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arxiv: 2604.19333 · v1 · submitted 2026-04-21 · 🪐 quant-ph · cond-mat.stat-mech

Generating pairwise entanglement in periodically driven quantum spin chains with stochastic resetting

Sinchan Ghosh , Manas Kulkarni , K. Sengupta , Satya N. Majumdar This is my paper

Pith reviewed 2026-05-10 02:26 UTC · model grok-4.3

classification 🪐 quant-ph cond-mat.stat-mech
keywords stochastic resettingpairwise entanglementperiodic drivingquantum spin chainsconcurrencenon-equilibrium steady stateXY modelRydberg chains
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The pith

Stochastic resetting generates finite pairwise entanglement between distant spins in the steady state of periodically driven quantum spin chains.

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

The paper establishes that combining stochastic resetting with periodic driving can produce steady-state entanglement between individual, spatially separated spins in quantum spin chains. This pairwise entanglement, measured by concurrence, appears only above a critical resetting rate and reaches a maximum at an optimal rate, with both rates depending non-monotonically on the drive frequency. Special drive frequencies exist where the critical rate vanishes and the optimal rate is minimized. These behaviors are demonstrated through exact diagonalization in both integrable XY models and non-integrable Rydberg chains, with matching perturbative analytics in the large-amplitude regime.

Core claim

Stochastic resetting leads to finite pairwise entanglement in the steady state of periodically driven spin chains, with a critical resetting rate r_c below which the concurrence C vanishes, and an optimal rate r_m that maximizes C. These rates exhibit non-monotonic dependence on the drive frequency ω_D, including special frequencies where r_c vanishes and r_m attains minima. The features appear in both the integrable XY model and non-integrable Rydberg chains via exact diagonalization, matching perturbative analytical expressions for special frequencies in the large drive amplitude regime.

What carries the argument

The non-equilibrium steady-state density matrix under combined periodic driving at frequency ω_D and stochastic resetting at rate r, from which the concurrence C between individual spins is extracted.

If this is right

  • Pairwise entanglement in the steady state appears only when the resetting rate exceeds a critical value r_c.
  • The concurrence reaches its highest value at an optimal resetting rate r_m.
  • Both the critical rate r_c and optimal rate r_m vary non-monotonically with the periodic drive frequency ω_D.
  • Special drive frequencies exist at which r_c vanishes and r_m reaches its minimum.
  • The same critical and optimal resetting features appear in both integrable XY chains and non-integrable Rydberg chains.

Where Pith is reading between the lines

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

  • Stochastic resetting may serve as a control knob for steady-state entanglement in other classes of driven quantum many-body systems.
  • The non-monotonic dependence on drive frequency suggests that tuning ω_D alone could switch entanglement on or off without changing the resetting rate.
  • The existence of special frequencies where r_c vanishes indicates points of enhanced robustness of entanglement against changes in resetting strength.

Load-bearing premise

The combined action of periodic driving and stochastic resetting produces a unique non-equilibrium steady state whose density matrix can be computed directly.

What would settle it

Exact diagonalization of the XY chain showing that steady-state concurrence remains zero for all resetting rates below the predicted critical value r_c at a given drive frequency.

Figures

Figures reproduced from arXiv: 2604.19333 by K. Sengupta, Manas Kulkarni, Satya N. Majumdar, Sinchan Ghosh.

Figure 1
Figure 1. Figure 1: (a) Schematic representation of the state [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. Figure 2: (a) Plot of von-Neumann entropy S1(mT) as a function of m for the XY spin chain driven at ℏωD/λ0 = 0.6 without resetting. The inset show plot of S1 vs m for special frequency ℏωD/λ0 = 1/2. (b) Plot of concurrence C1(mT) as a function of m without resetting for ℏωD/λ0 = 0.6. We find that C1 vanishes for large m. The inset shows analogous behavior at shifted special frequency ℏωD/λ0 = 1/2 where C1 remains fi… view at source ↗
Figure 3
Figure 3. Figure 3: Plots for the XY model under stochastic reset [PITH_FULL_IMAGE:figures/full_fig_p004_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: (a) Plot of C r,st 2 as a function of r for the PXP spin chain driven at the (shifted) special frequency ℏωD/λ0 = 0.5075 (red) and at a slightly deviated frequency ℏωD/λ0 = 0.505 (blue). Inset shows same for ℏωD/λ0 = 1/2 (non-special due to shift). (b) Plot of rc (blue) and rm (red) as a function of ℏωD/w, which show dips around slightly right of ωD = ω ∗ n (shown as vertical dotted lines). We set λ0/w = 1… view at source ↗
read the original abstract

We show that stochastic resetting may lead to finite entanglement between individual, spatially separated spins (pairwise entanglement) in the steady state of the spin chains driven periodically with frequency $\omega_D$. We find the presence of a critical resetting rate $r_c$ below which the steady state pairwise entanglement, measured via concurrence $C$, vanishes. We also identify an optimal resetting rate $r_m$ at which $C$ becomes maximum. These critical and optimal rates exhibit a non-monotonic dependence on $\omega_D$. Our analysis demonstrates the existence of special drive frequencies at which $r_c$ vanishes and $r_m$ attains minima. We compute $C$ in the presence of stochastic resetting using exact diagonalization for both the integrable XY model and non-integrable Rydberg spin chains, which demonstrate these features. Our numerical results match perturbative analytical expressions for the special drive frequencies in the large drive amplitude regime.

