Exploring one-particle orbitals in large many-body localized systems

Abstract

Strong disorder in interacting quantum systems can give rise to the phenomenon of Many-Body Localization (MBL), which defies thermalization due to the formation of an extensive number of quasi local integrals of motion. The one particle operator content of these integrals of motion is related to the one particle orbitals of the one particle density matrix and shows a strong signature across the MBL transition as recently pointed out by Bera et al. [Phys. Rev. Lett. 115, 046603 (2015); Ann. Phys. 529, 1600356 (2017)]. We study the properties of the one particle orbitals of many-body eigenstates of an MBL system in one dimension. Using shift-and-invert MPS (SIMPS), a matrix product state method to target highly excited many-body eigenstates introduced in [Phys. Rev. Lett. 118, 017201 (2017)], we are able to obtain accurate results for large systems of sizes up to L = 64. We find that the one particle orbitals drawn from eigenstates at different energy densities have high overlap and their occupations are correlated with the energy of the eigenstates. Moreover, the standard deviation of the inverse participation ratio of these orbitals is maximal at the nose of the mobility edge. Also, the one particle orbitals decay exponentially in real space, with a correlation length that increases at low disorder. In addition, we find a "1/f " distribution of the coupling constants of a certain range of the number operators of the OPOs, which is related to their exponential decay.

Many-body localization as a large family of localized ground states

“…The relatively small values of e 3 , even for the finite system sizes numerically available, make it possible to consider the input state as a very good approximation of an actual eigenstate ofH 3 to extend our study. We further note that contrary to recently proposed DMRGlike methods for excited states [40,49,[53][54][55][56][57][58] where the energy variance increases with the system size L, our method yields a power-law decaying σ[H, |Ψ 0 ] with L.…”

“…The GS of this model is known to be of the Bose-glass type for any h = 0 [9,10]. At higher energy, a finite amount of disorder h c 3.7 is necessary to eventually move from an ETH to a fully MBL regime [39,49].…”

Many-body localization in a quasiperiodic Fibonacci chain

“…The one-particle density matrix is defined for a given eigenvector |ψ as ρ i,j = ψ| c † i c j |ψ . It was used to characterize the MBL transition [66], and was subsequently studied as a probe of the MBL physics [43,67,68]. The study of the one-particle density matrix is especially relevant in the free Fibonacci case since it reveals signatures of its multifractality, as we are going to discuss now.…”

Many-body localization in the Fock space of natural orbitals

“…By numerically studying the participation ratio for a finite-size system, we identify a sharp crossover between different phases at a disorder strength close to the disorder strength at which subdiffusive behaviour [21] and the departure from Poissonian level statistics [7] sets in.We identify the crossover in the Fock basis constructed out of the natural orbitals, and repeat the analysis in the conventionally used computational basis. The natural orbitals and their corresponding occupation numbers resulting from the diagonalization of the oneparticle density matrix [22] recently gained significant attention in the field of MBL [23][24][25][26][27]. It was found [23] that the occupation numbers exhibit qualitatively different statistics in the thermal and the many-body localized phase, allowing them to be used as a probe for the MBL transition [7,28].…”