Understanding how entanglement spreads following sudden changes in quantum systems is key for predicting their behaviour; however, describing this process in interacting models has proven challenging beyond specific starting conditions. Elisa Sabadini and Vincenzo Alba from Università di Pisa have investigated quenches, sudden shifts to new energy levels, in an XXZ spin chain beginning with ‘n-rainbow’ states: macroscopically uniform arrangements of increasingly long-range entangled pairs. The behaviour of quantum systems following sudden disturbances relies on understanding how entanglement spreads within them; however, previous descriptions often assumed simple starting conditions.

The research reveals that even complex interactions allow entanglement to grow at predicted rates, challenging expectations from simpler models and offering new insights into information transfer. By studying these changes beyond standard scenarios, knowledge of interacting quantum systems relevant to materials science and future technologies improves. The researchers are investigating how entanglement spreads after sudden disturbances, akin to suddenly flipping the switch on a complicated machine, within quantum systems.

Previous studies often assumed simple starting conditions; however, this analysis began with ‘n-rainbow’ states: arrangements containing increasingly long-range entangled pairs. This approach allows exploration of scenarios beyond standard models and gains insight into information transfer relevant for materials science and future technologies. A key concept is *entanglement entropy*, which measures how much two parts of a system “know” about each other; higher values indicate stronger links despite physical separation.

But what happens when this initial entanglement becomes exceptionally large, potentially altering the path towards equilibrium. Further details on their analytical methods and computational modelling are presented below.

Entanglement Growth Mirrors Thermodynamic Entropy Exchange in Interacting Spin Chains

Entanglement measures now grow at a rate equivalent to thermodynamic entropy exchange, a relationship previously obscured by the difficulty of simulating quenches originating from highly entangled initial states beyond simple scenarios. Within interacting XXZ spin chains quenched from n-rainbow states, macroscopically uniform arrangements of increasingly long-range Bell pairs, this equivalence is apparent and notably free from entanglement growth suppression due to multiplet formation during accessible timescales. This contrasts sharply with non-interacting systems, where quasiparticle multiplets *do* suppress entanglement as rainbow connections increase, highlighting how information spreads differently under varying conditions.

Quenches originating from n-rainbow states exhibited an entanglement growth rate mirroring thermodynamic entropy transfer in these interacting spin chains; a direct link between the speed of entanglement spread and thermodynamic entropy exchange has thus been confirmed. Density matrix renormalization group (tDMRG) simulations revealed no reduction in this growth caused by ‘multiplet formation’ over the examined timescales. Local stationary states approach infinite temperature with corrections scaling inversely proportional to 1/n.

Wave-like Entanglement Propagation Validated Under High Connectivity Conditions

This research offers a new way to understand how entanglement spreads following disturbances in complex systems, a key resource for advancing quantum technologies; however, their analysis relies on computationally intensive time-dependent density matrix renormalization group simulations limited by accessible timescales. The authors acknowledge that longer simulation times or more precise methods could potentially uncover suppression effects despite finding no evidence of it during the study. Still, establishing this clear benchmark for understanding entanglement growth is significant and demonstrates established wave-like models hold up even under challenging conditions involving highly connected initial states. A connection between the rate of entanglement growth and thermodynamic entropy exchange has been established within interacting quantum spin chains, a finding which challenges expectations from simpler models predicting suppressed entanglement due to particle grouping (multiplet formation) when starting from highly disordered states. Their time-dependent density matrix renormalization group simulations revealed no such suppression within accessible timescales, even initiating changes from arrangements approaching infinite temperature; these results suggest a fundamental difference in information propagation compared to non-interacting systems.

This research demonstrated that entanglement grows at a rate corresponding to thermodynamic entropy exchange in XXZ spin chains following disturbances, a phenomenon observed using time-dependent density matrix renormalization group simulations. While simpler models predicted suppressed entanglement due to particle grouping, this effect was not found during their simulations on chains up to length seven. These findings clarify how entanglement spreads in interacting quantum systems and validate existing wave-like descriptions even under high connectivity conditions.

👉 More information
🗞 Going beyond the standard quasiparticle picture: Entanglement spreading after quenching from highly entangled states
✍️ Elisa Sabadini and Vincenzo Alba (Università di Pisa)
🧠 ArXiv: https://arxiv.org/abs/2611.15409

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