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A Statistical Approach to Quantum Many-Body Eigenstates near Criticality: Multifractality in Hilbert Space

Subject Area Statistical Physics, Nonlinear Dynamics, Complex Systems, Soft and Fluid Matter, Biological Physics
Term from 2018 to 2025
Project identifier Deutsche Forschungsgemeinschaft (DFG) - Project number 402552777
 
Final Report Year 2025

Final Report Abstract

The structural and dynamical properties of interacting many-particle quantum systems define a broad and multi-facetted research theme with relevance in diverse areas of physics, from particle physics over condensed matter to atomic and molecular physics, material science and quantum computation. Within the realm of cold atom physics, at the interface to condensed matter physics, stunning improvements of the experimental tools for diagnostics and control allow to explore manybody quantum dynamical and structural features with an unprecedented level of resolution, calling for refined theory. Within this broader context, the present project did target the structural and dynamical properties of interacting fermions or bosons in one dimensional, possibly disordered or tilted optical lattices, with a special focus on features indicative of many-body localisation (MBL) vs. ergodic many-body dynamics, and of the conditions which demarcate these distinct behaviours. The main achievements of our work are: a) An complete characterization of the spectral and eigenvector structure of the bosonic many-particle problem across the entire parameter space, for the in condensed matter contexts often investigated vicinity of the many-body ground state, featuring the prominent superfluid-Mott transition, as well as for the entire excitation spectrum – which is of interest for an improved understanding of diverse many-body non-equilibrium phenomena, from the foundations of thermodynamics to the robust control of engineered multi-component quantum systems such as quantum computing platforms. b) An unambiguous mapping between structural spectral and eigenstate properties and dynamical features, which provides clear guidance for experimental efforts to infer distinctive properties from dynamical observables, and discriminates signatures of many-body interaction from those of many-body interferences. We thereby succeeded to demarcate the localized from the ergodic phase of interacting many-body dynamics, consistently by inspecting various quantifiers, to identify system specific as well as universal statistical features characterizing the ergodic phase, and to distill out, for the first time, the manifestations of many-body interferences between the involved identical particles. Our work thereby offers a spectrally and dynamically complete characterization of Bose-Hubbard problem, and opens novel perspectives upon the competition between many-body interactions and many-body-interferences in such class of many-body quantum systems.

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