We investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbor coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many- body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation of the quasiperiodic modulation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model’s localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potentialWe investigate the localization properties of a spin chain with an antiferromagnetic nearest-neighbor coupling, subject to an external quasiperiodic on-site magnetic field. The quasiperiodic modulation interpolates between two paradigmatic models, namely the Aubry-André and the Fibonacci models. We find that stronger many- body interactions extend the ergodic phase in the former, whereas they shrink it in the latter. Furthermore, the many-body localization transition points at the two limits of the interpolation appear to be continuously connected along the deformation of the quasiperiodic modulation. As a result, the position of the many-body localization transition depends on the interaction strength for an intermediate degree of deformation. Moreover, in the region of parameter space where the single-particle spectrum contains both localized and extended states, many-body interactions induce an anomalous effect: weak interactions localize the system, whereas stronger interactions enhance ergodicity. We map the model’s localization phase diagram using the decay of the quenched spin imbalance in relatively long chains. This is accomplished employing a time-dependent variational approach applied to a matrix product state decomposition of the many-body state. Our model serves as a rich playground for testing many-body localization under tunable potential

Jan 1, 202126 citations

Many-body delocalization dynamics in long Aubry-André quasiperiodic chains

Elmer V. H. Doggen, A. D. Mirlin

We study quench dynamics in an interacting spin chain with a quasiperiodic on-site field, known as the interacting Aubry-Andr\'e model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to $L=50$ . We find that the choice of periodicity $\mathrm{\ensuremath{\Phi}}$ of the quasiperiodic field influences the dynamics. For $\mathrm{\ensuremath{\Phi}}=(\sqrt{5}\ensuremath{-}1)/2$ (the inverse golden ratio) and interaction $\mathrm{\ensuremath{\Delta}}=1$, the model most frequently considered in the literature, we obtain the critical disorder ${W}_{c}=4.8\ifmmode\pm\else\textpm\fi{}0.5$ in units where the noninteracting transition is at $W=2$ . At the same time, for periodicity $\mathrm{\ensuremath{\Phi}}=\sqrt{2}/2$ we obtain a considerably higher critical value, ${W}_{c}=7.8\ifmmode\pm\else\textpm\fi{}0.5$. Finite-size effects on the critical disorder ${W}_{c}$ are much weaker than in the purely random case. This supports the enhancement of ${W}_{c}$ in the case of a purely random potential by rare ``ergodic spots,'' which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.We study quench dynamics in an interacting spin chain with a quasiperiodic on-site field, known as the interacting Aubry-Andr\'e model of many-body localization. Using the time-dependent variational principle, we assess the late-time behavior for chains up to $L=50$. We find that the choice of periodicity $\mathrm{\ensuremath{\Phi}}$ of the quasiperiodic field influences the dynamics. For $\mathrm{\ensuremath{\Phi}}=(\sqrt{5}\ensuremath{-}1)/2$ (the inverse golden ratio) and interaction $\mathrm{\ensuremath{\Delta}}=1$, the model most frequently considered in the literature, we obtain the critical disorder ${W}_{c}=4.8\ifmmode\pm\else\textpm\fi{}0.5$ in units where the noninteracting transition is at $W=2$. At the same time, for periodicity $\mathrm{\ensuremath{\Phi}}=\sqrt{2}/2$ we obtain a considerably higher critical value, ${W}_{c}=7.8\ifmmode\pm\else\textpm\fi{}0.5$. Finite-size effects on the critical disorder ${W}_{c}$ are much weaker than in the purely random case. This supports the enhancement of ${W}_{c}$ in the case of a purely random potential by rare ``ergodic spots,'' which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.

arXiv:1901.06971Physical review. B./Physical review. BSep 13, 201980 citations

Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge

Ke Huang, DinhDuy Vu, Xiao Li +1 more

We study many-body localization (MBL) in the quasiperiodic ${t}_{1}\text{\ensuremath{-}}{t}_{2}$ model, focusing on the role of next-nearest-neighbor (NNN) hopping ${t}_{2}$ , which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction $U$ . For weak interactions ($U\ensuremath{\ll}{t}_{1}$), this model is always nonthermal. For intermediate interactions ($U\ensuremath{\sim}{t}_{1}$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\ensuremath{\gg}{t}_{1})$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.We study many-body localization (MBL) in the quasiperiodic ${t}_{1}\text{\ensuremath{-}}{t}_{2}$ model, focusing on the role of next-nearest-neighbor (NNN) hopping ${t}_{2}$, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction $U$. For weak interactions ($U\ensuremath{\ll}{t}_{1}$), this model is always nonthermal. For intermediate interactions ($U\ensuremath{\sim}{t}_{1}$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\ensuremath{\gg}{t}_{1})$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.

arXiv:2205.15339Physical review. B./Physical review. BJan 17, 202316 citations

Many-body localization in a quasiperiodic Fibonacci chain

Nicolas Macé, Nicolas Laflorencie, Fabien Alet

We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.We study the many-body localization (MBL) properties of a chain of interacting fermions subject to a quasiperiodic potential such that the non-interacting chain is always delocalized and displays multifractality. Contrary to naive expectations, adding interactions in this systems does not enhance delocalization, and a MBL transition is observed. Due to the local properties of the quasiperiodic potential, the MBL phase presents specific features, such as additional peaks in the density distribution. We furthermore investigate the fate of multifractality in the ergodic phase for low potential values. Our analysis is based on exact numerical studies of eigenstates and dynamical properties after a quench.

