Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:2402.11272

Many-body localization properties of fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor interaction

Jiameng Hong, Taotao Hu

Published Feb 17, 2024• 0 citations
arXivHTMLPDF

Abstract

Many-body localization (MBL) is an intriguing physical phenomenon that arises from the interplay of interaction and disorder, allowing quantum systems to prevent thermalization. In this study, we investigate the MBL properties of the fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor hopping interaction along the leg direction and compare it with the Heisenberg spin-1/2 single-chain model with next-nearest-neighbor hopping interaction. We explore the MBL transition using random matrix theory and study the characteristics of entanglement entropy and its variance. Our results show that for the single-chain model, the critical point $w _{1} \sim$ 7.5 $\pm$ 0.5, whereas for the frustrated ladder model, $w _{2} \sim$ 10.5 $\pm$ 0.5. Moreover, we observe the existence of a many-body mobility edge in the frustrated ladder model. We also investigate the dynamical properties of the frustrated ladder model and identify the logarithmic growth of entanglement entropy, high fidelity of initial information, and magnetic localization phenomenon in the localized phase. Finally, we explore the finite-size scaling of the two models. Our findings suggest that interpreting MBL transition as a continuous second-order phase transition yields a better scaling solution than the Kosterlitz-Thouless type transition for our two models, and this difference is more pronounced in the frustrated ladder model compared with the single-chain model.

DOI
10.48550/arxiv.2402.11272

Related papers

Many-body Localization Transition of Ising Spin-1 Chains

Taotao Hu, Yining Zhang, Ren, Hang +4 more

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.

arXiv:2405.02028•May 3, 2024•0 citations

Many-body localization and mobility edge in a disordered spin- 12 Heisenberg ladder

Elliott Baygan, S. P. Lim, D. N. Sheng

We examine the interplay of interaction and disorder for a Heisenberg spin-1/2 ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the dynamic phase transition at a critical random field strength ${h}_{c}\ensuremath{\sim}8.5\ifmmode\pm\else\textpm\fi{}0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuations of the bipartite magnetization show distinct probability distributions which characterize different phases. Furthermore, we show that for weaker $h$, energy eigenstates with higher-energy density are delocalized while states at lower-energy density are localized, which defines a mobility edge separating these two phases. With increasing disorder strength, the mobility edge moves towards higher-energy density, which drives the system to the phase of the full many-body localization.

arXiv:1509.06786•Physical Review B•Nov 30, 2015•51 citations

Many-body localization transition in a frustrated XY chain

M. S. Bahovadinov, Denis V. Kurlov, Sergey I. Matveenko +2 more

We show evidence of many-body localization (MBL) transition in a one-dimensional isotropic XY chain with a weak next-nearest-neighbor frustration in a random magnetic field. We perform finite-size exact diagonalization calculations of level-spacing statistics and fractal dimensions to characterize the MBL transition with increasing the random field amplitude. An equivalent representation of the model in terms of spinless fermions explains the presence of the delocalized phase by the appearance of an effective nonlocal interaction between the fermions. This interaction appears due to frustration provided by the next-nearest-neighbor hopping.

arXiv:2111.12687•Physical review. B./Physical review. B•Aug 2, 2022•15 citations

Finite-size scaling analysis of the many-body localization transition in quasiperiodic spin chains

Adith Sai Aramthottil, Titas Chanda, Piotr Sierant +1 more

We analyze the finite-size scaling of the average gap ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin chain with quasiperiodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of the Berezinskii-Kosterlitz-Thouless transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sublinear drift with the system size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.

arXiv:2109.08408•Physical review. B./Physical review. B•Dec 2, 2021•48 citations

Many-body localization transition through pairwise correlations

Jaime L. C. da C. Filho, A. Saguia, Léa Ferreira dos Santos +1 more

We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one- and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction $J$ and random on-site disorder of strength $h$. As a representative pairwise correlation measure obtained from one-point functions, we use global entanglement. Through its finite-size-scaling analysis, we locate the MBL critical point at ${h}_{c}/J=3.8$. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range ${h}_{c}/J\ensuremath{\in}[3,4]$. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.

arXiv:1705.01957•Physical review. B./Physical review. B•Jul 21, 2017•14 citations

Localization and dynamics in one-dimensional and two-dimensional Gaussian disordered quantum spin systems

Dongyan Guo, Taotao Hu, Jiameng Hong

We propose a Gaussian disorder to study many-body localization (MBL) in one-dimensional quantum system and coupled system-environment models. Unlike uniform disorder, Gaussian disorder is controlled by the standard deviation σ (driving MBL transitions) and the mean μ (causing global energy shifts). By calculating the von Neumann entropy, mean gap ratio, and dynamical indicators, we elucidate the ergodic-to-MBL transition as σ , with Gaussian disorder exhibiting more pronounced finite-size critical point drift effects compared to conventional random disorder. Through finite-size scaling analysis, it shows that there are no significant differences between the two disorder types at our assumed system sizes. We construct two system-environment coupling configurations (ladder and staggered), showing that under weak coupling, the system and environment evolve independently, whereas strong coupling induces cooperative localization. The ladder configuration shows a strong dependence on the initial state, which may lead to either the loss or retention of information, while no such dependence is observed in the staggered configuration. This can be explained by the changes in energy density of the initial state caused by variations in different model structures. When treating the system-environment as a unified two-dimensional ladder, asymmetric disorder on the two chains can drive a global MBL phase transition, with slightly different behaviors compared to symmetric disorder. Additionally, we emphasize the necessity of correctly selecting the initial state when characterizing the phase transition through dynamic indicators.

