We study a canonical many-body-localized (MBL) system with power-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magnetic field. The power-law-correlated disorder can control the critical regime between the MBL and thermal (ergodic) phases by varying its exponent, and it let us investigate the MBL transitions in detail. Static-eigenstate and dynamic properties of MBL are studied by numerical methods for systems with various long-range correlations. By using energy-resolved distribution of the participation ratio (PR) and calculating some physical quantities related to localization length, we show that the MBL transition exhibits certain universal behavior. We also investigate entanglement properties for the static and dynamics system. These studies elucidate the impact of power-law-correlated disorders in the canonical MBL system.We study a canonical many-body-localized (MBL) system with power-law-correlated disorders: $s=\frac{1}{2}$ spin chain in a random magnetic field. The power-law-correlated disorder can control the critical regime between the MBL and thermal (ergodic) phases by varying its exponent, and it let us investigate the MBL transitions in detail. Static-eigenstate and dynamic properties of MBL are studied by numerical methods for systems with various long-range correlations. By using energy-resolved distribution of the participation ratio (PR) and calculating some physical quantities related to localization length, we show that the MBL transition exhibits certain universal behavior. We also investigate entanglement properties for the static and dynamics system. These studies elucidate the impact of power-law-correlated disorders in the canonical MBL system.

arXiv:2002.12575Feb 28, 20201 citation

Phase Transitions and Quantum Correlations in Heisenberg XXZ Spin Chains

Mounaim Hamdoune, Mohammed Daoud A

International Journal of Theoretical PhysicsAug 8, 20260 citations

Response to a local quench of a system near the many-body localization transition

Canran Xu, Maxim Vavilov

We consider a one-dimensional spin- $\frac{1}{2}$ chain with Heisenberg interaction in a disordered parallel magnetic field. This system is known to exhibit the many-body localization (MBL) transition at critical strength of disorder. We analyze the response of the chain when additional perpendicular magnetic field is applied to an individual spin and propose a method for accurate determination of the mobility edge via local spin measurements. We further demonstrate that the exponential decrease of the spin response with the distance between perturbed spin and measured spin can be used to characterize the localization length in the MBL phase. We also studied the effect of the quench on statistics of the entire energy spectrum. We demonstrate that the quench introduces level repulsion between energy states corresponding to different eigenvalues of the total spin in the delocalized regime, while level spacing is described by the Poisson statistics in the localized regime even at strong quench.We consider a one-dimensional spin-$\frac{1}{2}$ chain with Heisenberg interaction in a disordered parallel magnetic field. This system is known to exhibit the many-body localization (MBL) transition at critical strength of disorder. We analyze the response of the chain when additional perpendicular magnetic field is applied to an individual spin and propose a method for accurate determination of the mobility edge via local spin measurements. We further demonstrate that the exponential decrease of the spin response with the distance between perturbed spin and measured spin can be used to characterize the localization length in the MBL phase. We also studied the effect of the quench on statistics of the entire energy spectrum. We demonstrate that the quench introduces level repulsion between energy states corresponding to different eigenvalues of the total spin in the delocalized regime, while level spacing is described by the Poisson statistics in the localized regime even at strong quench.

arXiv:1509.05158Physical review. B./Physical review. BFeb 24, 20174 citations

Many-Body Localization Transition in the Heisenberg Ising Chain

Yining Geng, Taotao Hu, Kang Xue +4 more

International Journal of Theoretical PhysicsFeb 17, 20202 citations

Detection and characterization of many-body localization in central spin models

Daniel Hetterich, Norman Y. Yao, Maksym Serbyn +2 more

We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one-dimensional (1D) random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a nonextensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.We analyze a disordered central spin model, where a central spin interacts equally with each spin in a periodic one-dimensional (1D) random-field Heisenberg chain. If the Heisenberg chain is initially in the many-body localized (MBL) phase, we find that the coupling to the central spin suffices to delocalize the chain for a substantial range of coupling strengths. We calculate the phase diagram of the model and identify the phase boundary between the MBL and ergodic phase. Within the localized phase, the central spin significantly enhances the rate of the logarithmic entanglement growth and its saturation value. We attribute the increase in entanglement entropy to a nonextensive enhancement of magnetization fluctuations induced by the central spin. Finally, we demonstrate that correlation functions of the central spin can be utilized to distinguish between MBL and ergodic phases of the 1D chain. Hence, we propose the use of a central spin as a possible experimental probe to identify the MBL phase.

arXiv:1806.08316Physical review. B./Physical review. BOct 29, 201821 citations

We study a canonical many-body-localized (MBL) system with power-law-correlated disorders:

s=\frac{1}{2}

spin chain in a random magnetic field. The power-law-correlated disorder can control the critical regime between the MBL and thermal (ergodic) phases by varying its exponent, and it let us investigate the MBL transitions in detail. Static-eigenstate and dynamic properties of MBL are studied by numerical methods for systems with various long-range correlations. By using energy-resolved distribution of the participation ratio (PR) and calculating some physical quantities related to localization length, we show that the MBL transition exhibits certain universal behavior. We also investigate entanglement properties for the static and dynamics system. These studies elucidate the impact of power-law-correlated disorders in the canonical MBL system.

We consider a one-dimensional spin-

\frac{1}{2}

chain with Heisenberg interaction in a disordered parallel magnetic field. This system is known to exhibit the many-body localization (MBL) transition at critical strength of disorder. We analyze the response of the chain when additional perpendicular magnetic field is applied to an individual spin and propose a method for accurate determination of the mobility edge via local spin measurements. We further demonstrate that the exponential decrease of the spin response with the distance between perturbed spin and measured spin can be used to characterize the localization length in the MBL phase. We also studied the effect of the quench on statistics of the entire energy spectrum. We demonstrate that the quench introduces level repulsion between energy states corresponding to different eigenvalues of the total spin in the delocalized regime, while level spacing is described by the Poisson statistics in the localized regime even at strong quench.