scholarly journals On intermediate statistics across many-body localization transition

2021 ◽  
Author(s):  
Bitan De ◽  
Piotr Sierant ◽  
Jakub Zakrzewski
Keyword(s):  
Joint Probability ◽  
Single Parameter ◽  
Joint Probability Distribution ◽  
Many Body ◽  
Localization Transition ◽  
Physical Systems ◽  
Level Statistics ◽  
Interacting Systems ◽  
Many Body Systems ◽  
Two Parameter

Abstract The level statistics in the transition between delocalized and localized {phases of} many body interacting systems is {considered}. We recall the joint probability distribution for eigenvalues resulting from the statistical mechanics for energy level dynamics as introduced by Pechukas and Yukawa. The resulting single parameter analytic distribution is probed numerically {via Monte Carlo method}. The resulting higher order spacing ratios are compared with data coming from different {quantum many body systems}. It is found that this Pechukas-Yukawa distribution compares favorably with {$\beta$--Gaussian ensemble -- a single parameter model of level statistics proposed recently in the context of disordered many-body systems.} {Moreover, the Pechukas-Yukawa distribution is also} only slightly inferior to the two-parameter $\beta$-h ansatz shown {earlier} to reproduce {level statistics of} physical systems remarkably well.

scholarly journals Quantum many-body attractors

2020 ◽  
Author(s):  
Berislav Buca ◽  
Archak Purkayastha ◽  
Giacomo Guarnieri ◽  
Mark Mitchison ◽  
Dieter Jaksch ◽  
...  
Keyword(s):  
Classical Limit ◽  
Initial Conditions ◽  
Quantum Level ◽  
Many Body ◽  
Dynamical Symmetries ◽  
Oscillatory Dynamics ◽  
Quantum Magnet ◽  
Interacting Systems ◽  
Symmetry Operators ◽  
Many Body Systems

Abstract Real-world complex systems often show robust, persistent oscillatory dynamics, e.g.~non-trivial attractors. On the quantum level this behaviour has only been found in semi-classical or weakly correlated systems under restrictive assumptions. However, strongly interacting systems without classical limits, e.g.~electrons on a lattice or spins, typically relax quickly to a stationary state (trivial attractors). This raises the puzzling question of how non-trivial attractors can arise from the quantum laws. Here, we introduce strictly local dynamical symmetries that lead to extremely robust and persistent oscillations in quantum many-body systems without a classical limit. Observables that do not have overlap with the symmetry operators can relax, losing memory of their initial conditions. The remaining observables enter complex dynamical cycles, signalling the emergence of a quantum many-body attractor. We provide a recipe for constructing Hamiltonians featuring local dynamical symmetries. As an example, we introduce the spin lace – a model of a quasi-1D quantum magnet.

scholarly journals From Bloch oscillations to many-body localization in clean interacting systems

2019 ◽  
Vol 116 (19) ◽  
pp. 9269-9274 ◽  
Author(s):  
Evert van Nieuwenburg ◽  
Yuval Baum ◽  
Gil Refael
Keyword(s):  
Potential Gradient ◽  
Machine Learning Techniques ◽  
Linear Potential ◽  
Many Body ◽  
Bloch Oscillations ◽  
Learning Techniques ◽  
Level Statistics ◽  
New Directions ◽  
Interacting Systems ◽  
Particle Localization

In this work we demonstrate that nonrandom mechanisms that lead to single-particle localization may also lead to many-body localization, even in the absence of disorder. In particular, we consider interacting spins and fermions in the presence of a linear potential. In the noninteracting limit, these models show the well-known Wannier–Stark localization. We analyze the fate of this localization in the presence of interactions. Remarkably, we find that beyond a critical value of the potential gradient these models exhibit nonergodic behavior as indicated by their spectral and dynamical properties. These models, therefore, constitute a class of generic nonrandom models that fail to thermalize. As such, they suggest new directions for experimentally exploring and understanding the phenomena of many-body localization. We supplement our work by showing that by using machine-learning techniques the level statistics of a system may be calculated without generating and diagonalizing the Hamiltonian, which allows a generation of large statistics.

scholarly journals Euler-scale dynamical correlations in integrable systems with fluid motion

2020 ◽  
Vol 3 (2) ◽  
Author(s):  
Frederik Skovbo Møller ◽  
Gabriele Perfetto ◽  
Benjamin Doyon ◽  
Jörg Schmiedmayer
Keyword(s):  
Iterative Scheme ◽  
Scaling Limit ◽  
Fluid Motion ◽  
Many Body ◽  
Fluctuation Dissipation ◽  
Long Time ◽  
Interacting Systems ◽  
Point Correlation ◽  
Many Body Systems ◽  
Scale Limit

We devise an iterative scheme for numerically calculating dynamical two-point correlation functions in integrable many-body systems, in the Eulerian scaling limit. Expressions for these were originally derived in Ref. [1] by combining the fluctuation-dissipation principle with generalized hydrodynamics. Crucially, the scheme is able to address non-stationary, inhomogeneous situations, when motion occurs at the Euler-scale of hydrodynamics. In such situations, in interacting systems, the simple correlations due to fluid modes propagating with the flow receive subtle corrections, which we test. Using our scheme, we study the spreading of correlations in several integrable models from inhomogeneous initial states. For the classical hard-rod model we compare our results with Monte-Carlo simulations and observe excellent agreement at long time-scales, thus providing the first demonstration of validity for the expressions derived in Ref. [1]. We also observe the onset of the Euler-scale limit for the dynamical correlations.

REGULAR STRUCTURE OF LOW-LYING STATES FOR ATOMIC NUCLEI UNDER RANDOM INTERACTIONS

2008 ◽  
Vol 17 (supp01) ◽  
pp. 304-317
Author(s):  
Y. M. ZHAO
Keyword(s):  
Ground State ◽  
Collective Motion ◽  
Regular Structure ◽  
Positive Parity ◽  
Many Body ◽  
Random Interactions ◽  
Atomic Nuclei ◽  
Many Body Systems

In this paper we review regularities of low-lying states for many-body systems, in particular, atomic nuclei, under random interactions. We shall discuss the famous problem of spin zero ground state dominance, positive parity dominance, collective motion, odd-even staggering, average energies, etc., in the presence of random interactions.

scholarly journals Emergence of a Renormalized 1/N Expansion in Quenched Critical Many-Body Systems

2021 ◽  
Vol 126 (11) ◽  
Author(s):  
Benjamin Geiger ◽  
Juan Diego Urbina ◽  
Klaus Richter
Keyword(s):  
Many Body ◽  
Many Body Systems
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