Results in Physics•Aug 27, 2025•0 citations
Many-body localization (MBL) is an intriguing physical phenomenon that arises from the interplay of interaction and disorder, allowing quantum systems to prevent thermalization. In this study, we investigate the MBL properties of the fully frustrated Heisenberg spin-1/2 ladder model with next-nearest-neighbor hopping interaction along the leg direction and compare it with the Heisenberg spin-1/2 single-chain model with next-nearest-neighbor hopping interaction. We explore the MBL transition using random matrix theory and study the characteristics of entanglement entropy and its variance. Our results show that for the single-chain model, the critical point w1∼w _{1} \simw1​∼ 7.5 ±\pm± 0.5, whereas for the frustrated ladder model, w2∼w _{2} \simw2​∼ 10.5 ±\pm± 0.5. Moreover, we observe the existence of a many-body mobility edge in the frustrated ladder model. We also investigate the dynamical properties of the frustrated ladder model and identify the logarithmic growth of entanglement entropy, high fidelity of initial information, and magnetic localization phenomenon in the localized phase. Finally, we explore the finite-size scaling of the two models. Our findings suggest that interpreting MBL transition as a continuous second-order phase transition yields a better scaling solution than the Kosterlitz-Thouless type transition for our two models, and this difference is more pronounced in the frustrated ladder model compared with the single-chain model.
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.
We examine the interplay of interaction and disorder for a Heisenberg spin-1/2 ladder system with random fields. We identify many-body localized states based on the entanglement entropy scaling, where delocalized and localized states have volume and area laws, respectively. We first establish the dynamic phase transition at a critical random field strength ${h}_{c}\ensuremath{\sim}8.5\ifmmode\pm\else\textpm\fi{}0.5$, where all energy eigenstates are localized beyond that value. Interestingly, the entanglement entropy and fluctuations of the bipartite magnetization show distinct probability distributions which characterize different phases. Furthermore, we show that for weaker hhh, energy eigenstates with higher-energy density are delocalized while states at lower-energy density are localized, which defines a mobility edge separating these two phases. With increasing disorder strength, the mobility edge moves towards higher-energy density, which drives the system to the phase of the full many-body localization.
We show evidence of many-body localization (MBL) transition in a one-dimensional isotropic XY chain with a weak next-nearest-neighbor frustration in a random magnetic field. We perform finite-size exact diagonalization calculations of level-spacing statistics and fractal dimensions to characterize the MBL transition with increasing the random field amplitude. An equivalent representation of the model in terms of spinless fermions explains the presence of the delocalized phase by the appearance of an effective nonlocal interaction between the fermions. This interaction appears due to frustration provided by the next-nearest-neighbor hopping.
We analyze the finite-size scaling of the average gap ratio and the entanglement entropy across the many-body localization (MBL) transition in one dimensional Heisenberg spin chain with quasiperiodic (QP) potential. By using the recently introduced cost-function approach, we compare different scenarios for the transition using exact diagonalization of systems up to 22 lattice sites. Our findings suggest that the MBL transition in the QP Heisenberg chain belongs to the class of the Berezinskii-Kosterlitz-Thouless transition, the same as in the case of uniformly disordered systems as advocated in recent studies. Moreover, we observe that the critical disorder strength shows a clear sublinear drift with the system size as compared to the linear drift seen in random disordered models, suggesting that the finite-size effects in the MBL transition for the QP systems are less severe than that in the random disordered scenario. Moreover, deep in the ergodic regime, we find an unexpected double-peak structure of distribution of on-site magnetizations that can be traced back to the strong correlations present in the QP potential.
We investigate the phenomenon of spatial many-body localization (MBL) through pairwise correlation measures based on one- and two-point correlation functions. The system considered is the Heisenberg spin-1/2 chain with exchange interaction JJJ and random on-site disorder of strength hhh. As a representative pairwise correlation measure obtained from one-point functions, we use global entanglement. Through its finite-size-scaling analysis, we locate the MBL critical point at hc/J=3.8{h}_{c}/J=3.8hc​/J=3.8. As for measures involving two-point functions, we analyze pairwise geometric classical, quantum, and total correlations. Similarly to what happens for continuous quantum phase transitions, it is the derivatives of these two-point correlation measures that identify the MBL critical point, which is found to be in the range ${h}_{c}/J\ensuremath{\in}[3,4]$. Our approach relies on very simple measures that do not require access to multipartite entanglement or large portions of the system.
We propose a Gaussian disorder to study many-body localization (MBL) in one-dimensional quantum system and coupled system-environment models. Unlike uniform disorder, Gaussian disorder is controlled by the standard deviation σ (driving MBL transitions) and the mean μ (causing global energy shifts). By calculating the von Neumann entropy, mean gap ratio, and dynamical indicators, we elucidate the ergodic-to-MBL transition as σ , with Gaussian disorder exhibiting more pronounced finite-size critical point drift effects compared to conventional random disorder. Through finite-size scaling analysis, it shows that there are no significant differences between the two disorder types at our assumed system sizes. We construct two system-environment coupling configurations (ladder and staggered), showing that under weak coupling, the system and environment evolve independently, whereas strong coupling induces cooperative localization. The ladder configuration shows a strong dependence on the initial state, which may lead to either the loss or retention of information, while no such dependence is observed in the staggered configuration. This can be explained by the changes in energy density of the initial state caused by variations in different model structures. When treating the system-environment as a unified two-dimensional ladder, asymmetric disorder on the two chains can drive a global MBL phase transition, with slightly different behaviors compared to symmetric disorder. Additionally, we emphasize the necessity of correctly selecting the initial state when characterizing the phase transition through dynamic indicators.