One-particle density matrix occupation spectrum of many-body localized states after a global quench

Lezama, Talía L. M.; Bera, Soumya; Schomerus, Henning; Heidrich-Meisner, Fabian; Bardarson, Jens H.

doi:10.1103/physrevb.96.060202

Cited by 36 publications

(33 citation statements)

References 60 publications

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“…The properties of OPDMs in systems of one-dimensional hardcore bosons on a lattice and in the presence of disorder were studied in [48,49]. Note that the occupation-spectrum discontinuity is smeared out in extensive superpositions of many-body eigenstates even in the MBL phase, while the distribution as such remains highly nonthermal (see the example of a quantum quench discussed in [50]). …”

Section: Model and Observables And Numerical Methodsmentioning

confidence: 99%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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We study the finite-energy density phase diagram of spinless fermions with attractive interactions in one dimension in the presence of uncorrelated diagonal disorder. Unlike the case of repulsive interactions, a delocalized Luttinger-liquid phase persists at weak disorder in the ground state, which is a well-known result. We revisit the ground-state phase diagram and show that the recently introduced occupation-spectrum discontinuity computed from the eigenspectrum of the one-particle density matrix is noticeably smaller in the Luttinger liquid compared to the localized regions. Moreover, we use the functional renormalization group scheme to study the finite-size dependence of the conductance, which also resolves the existence of the Luttinger liquid and is computationally cheap. Our main results concern the finite-energy density case. Using exact diagonalization and by computing various established measures of the many-body localization-delocalization transition, we argue that the zero-temperature Luttinger liquid smoothly evolves into a finite-energy density ergodic phase without any intermediate phase transition.

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Section: Model and Observables And Numerical Methodsmentioning

confidence: 99%

Many-body localization of spinless fermions with attractive interactions in one dimension

et al. 2018

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“…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].…”

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confidence: 99%

Many-body localization in the Fock space of natural orbitals

2018

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We study the eigenstates of a paradigmatic model of many-body localization in the Fock basis constructed out of the natural orbitals. By numerically studying the participation ratio, we identify a sharp crossover between different phases at a disorder strength close to the disorder strength at which subdiffusive behaviour sets in, significantly below the many-body localization transition. We repeat the analysis in the conventionally used computational basis, and show that many-body localized eigenstates are much stronger localized in the Fock basis constructed out of the natural orbitals than in the computational basis. arXiv:1712.06892v3 [cond-mat.dis-nn] 30 May 2018 SciPost Physics Submission 3]. Inspired by the seminal work of Basko, Aleiner and Althshuler [4], a large number of investigations has revealed various intriguing properties of the many-body localized phase, among them the persistance up to infinite temperature [5], the separation from the thermal phase by a phase transition [6,7], and the growth of entanglement in the absence of transport [8,9]. The interest for MBL is mainly driven by the notion that many-body localized systems violate the fundamental assumption of statistical mechanics that a non-integrable system can serve as its own heath bath, a phenomenon that has been near-rigorously proven to exist only recently [10].Over the last few years, it has become clear [11] that not only the many-body localized phase, but also the thermal phase in the vicinity of the MBL transition ('critical phase') displays remarkable properties [12], such as subdiffusion [13,14], subthermal entanglement scaling [15], bimodality of the entanglement entropy distribution [16,17], and the violation of the eigenstate thermalization hypothesis [18,19]. The latter can be deduced from the violation of the Berry conjecture [20], roughly stating that the eigenstates of thermal systems are spread out over the full Hilbert space in any local basis. In this work, we study the spreading of eigenstates over the Hilbert space for a paradigmatic model of many-body localization. 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]. Based on these statistics, we argue that the scope can be naturally broadened by studying MBL in the Fock...

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“…Finally, it should be noted that we do not expect to observe the exponentially vanishing gap along with the smearing effects suggested in Ref. 84. There, these behaviors are justified by considering the spectrum of the OPDM in the level of each individual random realization.…”

Section: Appendix B: Derivation Of the Opdm In Terms Of The Matter Fimentioning

confidence: 74%

“…In order to characterize the imprints of primary fermionic patterns on the emergent SBL, we turn to investigate the instantaneous and asymptotic behaviors of one-particle density matrix (OPDM) spectrum 25,26,84 ,…”

Section: Domain Wall Dynamicsmentioning

confidence: 99%

Emergent statistical bubble localization in aZ2lattice gauge theory

2019

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We introduce a clean cluster spin chain coupled to fully interacting spinless fermions, forming an unconstrained Z2 lattice gauge theory (LGT) which possesses dynamical proximity effect controlled by the entanglement structure of the initial state. We expand the machinery of interaction-driven localization to the realm of LGTs such that for any starting product state, the matter fields exhibits emergent statistical bubble localization, which is driven solely by the cluster interaction, having no topologically trivial non-interacting counterpart, and thus is of a pure dynamical many-body effect. In this vein, our proposed setting provides possibly the minimal model dropping all the conventional assumptions regarding the existence of many-body localization. Through projective measurement of local constituting species, we also identify the coexistence of the disentangled nonergodic matter and thermalized gauge degrees of freedom which stands completely beyond the standard established phenomenology of quantum disentangled liquids. As a by product of self-localization of the proximate fermions, the spin subsystem hosts the long-lived topological edge zero modes, which are dynamically decoupled from the thermalized background Z2 charges of the bulk, and hence remains cold at arbitrary highenergy density. This provides a convenient platform for strong protection of the quantum bits of information which are embedded at the edges of completely ergodic sub-system; the phenomenon that in the absence of such proximity-induced self-localization could, at best, come about with a pre-thermal manner in translational invariant systems. Finally, by breaking local Z2 symmetry of the model, we argue that such admixture of particles no longer remains disentangled and the ergodic gauge degrees of freedom act as a "small bath" coupled to the localized components. arXiv:1810.08434v2 [cond-mat.str-el]

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One-particle density matrix occupation spectrum of many-body localized states after a global quench

Cited by 36 publications

References 60 publications

Many-body localization of spinless fermions with attractive interactions in one dimension

Many-body localization of spinless fermions with attractive interactions in one dimension

Many-body localization in the Fock space of natural orbitals

Emergent statistical bubble localization in aZ2lattice gauge theory

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