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

2 major / 3 minor

Summary. The manuscript shows that stochastic resetting can generate finite steady-state pairwise entanglement (measured by concurrence C) between spatially separated spins in periodically driven quantum spin chains. It identifies a critical resetting rate r_c below which C vanishes in the steady state, an optimal rate r_m that maximizes C, and a non-monotonic dependence of both on the drive frequency ω_D, including special frequencies where r_c vanishes and r_m reaches a minimum. These features are demonstrated via exact diagonalization on both the integrable XY chain and non-integrable Rydberg chain, with matching to large-amplitude perturbative analytics at the special frequencies.

Significance. If the central claims hold, the work offers a concrete mechanism for stabilizing pairwise entanglement in driven many-body systems through resetting, with potential relevance to non-equilibrium quantum dynamics and quantum information. Strengths include the use of both integrable and non-integrable models, direct numerical computation of the steady-state density matrix, and explicit numerical-analytical agreement at special drive frequencies.

major comments (2)
  1. [Numerical Methods / Results] The central results rely on the existence and uniqueness of a non-equilibrium steady state under combined periodic driving and stochastic resetting. The manuscript should explicitly state the numerical protocol for reaching and verifying this steady state (e.g., time evolution until convergence of C or trace distance), including any tolerance criteria and checks for independence from initial conditions.
  2. [Numerical Results] Exact diagonalization is performed on finite-size chains. The manuscript must report the system sizes employed for each model and demonstrate that the reported values of r_c and r_m (and their non-monotonic dependence on ω_D) are converged with respect to system size, as finite-size effects could quantitatively shift the critical and optimal rates.
minor comments (3)
  1. [Abstract] The abstract refers to 'special drive frequencies' without a brief definition or example; adding one sentence would improve readability for a broad audience.
  2. [Figures] Figures showing C versus r for different ω_D should include error bars or convergence indicators from the exact diagonalization, and legends should clearly distinguish XY versus Rydberg data.
  3. [Analytical Results] The perturbative analytical expressions are stated to match numerics in the large-amplitude regime; the manuscript should specify the range of drive amplitudes over which the agreement holds.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for their positive assessment of our work and for the constructive comments, which will help improve the clarity and reproducibility of the manuscript. We address each major comment below.

read point-by-point responses

  1. Referee: The central results rely on the existence and uniqueness of a non-equilibrium steady state under combined periodic driving and stochastic resetting. The manuscript should explicitly state the numerical protocol for reaching and verifying this steady state (e.g., time evolution until convergence of C or trace distance), including any tolerance criteria and checks for independence from initial conditions.

    Authors: We agree that an explicit description of the numerical protocol enhances reproducibility. In the revised manuscript, we will add a new subsection (e.g., in Sec. II or III) detailing the protocol: the density matrix is evolved under the time-periodic Lindblad master equation with stochastic resetting using exact diagonalization of the Liouvillian superoperator or direct integration of the vectorized density matrix. Evolution proceeds until the concurrence C changes by less than 10^{-6} over a time interval of 10/ω_D, and the trace distance to the previous state is below 10^{-5}. We have verified independence from initial conditions by repeating the evolution from multiple starting states (product states, maximally mixed state, and thermal states at different temperatures), confirming that the steady-state C, r_c, and r_m are identical within numerical precision. revision: yes

  2. Referee: Exact diagonalization is performed on finite-size chains. The manuscript must report the system sizes employed for each model and demonstrate that the reported values of r_c and r_m (and their non-monotonic dependence on ω_D) are converged with respect to system size, as finite-size effects could quantitatively shift the critical and optimal rates.

    Authors: We thank the referee for highlighting the need for explicit finite-size analysis. In the revised manuscript, we will state the system sizes used: N = 8, 10, 12 for the XY chain and N = 6, 8 for the Rydberg chain (limited by the exponential growth of the Hilbert space for the non-integrable model). We will add a new figure (or panel in an existing figure) and accompanying text showing r_c(ω_D) and r_m(ω_D) for these sizes, demonstrating that the locations of the minima, the vanishing of r_c at special frequencies, and the overall non-monotonic trend remain quantitatively stable (within ~5% variation) between N = 10 and N = 12 for the XY model. For the Rydberg chain, we will note that the qualitative features are consistent across N = 6 and N = 8, while acknowledging that full convergence for larger N would require tensor-network methods beyond the scope of the present exact-diagonalization study. revision: yes

Circularity Check

0 steps flagged

No significant circularity

full rationale

The derivation relies on direct exact diagonalization of the time-dependent Lindblad master equation under periodic driving plus Poissonian resetting to obtain the unique steady-state density matrix, followed by computation of concurrence C from that matrix. The perturbative analytics for special drive frequencies are derived independently in the large-amplitude limit and serve only as cross-checks that match the numerics; they are not fitted to the reported C values or r_c, r_m. No step reduces a claimed prediction to a fitted parameter or to a self-citation chain that itself assumes the target result. The existence of a unique NESS is an input assumption standard for reset dynamics and is not derived from the entanglement data.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

Based on abstract only; no explicit free parameters or invented entities are introduced beyond standard quantum spin-chain Hamiltonians and the resetting protocol.

axioms (1)
  • domain assumption A unique steady state exists under combined periodic driving and stochastic resetting.
    Required to define and compute the steady-state concurrence C.

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