Quantum Systems Can Be ‘burst’ into Life with Tailored Initial Conditions

Researchers have demonstrated that isolated quantum systems exhibit non-monotonic thermalisation, dependent on their initial conditions. Shozo Yamada, Akihiro Hokkyo, and Masahito Ueda, all from the Department of Physics at the University of Tokyo, detail a novel numerical method for constructing low-entangled initial states that generate a transient ‘burst’ of activity, a temporary deviation from thermal equilibrium. Their work reveals that this burst of magnetization can occur in a non-integrable mixed-field Ising chain on a timescale comparable to quantum scrambling, accompanied surprisingly by slowed or even reversed entanglement growth. This finding challenges conventional understandings of information spreading in such systems and suggests the possibility of maintaining a non-equilibrium state through careful initial state preparation, a prediction testable using programmable quantum simulators. This work addresses a longstanding question in quantum mechanics concerning how irreversible thermalization arises from reversible microscopic laws. The study introduces a novel numerical method for constructing low-entangled initial states capable of generating these bursts of magnetization in a nonintegrable mixed-field Ising chain, a timescale comparable to the onset of quantum scrambling. Contrary to expectations for this regime, the generated burst is accompanied by remarkably slow, or even negative, growth of entanglement. The research centres on a method to design initial states with minimal quantum entanglement, circumventing the need for highly complex starting conditions often required for observing such transient phenomena. By employing matrix product states and the density matrix renormalization group algorithm, scientists were able to tailor an initial state that produces a measurable burst of magnetization at a pre-designated time. This approach allows for quantitative evaluation of the maximum transient deviation from equilibrium achievable with low-entangled states, a significant step towards understanding the dynamics of isolated quantum systems. Analytically, the team established that the probability of observing a burst diminishes exponentially over time, suggesting that a non-equilibrium state can be maintained for a specifically chosen initial state until quantum scrambling dominates. This prediction is particularly significant as it opens avenues for experimental verification using programmable quantum simulators. The ability to create a substantial burst even with a bond dimension independent of system size implies that this phenomenon is potentially within reach of current experimental capabilities, utilising quantum quenches or shallow quantum circuits. Furthermore, the study’s findings suggest that the observed deviation persists until overwhelmed by quantum scrambling, even in systems destined to eventually reach thermal equilibrium. This persistence, coupled with the low-entanglement requirement, positions the research as a crucial contribution to the field, offering a testable prediction for future investigations with advanced quantum simulation platforms. The method presented allows for a precise assessment of the transient deviation from equilibrium accessible through low-entangled initial states, providing valuable insights into the dynamics of isolated quantum many-body systems. Constructing low-entanglement initial states for transient magnetization bursts Researchers developed a numerical method to construct low-entangled initial states capable of generating a transient deviation in observable values, termed a “burst”, within isolated quantum systems. This work centres on the investigation of thermalization dynamics in nonintegrable systems, specifically employing matrix product states (MPSs) and the density matrix renormalization group (DMRG) algorithm to identify initial states that produce a designated burst of magnetization. The DMRG algorithm was utilised to search for MPS configurations that create a burst for a given Hamiltonian and observable at a specific time. The study focused on a one-dimensional mixed-field Ising chain, and the methodology involved systematically searching for initial states with minimal entanglement that exhibit a burst in magnetization. A key innovation was the ability to tailor-make these bursts, achieving a substantial deviation from thermal equilibrium using initial states accessible through ground states or shallow quantum circuits. Calculations of entanglement entropy for half of the system were performed alongside the observation of magnetization dynamics, revealing a slow or even negative entanglement growth preceding the burst time. Furthermore, the research demonstrated that a fixed bond dimension, independent of system size, is sufficient to generate a significant burst even for large systems, suggesting experimental feasibility. Analytical arguments, based on local random quantum circuits, were then used to establish a probabilistic no-go result, showing that bursts become exponentially rare as the burst time increases relative to system size. This methodology allows for quantitative evaluation of the maximum transient deviation from equilibrium achievable with low-entangled initial states, persisting until overwhelmed by quantum scrambling.

Transient Magnetization Bursts in Nonintegrable Ising Chains via Low-Entangled Initial States Researchers demonstrated the creation of a transient magnetization burst in a nonintegrable mixed-field Ising chain, achieved through a novel numerical method for constructing low-entangled initial states. This burst, a deviation from thermal equilibrium, was realised on a timescale comparable to the onset of quantum scrambling. The study focused on one-dimensional quantum systems utilising matrix product states, with calculations performed using the density matrix renormalization group algorithm. Specifically, the work reveals that a burst of magnetization can be generated from an initial state possessing a bond dimension independent of system size, implying experimental feasibility via quantum quenches or shallow quantum circuits. Entanglement entropy measurements accompanying the burst exhibited slow or even negative growth prior to the designated burst time. For a fixed and short burst time, a bond dimension independent of the system size proved sufficient to create a substantial burst even for larger systems. Analytical arguments, based on local random quantum circuits, indicate that the probability of observing a burst decreases exponentially as the burst time increases relative to the system size. The research quantitatively evaluates the maximal transient deviation from equilibrium achievable with low-entangled initial states, demonstrating its persistence until overwhelmed by quantum scrambling. These findings suggest a maintained nonequilibrium state for appropriately chosen initial states until scrambling dominates, a prediction suitable for testing with programmable quantum simulators. The entanglement entropy, calculated for a half system, remained bounded by ln χ, where χ represents the bond dimension. The method employed utilizes matrix product states expressed as |ψ⟩= P {σi} Aσ1 1 Aσ2 2 · · · AσL L |σ1σ2 · · · σL⟩, where Di represents the bond dimension and is constrained by SA(|ψ⟩) ≤ln χ for any subsystem A. This approach allows for the creation of a tailor-made burst for a given Hamiltonian and observable at a designated time. Initial state control delays thermalisation via transient magnetisation bursts Researchers demonstrated a transient deviation from thermal equilibrium, termed a “burst”, in the magnetization of a nonintegrable mixed-field Ising chain. This burst originates from a specifically constructed, low-entangled initial state and occurs on a timescale comparable to the onset of quantum scrambling. Notably, the emergence of this burst is accompanied by either slow or negative growth of entanglement, a behaviour contrary to typical information spreading. The findings suggest that a carefully chosen initial state can maintain a nonequilibrium condition for a limited duration, delaying the system’s progression towards thermalization until scrambling dominates. Analytical work confirms that these bursts become increasingly improbable over extended timescales, establishing a probabilistic limit on their occurrence.

This research identifies a mechanism by which a local observable can temporarily defy the expected thermal behaviour, even when its initial value aligns with equilibrium predictions, while simultaneously exhibiting suppressed entanglement entropy. The authors acknowledge limitations related to computational cost when investigating systems with long-range interactions, anticipating a faster decay of the burst phenomenon in such scenarios. Future research directions include adapting the variational method used to explore other nonequilibrium trajectories, such as revivals and oscillations, and investigating the impact of interaction locality on thermalization. Furthermore, the observed burst phenomenon presents potential applications in quantum metrology, offering a high signal-to-noise ratio for estimating system parameters or benchmarking quantum simulators due to the burst amplitude’s independence from system size. 👉 More information 🗞 Tunable many-body burst in isolated quantum systems 🧠 ArXiv: https://arxiv.org/abs/2602.09665 Tags: