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International Journal of Theoretical Physics

Property of Many-Body Localization in Heisenberg Ising Chain Under Periodic Driving

Shuangyuan Ni, Taotao Hu, Hang Ren, Kang Xue, Jiali Zhang, Xiaodan Li, Shuang Lü, Xiaoxuan Gu

Published Mar 9, 2023• 0 citations
Publisher
DOI
10.1007/s10773-023-05309-9

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In this paper, we theoretically investigate the many-body localization properties of one-dimensional Ising spin-1 chains by using the methods of exact matrix diagonalization. We compare it with the MBL properties of the Ising spin-1/2 chains. The results indicate that the one-dimensional Ising spin-1 chains can also undergo MBL phase transition. There are various forms of disorder, and we compare the effects of different forms of quasi-disorder and random disorder on many-body localization in this paper. First, we calculate the exctied-state fidelity to study the MBL phase transtion. By changing the form of the quasi-disorder, we study the MBL transition of the system with different forms of quasi-disorder and compare them with those of the random disordered system. The results show that both random disorder and quasi-disorder can cause the MBL phase transition in the one-dimensional Ising spin-1 chains. In order to study the effect of spin interactions, we compare Ising spin-1 chains and spin-1/2 chains with the next-nearest-neighbour(N-N) two-body interactions and the next-next-nearest-neighbour (N-N-N)interactions. The results show that the critical point increases with the addition of the interaction. Then we study the dynamical properties of the model by the dynamical behavior of diagonal entropy (DE), local magnetization and the time evolution of fidelity to further prove the occurrence of MBL phase transition in the disordered Ising spin-1 chains with the (N-N) coupling term and distinguish the ergodic phase (thermal phase) and the many-body localized phase. Lastly, we delve into the impact of periodic driving on one-dimensional Ising spin-1 chains. And we compare it with the results obtained from the Ising spin-1/2 chains. It shows that periodic driving can cause Ising spin-1 chains and Ising spin-1/2 chains to occur the MBL transition.
Many-body localized (MBL) systems are known to thermalize in periodically driven systems. In this work, we demonstrate that under proper driving protocol, this thermalization this thermalization can be resisted such that the MBL phase turns into a non-ergodic extended phase, known as the many-body critical (MBC) phase. Considering a kicked quasiperiodic Ising chain, we show that while at high-frequency driving the ergodic, MBL, and the MBC phases coexist, at moderate driving frequencies the MBL phase is completely suppressed and the MBC phase proliferates in the parameter space. Using quasienergy statistics, Floquet eigenstates, autocorrelation dynamics, and entanglement growth, we characterize the emergent phases and identify non-monotonic signatures revealing richness of the nonergodic phases. Our results establish Floquet driving as a powerful route to stabilizing nonergodic extended many-body phases beyond the conventional Floquet-MBL paradigm.