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

Lin, Sheng-Hsuan; Sbierski, Björn; Dorfner, Florian; Karrasch, Christoph; Heidrich-Meisner, Fabian

doi:10.21468/scipostphys.4.1.002

Cited by 31 publications

(23 citation statements)

References 91 publications

(219 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…On the other hand, IRC at δ = 0 was found [34] unstable towards localization and topological ordering for g > 0 (repulsive interactions), while attraction is also relevant but could apparently drive IRC to a different (Ising) criticality [34]. Anyhow, in our case at high energy the interaction sign is expected to be irrelevant, as confirmed for the XXZ chain [37], such that we work with g > 0, assuming similar results for attractive couplings. We then take box distributions for both random couplings J i and fields h i , P J/h = Box[0 , W J/h ] being uniform between 0 and W J/h , with W J = W −1 h = W so that the control parameter is δ = ln J − ln h = 2 ln W .…”

supporting

confidence: 75%

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

Laflorencie,

Lemarié,

Macé

2022

Preprint

View full text Add to dashboard Cite

supporting

confidence: 75%

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

Laflorencie,

Lemarié,

Macé

2022

Preprint

View full text Add to dashboard Cite

“…with {n i } sorted in descending order can be used as a probe for the MBL transition, being given by ∆n ≈ 1 in the many-body localized and ∆n significantly smaller than 1 in the thermal phase [23,25]. This observation initiated studies on various aspects of OPDMs [24][25][26][27]30] of many-body localized eigenstates. The characterization ∆n ≈ 1 is reminiscent of Anderson localization, where states are characterized by ∆n = 1.…”

Section: The Modelmentioning

confidence: 99%

Many-body localization in the Fock space of natural orbitals

2018

View full text Add to dashboard Cite

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...

show abstract

“…In particular, it is interesting to note that in the OPDM basis, the Fock-space IPR is well approximated by a 4 0 implying that when a finite jump occurs in D q it is also expected to occur in the local purity. where in the first line, we have rewritten the Fock representation {n j } in a different notation (45), which is more convenient here. The last identity signifies that the the coefficients a [α] in the opdm basis can be computed from a {nj } or from a [j] , using the relation:…”

Section: Discussionmentioning

confidence: 99%

“…In a more generic situation in the MBL phase they are assumed to be still good approximations of the LIOMs. The OPDM approach has been employed in the study of MBL in various models [44][45][46][47][48][49] and in the study of out-ofequilibrium phenomena. 50,51 The eigenenergies ρ α of the OPDM (occupation spectrum) shows a characteristic gapped distribution in the MBL phase, reminiscent of a renormalized Fermi distribution in Fermi liquids.…”

Section: Introductionmentioning

confidence: 99%

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

Orito,

Imura

2021

Preprint

View full text Add to dashboard Cite

Many-body localization (MBL) is well characterized in Fock space. To quantify the degree of this Fock space localization, the multifractal dimension Dq is employed; it has been claimed that Dq shows a jump from the delocalized value Dq = 1 in the ETH phase (ETH: eigenstate thermalization hypothesis) to a smaller value 0 < Dq < 1 at the ETH-MBL transition, yet exhibiting a conspicuous discrepancy from the fully localized value Dq = 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 Dq and other indices quantifying the Fock space localization, such as the local purity S, which is derived from the occupation spectrum {nα} (eigenvalues of the OPDM). We highlight the statistical distribution of Hamming distance xµν occurring in the pair-wise coefficients |aµ| 2 |aν | 2 in S, and compare this with a related quantity reported in the literature.

show abstract

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

Cited by 31 publications

References 91 publications

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

Topological order in random interacting Ising-Majorana chains stabilized by many-body localization

Many-body localization in the Fock space of natural orbitals

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

Contact Info

Product

Resources

About