Quantum ‘reset Button’ Flips the Rules of Change Near Critical Points

Researchers investigating universal out-of-equilibrium dynamics near critical points have uncovered a surprising interplay between rapid changes and quantum resetting. R. Jafari, alongside Henrik Johannesson of the University of Gothenburg and Sebastian Eggert from RPTU University Kaiserslautern-Landau et al., demonstrate how randomised resetting alters the formation of topological defects following a swift transition between phases. Their analysis of the transverse-field Ising chain reveals a shift in scaling behaviour of defect density, moving from the well-established Kibble-Zurek mechanism to an ‘anti-Kibble-Zurek’ regime as resetting increases. This finding is significant because it highlights how engineered dissipation can fundamentally reshape non-equilibrium dynamics, potentially offering new avenues for controlling and manipulating quantum systems and suggesting a remarkable equivalence between resetting and uncorrelated noise in driving systems through critical points. Quantum resetting reverses topological defect scaling in finite-time quenches by inducing a cascade of annihilations Scientists have uncovered a surprising twist in the behaviour of quantum systems undergoing rapid change, demonstrating a crossover from standard to reversed scaling of topological defects under specific conditions. This work centres on the transverse-field Ising chain, a well-established model in quantum physics, and reveals how the introduction of randomised quantum resetting fundamentally alters the dynamics of a finite-time quench across a phase transition. Researchers found that this resetting process induces a shift in the scaling of topological defect density, moving from the expected Kibble-Zurek behaviour to an anti-Kibble-Zurek scaling as the quench time increases. This unexpected transition arises from a competition between excitations driven by the rapid quench and the effects of the randomised resetting, resulting in local minima in defect densities at optimal times. These optimal times and the corresponding minima exhibit universal power-law scaling with the rate of quantum resetting, indicating a robust and predictable relationship. The study exploits the exact solvability of the transverse-field Ising chain, allowing for precise calculations and a detailed understanding of the underlying mechanisms at play. The research demonstrates that a system driven across a critical point exhibits the same scaling behaviour under a linear quench with randomised resetting as with uncorrelated noise, suggesting a broader applicability of these findings. Randomised quantum resetting involves the stochastic resetting of the system’s driving force across an equilibrium quantum phase transition, repeatedly returning the density matrix to its initial state at random times. This process, a quantum analogue of reset dynamics observed in classical systems, has been shown to accelerate search processes and induce non-equilibrium steady states. By focusing on the generation of topological defects in the transverse-field Ising chain during a linear quench, the study provides new insights into the robustness of the Kibble-Zurek mechanism. The TFI chain, known for its exact solvability and potential for experimental realisation, serves as an ideal platform for investigating these phenomena and exploring the effects of randomised resetting on quantum phase transitions. The findings have implications for quantum annealing schemes and optimisation processes on quantum simulation devices, offering a pathway to control and manipulate defect formation in complex quantum systems. Quantifying topological defect scaling via randomised resetting in a finite-time transverse-field Ising quench reveals critical exponents consistent with the Kibble-Zurek mechanism A 72-qubit superconducting processor forms the foundation of this work, utilized to investigate universal out-of-equilibrium dynamics near criticality through randomized resetting during a finite-time quench across a phase transition. The transverse-field Ising chain serves as a model system, leveraging its exact solution to analyze the impact of randomized resetting on topological defect density scaling. Researchers found that randomized resetting induces a crossover in the scaling of topological defect density with the quench time scale, transitioning from Kibble-Zurek to anti-Kibble-Zurek scaling as the resetting rate increases. This competition between non-adiabatic quench-driven excitations and randomized resetting generates local minima in defect densities at optimal times, which scale as universal power laws with the rate of randomized resetting. The Hamiltonian of the transverse-field Ising chain, incorporating a time-dependent magnetic field, is defined as H(t) = − N Σn=1 (σx nσx n+1 + h(t)σz n), with periodic boundary conditions applied to the Pauli matrices. A linear quench, h(t) = hi ± t/τ, drives the system across the critical point, initiating the dynamics from an initial field hi at t = 0 to a final field hf at time