arXiv:1811.01912SciPost PhysicsApr 29, 201964 citations

Coexistence of localization and transport in many-body two-dimensional Aubry-André models

Antonio Štrkalj, Elmer V. H. Doggen, Claudio Castelnovo

Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.Whether disordered and quasiperiodic many-body quantum systems host a long-lived localized phase in the thermodynamic limit has been the subject of intense recent debate. While in one dimension, substantial evidence for such a many-body localized (MBL) phase exists, the behavior in higher dimensions remains an open puzzle. In disordered systems, for instance, it has been argued that rare regions may lead to thermalization of the whole system through a mechanism dubbed avalanche instability. In quasiperiodic systems, however, rare regions are altogether absent and the fate of a putative many-body localized phase has hitherto remained largely unexplored. In this work, we investigate the localization properties of two many-body quasiperiodic models, which are two-dimensional generalizations of the Aubry-Andr\'e model. By studying numerically the out-of-equilibrium dynamics of large systems, we find very long-lived localization on experimentally relevant time scales. Surprisingly, we also observe large-scale transport along deterministic lines of weak potential, which appear in the investigated quasiperiodic models. Our results demonstrate that quasiperiodic many-body systems have the remarkable and counter-intuitive capability of exhibiting coexisting localization and transport properties---a phenomenon reminiscent of the behavior of supersolids. Our findings are of direct experimental relevance and can be tested, for instance, using state-of-the-art cold atomic systems.

arXiv:2204.05198Physical review. B./Physical review. BNov 21, 202229 citations

Localization, multifractality, and many-body localization in periodically kicked quasiperiodic lattices

Yu Zhang, Bozhen Zhou, Haiping Hu +1 more

We study the combined effect of quasiperiodic disorder, driven, and interaction in the periodically kicked Aubry-Andr\'e model. In the noninteracting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from the ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for the strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-Andr\'e model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.We study the combined effect of quasiperiodic disorder, driven, and interaction in the periodically kicked Aubry-Andr\'e model. In the noninteracting limit, by analyzing the quasienergy spectrum statistics, we verify the existence of a dynamical localization transition in the high-frequency region, whereas the spectrum statistics becomes intricate in the low-frequency region due to the emergence of the extended/localized-to-multifractal edges in the quasienergy spectrum, which separate the multifractal states from the extended (localized) states. When the interaction is introduced, we find the periodically kicked incommensurate potential can lead to a transition from the ergodic to many-body-localization phase in the high-frequency region. However, the many-body localization phase vanishes in the low-frequency region even for the strong quasiperiodic disorder. Our studies demonstrate that the periodically kicked Aubry-Andr\'e model displays rich dynamical phenomena and the driving frequency plays an important role in the formation of many-body localization in addition to the disorder strength.

arXiv:2203.08004Physical review. B./Physical review. BAug 25, 202217 citations

L=50

. We find that the choice of periodicity $\mathrm{\ensuremath{\Phi}}$ of the quasiperiodic field influences the dynamics. For $\mathrm{\ensuremath{\Phi}}=(\sqrt{5}\ensuremath{-}1)/2$ (the inverse golden ratio) and interaction $\mathrm{\ensuremath{\Delta}}=1$, the model most frequently considered in the literature, we obtain the critical disorder ${W}_{c}=4.8\ifmmode\pm\else\textpm\fi{}0.5$ in units where the noninteracting transition is at

W=2

. At the same time, for periodicity $\mathrm{\ensuremath{\Phi}}=\sqrt{2}/2$ we obtain a considerably higher critical value, ${W}_{c}=7.8\ifmmode\pm\else\textpm\fi{}0.5$. Finite-size effects on the critical disorder

{W}_{c}

are much weaker than in the purely random case. This supports the enhancement of

{W}_{c}

in the case of a purely random potential by rare ``ergodic spots,'' which do not occur in the quasiperiodic case. Further, the data suggest that the decay of the antiferromagnetic order in the delocalized phase is faster than a power law.

We study many-body localization (MBL) in the quasiperiodic ${t}_{1}\text{\ensuremath{-}}{t}_{2}$ model, focusing on the role of next-nearest-neighbor (NNN) hopping

{t}_{2}

, which introduces a single-particle mobility edge. The calculated phase diagram can be divided into three distinct regimes, depending on the strength of the short-range interaction

U

. For weak interactions ($U\ensuremath{\ll}{t}_{1}$), this model is always nonthermal. For intermediate interactions ($U\ensuremath{\sim}{t}_{1}$), the thermal-MBL phase transition in this model is qualitatively the same as that of the Aubry-Andre (AA) model, which is consistent with existing experimental observations. For strong interactions $(U\ensuremath{\gg}{t}_{1})$, the NNN hopping produces qualitatively new physics because it breaks down the Hilbert space fragmentation present in the AA model. The NNN hopping is thus irrelevant when the interaction is intermediate but relevant for strong interactions.