Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective

Takahiro Orito; Ken-Ichiro Imura

doi:10.1103/PhysRevB.103.214206

paper

Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective

arXiv:2104.09156 · doi:10.1103/PhysRevB.103.214206

Abstract

Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension $D_{q}$ is employed; it has been claimed that $D_{q}$ shows a jump from the delocalized value $D_{q} = 1$ in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value $0 < D_{q} < 1$ at the ETH-MBL transition, yet exhibiting a conspicuous discrepancy from the fully localized value $D_{q} = 0$ , which indicate that multifractality remains inside the MBL phase. Here, to better quantify the situation we employ, instead of the commonly used computational basis, the one-particle density matrix (OPDM) and use its eigenstates (natural orbitals) as a Fock state basis for representing many-body eigenstates $∣ ψ ⟩$ of the system. Using this basis, we compute $D_{q}$ and other indices quantifying the Fock space localization, such as the local purity $S$ , which is derived from the occupation spectrum ${n_{α}}$ (eigenvalues of the OPDM). We highlight the statistical distribution of Hamming distance $x_{μν}$ occurring in the pair-wise coefficients $∣ a_{μ} ∣^{2} ∣ a_{ν} ∣^{2}$ in $S$ , and compare this with a related quantity considered in the literature.

arXiv comment19 pages, 8 figures, Phys. Rev. B in press

Multifractality and Fock-space localization in many-body localized states: one-particle density matrix perspective

Abstract

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