U/t = 10.0, gf = 0.8 [PITH_FULL_IMAGE:figures/full_fig_p017_7.png] view at source ↗
Figure 8
Figure 8. Figure 8: Parameters: U/t = 10.0, gf = 0.6. 0.16 0.17 0.18 0.19 0.20 Teff/Ti (a) O = nj,↑ − nj,↓ 0 5 10 15 (b) O = P σ c † j,σcj+1,σ + h.c. 3 4 5 6 7 8 9 10 L 2 4 6 FDR violation [%] (c) 3 4 5 6 7 8 9 10 L 4 5 6 (d) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Ti/J [PITH_FULL_IMAGE:figures/full_fig_p018_8.png] view at source ↗
Figure 9
Figure 9. Figure 9: Parameters: U/t = 10.0, gf = 0.4. 0.040 0.045 0.050 Teff/Ti (a) O = nj,↑ − nj,↓ 0 5 10 15 (b) O = P σ c † j,σcj+1,σ + h.c. 3 4 5 6 7 8 9 10 L 2 4 6 8 FDR violation [%] (c) 3 4 5 6 7 8 9 10 L 4.5 5.0 5.5 6.0 (d) 0.2 0.4 0.6 0.8 1.0 1.2 1.4 Ti/J [PITH_FULL_IMAGE:figures/full_fig_p018_9.png] view at source ↗
Figure 10
Figure 10. Figure 10: Parameters: U/t = 10.0, gf = 0.2 [PITH_FULL_IMAGE:figures/full_fig_p018_10.png] view at source ↗
read the original abstract

Many-body quantum quenches are typically associated with heating. In this work, we show that quantum quenches that perform positive work on the system can still lead to effective cooling of low-energy degrees of freedom if the quench energy is deposited in long-lived high-energy excitations. We discuss this explicitly for a quench of the hopping term t in the strong-coupling (U >> t) fermionic Hubbard model at half filling, where the quench induces a very long-lived non-equilibrium doublon density. The associated prethermal state persists for a time exponentially large in (U/t)^2. During this time window, we find an effective prethermal temperature that is reduced by the square of the ratio of final to initial hopping amplitude with respect to the initial temperature. This manifests as an effective fluctuation-dissipation relation that holds for doublon-number conserving operators. In a practical implementation the Hubbard system acts as a refrigerant to cool a target system provided the coupling conserves doublon number. Our protocol can be thought of as a quantum quench many-body generalization of adiabatic demagnetization.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

0 major / 2 minor

Summary. The manuscript claims that a positive-work quench of the hopping amplitude t in the strong-coupling half-filled Hubbard model deposits excess energy into a long-lived non-equilibrium doublon density. This density persists for a time exponentially large in (U/t)^2, enabling a prethermal regime in which low-energy degrees of freedom reach an effective temperature reduced by the factor (t_f/t_i)^2 relative to the initial temperature. The prethermal state obeys an effective fluctuation-dissipation relation restricted to doublon-number-conserving operators and can refrigerate a weakly coupled target system whose coupling conserves doublon number. The protocol is presented as a many-body generalization of adiabatic demagnetization.

Significance. If the central claims hold, the work supplies a concrete, quench-based route to effective cooling that exploits established prethermalization physics rather than external baths or slow ramps. The explicit scaling of the effective temperature with (t_f/t_i)^2 and the restriction to doublon-conserving operators furnish falsifiable predictions that could be tested in cold-atom or quantum-dot platforms. The manuscript correctly situates the result within the existing literature on Hubbard-model prethermalization and virtual-process lifetimes.

minor comments (2)
  1. The abstract states the temperature reduction factor without indicating the section or equation where the effective-temperature definition and the fluctuation-dissipation relation are derived; adding an explicit forward reference would improve readability.
  2. Figure captions should explicitly state the system size, the value of U/t, and the observable used to extract the effective temperature so that the numerical evidence for the (t_f/t_i)^2 scaling can be assessed at a glance.

Simulated Author's Rebuttal

0 responses · 0 unresolved

We thank the referee for their positive assessment of the manuscript, accurate summary of the central claims, and recommendation for minor revision. The referee correctly situates the work within the prethermalization literature and identifies the falsifiable predictions. No specific major comments were listed in the report.

Circularity Check

0 steps flagged

No significant circularity; derivation self-contained in standard prethermalization physics

full rationale

The central claim follows from partitioning excess quench energy into the long-lived doublon sector of the strong-coupling Hubbard model, with the effective temperature scaling as (t_f/t_i)^2 arising directly from the known virtual-process effective Hamiltonian J ~ 4t^2/U. No parameter is fitted to data and then relabeled as a prediction, no self-citation supplies a uniqueness theorem or ansatz, and the doublon lifetime is justified by high-order virtual processes already established in the literature. The protocol is presented as an analogy to adiabatic demagnetization without redefining any input quantity in terms of the output. The derivation chain is therefore independent of its own results.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claim rests on the standard Hubbard model in the strong-coupling limit and the assumption of long-lived doublons; no free parameters or invented entities are introduced in the abstract.

axioms (1)
  • domain assumption Strong coupling limit U >> t in the fermionic Hubbard model at half filling
    This is the regime where doublons are long-lived and the prethermal state can form.

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