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Bulletin of the American Physical Society

Localization in systems with long-range interactions

Léa Ferreira dos Santos, Francisco Pérez-Bernal, Fausto Brogonovi, G. L. Celardo

Published Mar 15, 2016• 0 citations
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We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions and long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single-particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping [$t(r)\ensuremath{\sim}{t}_{0}/{r}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<2$], there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with $1<\ensuremath{\alpha}<2$ delocalizes the system partially, with almost all the states extended for $\ensuremath{\alpha}\ensuremath{\le}1$. Even in a system which has single-particle mobility edges in the noninteracting limit, turning on long-range interactions does not cause delocalization.

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Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fueling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions, long-range interacting systems display novel physics, such as nonlinear light cones for the propagation of information or inequivalent thermodynamic ensembles. In this work, we consider generic long-range open quantum systems in arbitrary dimensions and focus on the so-called strong long-range regime. We prove that in the thermodynamic limit local properties, captured by reduced quantum states, are described by an emergent noninteracting theory. Here, the dynamics factorizes and the individual constituents of the system evolve independently such that no correlations are generated over time. In this sense, long-range interacting systems are locally noninteracting. This has significant implications for their relaxation behavior, for instance, in relation to the emergence of long-lived quasistationary states or to the absence of thermalization.

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We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of long-range interactions and long-range hopping. Based on perturbative arguments there is a common belief that MBL can exist only in systems with short-range interactions and short-range hopping. We analyze effects of power-law interactions and power-law hopping, separately, on a system which has all the single-particle states localized in the absence of interactions. Since delocalization is driven by proliferation of resonances in the Fock space, we mapped this model to an effective Anderson model on a complex graph in the Fock space and calculated the probability distribution of the number of resonances up to third order. Though the most-probable value of the number of resonances diverge for the system with long-range hopping [$t(r)\ensuremath{\sim}{t}_{0}/{r}^{\ensuremath{\alpha}}$ with $\ensuremath{\alpha}<2$], there is no enhancement of the number of resonances as the range of power-law interactions increases. This indicates that the long-range hopping delocalizes the many-body localized system but in contrast to this, there is no signature of delocalization in the presence of long-range interactions. We further provide support in favor of this analysis based on dynamics of the system after a quench starting from a charge density wave ordered state, level spacing statistics, return probability, participation ratio and Shannon entropy in the Fock space. We demonstrate that MBL persists in the presence of long-range interactions though long-range hopping with $1<\ensuremath{\alpha}<2$ delocalizes the system partially, with almost all the states extended for $\ensuremath{\alpha}\ensuremath{\le}1$. Even in a system which has single-particle mobility edges in the noninteracting limit, turning on long-range interactions does not cause delocalization.
Enhanced experimental capabilities to control nonlocal and power-law decaying interactions are currently fueling intense research in the domain of quantum many-body physics. Compared to their counterparts with short-ranged interactions, long-range interacting systems display novel physics, such as nonlinear light cones for the propagation of information or inequivalent thermodynamic ensembles. In this work, we consider generic long-range open quantum systems in arbitrary dimensions and focus on the so-called strong long-range regime. We prove that in the thermodynamic limit local properties, captured by reduced quantum states, are described by an emergent noninteracting theory. Here, the dynamics factorizes and the individual constituents of the system evolve independently such that no correlations are generated over time. In this sense, long-range interacting systems are locally noninteracting. This has significant implications for their relaxation behavior, for instance, in relation to the emergence of long-lived quasistationary states or to the absence of thermalization.