Many-body localization due to random interactions

Il Nuovo Cimento B, 1988

Quantum mechanics with spontaneous localization is a recently proposed stochastic modification of the N-body Schrbdinger equation which is consistent both with microphysics and macrophysics and leads to a natural solution of the problem of quantum measurement.

Physical Review B, 1997

We investigate the localization of two interacting particles in one-dimensional random potential. Our definition of the two-particle localization length, ξ, is the same as that of v. Oppen et al. [Phys. Rev. Lett. 76, 491 (1996)] and ξ's for chains of finite lengths are calculated numerically using the recursive Green's function method for several values of the strength of the disorder, W , and the strength of interaction, U. When U = 0, ξ approaches a value larger than half the single-particle localization length as the system size tends to infinity and behaves as ξ ∼ W −ν 0 for small W with ν0 = 2.1 ± 0.1. When U = 0, we use the finite size scaling ansatz and find the relation ξ ∼ W −ν with ν = 2.9 ± 0.2. Moreover, data show the scaling behavior ξ ∼ W −ν 0 g(b|U |/W ∆) with ∆ = 4.0 ± 0.5.

Nature Physics

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Physical Review Research, 2020

The European Physical Journal Special Topics

This text presents a brief overview of the recent development of topics addressed by the original papers of this volume related to nonequilibrium phenomena in various (especially mesoscopic) systems and the foundations of quantum physics. A selection of relevant literature is included. 2 The European Physical Journal Special Topics time evolution of systems; quantum to classical transitions; dynamics of quantum phase transitions; and topological states of systems. The above mentioned phenomena, related problems and challenges occur in many fields of physics, astrophysics, chemistry, and biology. As for systems, which enable study of various related questions, mesoscopic systems are especially suitable for this purpose due to their vast variety of structures and parameters. Various systems, of natural and artificial origin, can exhibit mesoscopic features depending on inner parameters of those systems and interactions with their environment. Typical mesoscopic systems can be of nanoscale size, composed from atoms (molecules). Nanoscale structures include not only very small physical structures, but also structures occurring in living cells, as for example complex molecules, proteins and molecular motors. At the same time, nanoscale technologies enable the preparation of well-defined artificial structures composed of between a few to hundreds of atoms (molecules) to create an enormous diversity of systems with well-defined inner parameters which can be influenced by external fields. These structures can be studied by methods of condensed matter physics and quantum optics in such detail that affords a deeper understanding of quantum physics, as represented by quantum interference, entanglement, the uncertainty principle, quantum measurement and what is often termed "non-locality". Of particular interest are carbon allotropes, quantum wires and dots, microcavities, single molecule nanomagnets, molecular motors and active gels, various structures in living cells, as well as specific arrangements featuring cold atoms and molecules which can exhibit macroscopic quantum effects and which can be used for testing methods of quantum many-body theory. Recent advances in technologies have led to enormous improvements of measurement, imaging and observation techniques at microscopic, mesoscopic and macroscopic scales. At the same time, various methods allow investigation into not only equilibrium features, but also time evolution of classical and quantum systems (which are in general far from equilibrium) at different time scales. This increasing ability to study subtle details of the dynamics of systems yields new versions of old questions and creates new challenges in many fields of physics. A good understanding of the time evolution of both classical and quantum systems is essential for an explanation of many observations and experiments of contemporary physics. Observed systems must often be treated as non-equilibrium, open systems in which their behavior is influenced not only by their inner parameters, but also by properties of their environment and time dependent external fields. The theory of non-equilibrium behavior of quantum many-body systems is, however, far from complete. There are lasting and extremely important problems related to modern technologies, including questions of irreversible behavior of real systems in comparison with reversible microscopic laws, emergence of classical macroscopic behavior from microscopic quantum behavior, charge (electron), spin and heat transport, limits to "phenomenological" thermodynamic descriptions, and the problem of how to describe properly open quantum systems far from equilibrium, especially in the case of strong interaction between a small system and reservoirs. Another challenging problem is stochastic behavior of systems caused either by innate features of the systems or by noise related to the fact that the studied systems are open. Studies of quantum and temperature fluctuations, as well as quantum noise, dephasing and dissipation create an essential part of the research in this direction. Recently, various versions of non-equilibrium fluctuation and fluctuationdissipation theorems for quantum systems have been discussed. These studies are of key importance since the fluctuations, dissipation and noise are closely related to the performance and the reliability of both artificially created nano-devices as well as natural "engines", as are for example molecular motors in cells.

