We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.We study the non-equilibrium dynamics of a disordered periodically driven quantum spin chain, with the competition between the interaction, disorder, and Floquet driving being of particular interest. We study dynamics of entanglement entropy, energy absorption to characterize dynamical regimes of the system whether it stays in the Floquet-MBL(many-body localization) region or thermalized region. Starting with a product state in the computational basis, followed by reduced density matrix which in turn gives rise to the entanglement entropy density. With the strength of the interaction, the transverse field, the parallel field, the disorder strength W and the driving frequency, we discover the distinct behaviors of fast delocalization and logarithmic entanglement growth and long-lasting memory of the initial state, indicative of localized or prethermal Floquet regimes. We observe that strong disorder arrests transport and enables slow entanglement dynamics, whereas strong driving frequency arrests energy absorption and creates a long-lived non-equilibrium state. Conversely, weak disorder or low driving frequency leads to delocalization. The outcomes show strong support for non-equilibrium phases in driven many-body systems.

arXiv:2606.04976Jun 3, 20260 citations

Multipoint entanglement in disordered systems

Javier M. Magán, Simone Paganelli, Vadim Oganesyan

arXiv:1610.00273Physics Letters ADec 7, 20162 citations

Equilibrium State and Entanglement

Sho Sugiura

Springer thesesJan 1, 20170 citations

Non-equilibrium dynamics of the disordered Power of Two model

Kunal Singh, Sayan Choudhury

Motivated by recent experimental realizations of programmable spin models with long-range interactions, we investigate the non-equilibrium dynamics of the Power-of-Two (PWR2) model. This model consists of sparse long-range couplings between spin- $1/2$ objects separated by $d = 2^n$ . In the absence of disorder, the system exhibits rapid scrambling and fast thermalization. We explore the impact of disorder in this system by analyzing the time evolution of the survival probability, half-chain entanglement entropy, and out-of-time-ordered correlators (OTOCs). We find that sufficiently strong disorder suppresses information spreading and induces localization. Remarkably, in the strong-disorder regime, the OTOCs display a non-monotonic spatial profile arising from the intrinsic nonlocality of the interactions, signaling qualitatively distinct scrambling dynamics compared to conventional long-range interacting systems. To characterize the localization transition, we extract the critical disorder strength $h_c$ from the spectral statistics and the eigenstate entanglement. We observe that $h_c$ increases with system size. Furthermore, at a fixed disorder strength, the eigenstate-averaged entanglement entropy increases with system size, while the inverse participation ratio decreases, indicating enhanced delocalization at larger sizes. These results collectively suggest that the PWR2 model remains ergodic in the thermodynamic limit for any finite disorder strength.Motivated by recent experimental realizations of programmable spin models with long-range interactions, we investigate the non-equilibrium dynamics of the Power-of-Two (PWR2) model. This model consists of sparse long-range couplings between spin-$1/2$ objects separated by $d = 2^n$. In the absence of disorder, the system exhibits rapid scrambling and fast thermalization. We explore the impact of disorder in this system by analyzing the time evolution of the survival probability, half-chain entanglement entropy, and out-of-time-ordered correlators (OTOCs). We find that sufficiently strong disorder suppresses information spreading and induces localization. Remarkably, in the strong-disorder regime, the OTOCs display a non-monotonic spatial profile arising from the intrinsic nonlocality of the interactions, signaling qualitatively distinct scrambling dynamics compared to conventional long-range interacting systems. To characterize the localization transition, we extract the critical disorder strength $h_c$ from the spectral statistics and the eigenstate entanglement. We observe that $h_c$ increases with system size. Furthermore, at a fixed disorder strength, the eigenstate-averaged entanglement entropy increases with system size, while the inverse participation ratio decreases, indicating enhanced delocalization at larger sizes. These results collectively suggest that the PWR2 model remains ergodic in the thermodynamic limit for any finite disorder strength.

arXiv:2603.04220Mar 4, 20260 citations

Disorder in non-equilibrium models

Robin B. Stinchcombe

An overview is presented of non-equilibrium systems in the presence of disorder, which typically strongly affects their behaviour. The examples considered here are those for which most progress is currently being made, namely low-dimensional collective models of the lattice-based exclusion type with substitutional disorder. Discussions are given of such effects as localization, and of disorder-induced crossovers to new critical or singular behaviour at steady state non-equilibrium transitions, and to new asymptotic or critical dynamics. Mappings to disordered quantum spin systems are used to provide some exact results (exploiting Goldstone symmetries or free fermion equivalences) and to introduce non-equilibrium/disorder effects analogous to Griffiths phases and McCoy-Wu singularities. Among other topics also discussed here are criteria for crossovers, and non-equilibrium transitions and dynamics on diluted and possibly scale-invariant backgrounds. As well as mappings, direct approaches of various sorts are used, such as mean field methods, and scaling procedures typically scaling a disorder distribution. Scaling for the non-equilibrium dynamics is relatively simple and very effective when the equations of motion are linear or linearizable by certain transformations presented here. The current situation regarding scaling approaches to the more resistant non-linear cases is briefly discussed.An overview is presented of non-equilibrium systems in the presence of disorder, which typically strongly affects their behaviour. The examples considered here are those for which most progress is currently being made, namely low-dimensional collective models of the lattice-based exclusion type with substitutional disorder. Discussions are given of such effects as localization, and of disorder-induced crossovers to new critical or singular behaviour at steady state non-equilibrium transitions, and to new asymptotic or critical dynamics. Mappings to disordered quantum spin systems are used to provide some exact results (exploiting Goldstone symmetries or free fermion equivalences) and to introduce non-equilibrium/disorder effects analogous to Griffiths phases and McCoy-Wu singularities. Among other topics also discussed here are criteria for crossovers, and non-equilibrium transitions and dynamics on diluted and possibly scale-invariant backgrounds. As well as mappings, direct approaches of various sorts are used, such as mean field methods, and scaling procedures typically scaling a disorder distribution. Scaling for the non-equilibrium dynamics is relatively simple and very effective when the equations of motion are linear or linearizable by certain transformations presented here. The current situation regarding scaling approaches to the more resistant non-linear cases is briefly discussed.

Journal of Physics Condensed MatterFeb 8, 200233 citations

Entanglement and entropy

Sibel Başkal, Young S Kim, Marilyn E. Noz

Institute of Physics eBooksJun 1, 20190 citations

1/2

objects separated by

d = 2^n

. In the absence of disorder, the system exhibits rapid scrambling and fast thermalization. We explore the impact of disorder in this system by analyzing the time evolution of the survival probability, half-chain entanglement entropy, and out-of-time-ordered correlators (OTOCs). We find that sufficiently strong disorder suppresses information spreading and induces localization. Remarkably, in the strong-disorder regime, the OTOCs display a non-monotonic spatial profile arising from the intrinsic nonlocality of the interactions, signaling qualitatively distinct scrambling dynamics compared to conventional long-range interacting systems. To characterize the localization transition, we extract the critical disorder strength

h_c

from the spectral statistics and the eigenstate entanglement. We observe that

h_c

increases with system size. Furthermore, at a fixed disorder strength, the eigenstate-averaged entanglement entropy increases with system size, while the inverse participation ratio decreases, indicating enhanced delocalization at larger sizes. These results collectively suggest that the PWR2 model remains ergodic in the thermodynamic limit for any finite disorder strength.