Statistics of noninteracting many-body fermionic states: The question of a many-body mobility edge
arXiv:2306.11692 · doi:10.1103/PhysRevB.109.174214
Abstract
In this work, we study the statistics of a generic noninteracting many-body fermionic system whose single-particle counterpart has a single-particle mobility edge (SPME). We first prove that the spectrum and the extensive conserved quantities follow the multivariate normal distribution with a vanishing standard deviation in the thermodynamic limit, regardless of SPME. Consequently, the theorem rules out an infinite-temperature or high-temperature many-body mobility edge (MBME) for generic noninteracting fermionic systems. Further, we also prove that the spectrum of a fermionic many-body system with short-range interactions is qualitatively similar to that of a noninteracting many-body system up to the third-order moment. These results partially explain why neither short-range [1] nor long-range interacting systems exhibit an infinite-temperature MBME.
arXiv comment14 pages, 5 figures. Comments are welcome
References in corpus (36)
- Many body localization and thermalization in quantum statistical mechanics
- Metal-insulator transition in a weakly interacting many-electron system with localized single-particle states
- Localization of interacting fermions at high temperature
- Many-body localization, thermalization, and entanglement
- Many-body localization edge in the random-field Heisenberg chain
- The distribution of the ratio of consecutive level spacings in random matrix ensembles
- Interacting electrons in disordered wires: Anderson localization and low-temperature transport
- On Many-Body Localization for Quantum Spin Chains
- Many-body localization in a disordered quantum Ising chain
- Universal dynamics and renormalization in many body localized systems
- Nearest neighbor tight binding models with an exact mobility edge in one dimension
- Predicted mobility edges in one-dimensional incommensurate optical lattices: An exactly solvable model of Anderson localization
- Diagonalization and Many-Body Localization for a Disordered Quantum Spin Chain
- Avalanches and many-body resonances in many-body localized systems
- Mobility Edges in 1D Bichromatic Incommensurate Potentials
- One dimensional quasiperiodic mosaic lattice with exact mobility edges
- Observation of many-body localization in a one-dimensional system with single-particle mobility edge
- Hilbert-Space Fragmentation from Strict Confinement
- Localization in one dimensional lattices with non-nearest-neighbor hopping: Generalized Anderson and Aubry-André models
- Many body localization and quantum non-ergodicity in a model with a single-particle mobility edge
- Absence of many-body mobility edges
- Early breakdown of area-law entanglement at many-body delocalization transition
- Dynamics of strongly interacting systems: From Fock-space fragmentation to Many-Body Localization
- Mobility edge and intermediate phase in one-dimensional incommensurate lattice potentials
- The spectral form factor is not self-averaging
- Dynamics and Transport at the Threshold of Many-Body Localization
- Many-body mobility edge due to symmetry-constrained dynamics and strong interactions
- Fermionic many-body localization for random and quasiperiodic systems in the presence of short- and long-range interactions
- Many-body mobility edges in a one-dimensional model of interacting fermions
- Many-body localization transition in large quantum spin chains: The mobility edge
- Exploring one particle orbitals in large Many-Body Localized systems
- Investigating many-body mobility edges in isolated quantum systems
- Mobility edge in long-range interacting many-body localized systems
- Incommensurate many-body localization in the presence of long-range hopping and single-particle mobility edge
- Localization spectrum of a bath-coupled generalized Aubry-André model in the presence of interactions
- Many Body Density of States of a system of non interacting spinless fermions