Physical Review B, 1997

Coherent propagation of two interacting particles in 1d weak random potential is considered. An accurate estimate of the matrix element of interaction in the basis of localized states leads to mapping onto the relevant matrix model. This mapping allows to clarify the mechanism of enhancement of the localization length which turns out to be rather different from the one considered in the literature. Although the existence of enhancement is transparent, an analytical solution of the matrix model was found only for very short samples. For a more realistic situation numerical simulations were performed. The result of these simulations is consistent with where l1 and l2 are the single and two particle localization lengths and the exponent γ depends on the strength of the interaction. In particular, in the limit of strong particle-particle interaction there is no enhancement of the coherent propagation at all (l2 ≈ l1).

Physics Today, 2005

For most of the last century, condensed matter physics has been dominated by band theory and Landau's symmetry breaking theory. In the last twenty years, however, there has been an emergence of a new paradigm associated with fractionalization, emergent gauge bosons and fermions, topological order, string-net condensation, and long range entanglements. These new physical concepts are so fundamental that they may even influence our understanding of the origin of light and electrons in the universe.

Physical Review B

We study many-body localization (MBL) in a one-dimensional system of spinless fermions with a deterministic aperiodic potential in the presence of random interactions V i j decaying as power-law V i j /(r i j) α with distance r i j. We demonstrate that MBL survives even for α < 1 and is preceded by a broad nonergodic subdiffusive phase. Starting from parameters at which the short-range interacting system shows an infinite temperature MBL phase, turning on random power-law interactions results in many-body mobility edges in the spectrum with a larger fraction of ergodic delocalized states for smaller values of α. Hence, the critical disorder h r c , at which ergodic to nonergodic transition takes place, increases with the range of interactions. Time evolution of the density imbalance I (t), which has power-law decay I (t) ∼ t −γ in the intermediate to large time regime, shows that the critical disorder h I c , above which the system becomes diffusionless (with γ ∼ 0) and transits into the MBL phase, is much larger than h r c. In between h r c and h I c there is a broad nonergodic subdiffusive phase, which is characterized by the Poissonian statistics for the level spacing ratio, multifractal eigenfunctions, and a nonzero dynamical exponent γ 1/2. The system continues to be subdiffusive even on the ergodic side (h < h r c) of the MBL transition, where the eigenstates near the mobility edges are multifractal. For h < h 0 < h r c , the system is superdiffusive with γ > 1/2. The rich phase diagram obtained here is unique to the random nature of long-range interactions. We explain this in terms of the enhanced correlations among local energies of the effective Anderson model induced by random power-law interactions.

This textbook deals with advanced topics in the field of quantum mechanics, material which is usually encountered in a second university course on quantum mechanics. The book, which comprises a total of 15 chapters, is divided into three parts: I. Many-Body Systems, II. Relativistic Wave Equations, and III. Relativistic Fields. The text is written in such a way as to attach importance to a rigorous presentation while, at the same time, requiring no prior knowledge, except in the field of basic quantum mechanics. The inclusion of all mathematical steps and full presentation of intermediate calculations ensures ease of understanding. A number of problems are included at the end of each chapter. Sections or parts thereof that can be omitted in a first reading are marked with a star, and subsidiary calculations and remarks not essential for comprehension are given in small print. It is not necessary to have read Part I in order to understand Parts II and III. References to other works in the literature are given whenever it is felt they serve a useful purpose. These are by no means complete and are simply intended to encourage further reading. A list of other textbooks is included at the end of each of the three parts.