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Complete Dynamical Localization in Disordered Quantum Multi-Particle Systems∗

Published Jan 1, 2009• 8 citations
OpenAlex

Abstract

We present some recent results concerning the persistence of dynamical local-ization for disordered systems of n particles under weak interactions. 1

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Localization due to interaction‐enhanced disorder in bosonic systems

Rajeev Singh, Efrat Shimshoni

Localization in interacting systems caused by disorder, known as many‐body localization (MBL), has attracted a lot of attention in recent years. Most systems studied in this context also show single‐particle localization, and the question of MBL is whether the phenomena survives the effects of interactions. It is intriguing to consider a system with no single‐particle localization but which does localize in the presence of many particles. The localization phenomena occurs “due to” rather than “in spite of” interactions in such systems. We consider a simple bosonic system and show that interactions enhance the effects of very weak disorder and result in localization when many particles are present. We provide physical insights into the mechanism involved and support our results with analytical and numerical calculations. image

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Two interacting particles in lattices, in the absence of dissipation, can not distin- guish between attractive or repulsive interaction when the range of their tunnelling is limited to nearest neighbor sites. However, we find that, in the case of long-range tunnelling, the particles exhibit different dynamics for different types of interactions of the same strength. The nature of dynamical correlations between particles also becomes significantly different. For weak interactions, particles develop a character in correlation which is in between that of antiwalking and cowalking when the tunnelling is long-range. For strong interactions, particles cowalk independently of their statistics. A few recent experiments have demonstrated such effects of interactions on quantum walk of photons, atoms and spin excitations on various lattice platforms. In disordered lattices the effect of coherent backscattering makes particles localize to their initial position. We find that a weak repulsive interaction reduces localization and a strong interaction enhances localization. We also calculate the correlations between the particles in the disordered 1D and 2D systems. The effect of long-range tunnelling on localization of particles in disordered 1D systems has been explored. For large ordered or disordered lattices, computation of localization parameters becomes difficult. In these cases, an efficient recursive algorithm is used to calculate Green’s functions exactly. We extend such algorithm to disordered systems in both one and two dimensions. We also illustrate that this recursive algorithm maps directly to some graph structures like binary trees. We perform calculations for quantum walk of interacting particles on such graphs. The method is also used to calculate the properties of interacting particles on lattices with gauge fields. For disordered 2D lattices, we introduce and test approximations which produce accurate results and make the calculations more efficient. We examine the localization parameters for a broad range of interaction and disorder strengths and try to find differences among parameters within the range.
We systematically study the effect of disorder and interactions on a quasi-one-dimensional diamond chain possessing flat bands.Disorder localizes all the single-particle eigenstates, while at low disorder strengths, we obtain weak flat-band based localization (FBL), at high disorder strengths, we see conventional Anderson localization (AL).The compactly localized (CL) eigenstates of flat bands show a persisting oscillatory recurrence in the study of single-particle wave-packet dynamics.For low disorder, a damped oscillatory recurrence behavior is observed which is absent for high disorder.Noninteracting many-particle fermion states also follow the same trend except showing a delocalizing tendency at intermediate disorder due to the fermionic statistics in the system.As interactions are switched on, for the finite sizes that we are able to study, a nonergodic "mixed phase" is observed at low disorder which is separated from the MBL phase at high disorder by a thermal phase at intermediate disorder.A study of many-body nonequilibrium dynamics reinforces these findings.
Localization in interacting systems caused by disorder, known as many‐body localization (MBL), has attracted a lot of attention in recent years. Most systems studied in this context also show single‐particle localization, and the question of MBL is whether the phenomena survives the effects of interactions. It is intriguing to consider a system with no single‐particle localization but which does localize in the presence of many particles. The localization phenomena occurs “due to” rather than “in spite of” interactions in such systems. We consider a simple bosonic system and show that interactions enhance the effects of very weak disorder and result in localization when many particles are present. We provide physical insights into the mechanism involved and support our results with analytical and numerical calculations. image