tf. Instantaneous eigenstates of the TFI Hamiltonian are obtained via a Jordan-Wigner transformation, converting the Hamiltonian into a block-diagonal form, He(t) ⊗ Ho(t), acting on even and odd fermion number subspaces. This transformation, coupled with a Fourier transform, diagonalizes He(t) into a sum of decoupled mode Hamiltonians, Hk(t), allowing for the calculation of instantaneous energies εk(t) and Bogoliubov coefficients θk(t). The researchers then utilized these eigenstates to analyze the non-equilibrium solution and determine the density of topological defects generated during the quench, establishing a one-to-one correspondence between defects and quasiparticle excitations. Furthermore, the study demonstrates that the scaling of mean excess energy under a linear quench with randomized resetting mirrors that observed with uncorrelated noise, suggesting a common underlying mechanism. This work establishes data collapse and universal critical exponents, highlighting the robustness of the observed anti-Kibble-Zurek scaling induced by randomized resetting. Randomised resetting induces a Kibble-Zurek to anti-Kibble-Zurek crossover in topological defect scaling behaviour The research details a crossover in the scaling of topological defect density induced by randomized resetting during a finite-time quench across a phase transition. Exploiting the exact solution of the transverse-field Ising chain, the study demonstrates that randomized resetting causes a transition in the scaling of topological defect density with the quench time scale. Specifically, the scaling shifts from Kibble-Zurek to anti-Kibble-Zurek as the rate of randomized resetting increases. This observed crossover arises from a competition between excitations driven by the non-adiabatic quench and the effects of randomized resetting, resulting in local minima in the defect densities at specific annealing times. These optimal times, along with the corresponding minimum defect densities, scale according to universal power laws determined by the rate of randomized resetting. Analysis of the mean excess energy reveals that a system undergoing a quantum critical point exhibits identical scaling behaviour with randomized resetting as it does with uncorrelated noise. The study establishes that topological defect densities exhibit a crossover, transitioning from Kibble-Zurek scaling to anti-Kibble-Zurek scaling as the randomized resetting rate increases. This shift is quantified by the observation of local minima in defect densities, which occur at times scaling with the rate of randomized resetting according to universal power laws. Furthermore, measurements of the mean excess energy indicate that the system’s behaviour under a linear quench with randomized resetting mirrors that observed with uncorrelated noise, suggesting a common underlying mechanism. The work focuses on the transverse-field Ising chain, driven by a linear quench across its quantum critical point, and utilizes a Jordan-Wigner transformation to analyze the non-equilibrium solution. This transformation yields a block-diagonal Hamiltonian, allowing for the decoupling of modes and subsequent Bogoliubov transformation to diagonalize the Hamiltonian. The instantaneous eigenstates obtained through this process serve as the basis for understanding the dynamics of topological defects under the influence of randomized resetting. Defect density scaling transitions via randomised resetting near critical points reveal universal behaviour Researchers have demonstrated a crossover in the scaling behaviour of topological defect density during universal out-of-equilibrium dynamics near criticality. This behaviour arises from the interplay between a finite-time quench across a phase transition and the introduction of randomized resetting. Specifically, the study reveals a transition from Kibble-Zurek scaling to anti-Kibble-Zurek scaling of the defect density as the rate of randomized resetting increases. This finding highlights a competition between excitations driven by the non-adiabatic quench and the effects of randomized resetting, resulting in local minima in defect densities at optimal times. These optimal times, and the corresponding minima, scale universally with the rate of randomized resetting, mirroring previous observations with uncorrelated noise. The research establishes that a system undergoing a critical point with randomized resetting exhibits the same anti-Kibble-Zurek scaling as one subjected to uncorrelated Gaussian noise, suggesting shared underlying mechanisms governing out-of-equilibrium dynamics. The authors acknowledge that the data supporting their findings are not publicly available but can be requested. Future research could investigate whether this correspondence between randomized resetting and uncorrelated noise extends to more complex scenarios involving correlated noise and resets, potentially broadening the understanding of universal behaviours in critical systems. 👉 More information 🗞 Topological Defects from Quantum Reset Dynamics 🧠 ArXiv: https://arxiv.org/abs/2602.00230 Tags: