Fock-space correlations and the origins of many-body localisation

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  • Additional Information
    • Publication Date:
      2019
    • Collection:
      Condensed Matter
    • Abstract:
      We consider the problem of many-body localisation on Fock space, focussing on the essential features of the Hamiltonian which stabilise a localised phase. Any many-body Hamiltonian has a canonical representation as a disordered tight-binding model on the Fock-space graph. The underlying physics is however fundamentally different from that of conventional Anderson localisation on high-dimensional graphs because the Fock-space graph possesses non-trivial correlations. These correlations are shown to lie at the heart of whether or not a stable many-body localised phase can be sustained in the thermodynamic limit, and a theory is presented for the conditions the correlations must satisfy for a localised phase to be stable. Our analysis is rooted in a probabilistic, self-consistent mean-field theory for the local Fock-space propagator and its associated self-energy; in which the Fock-space correlations, together with the extensive nature of the connectivity of Fock-space nodes, are key ingredients. The origins of many-body localisation in typical local Hamiltonians where the correlations are strong, as well as its absence in uncorrelated random energy-like models, emerge as predictions from the same overarching theory. To test these, we consider three specific microscopic models, first establishing in each case the nature of the associated Fock-space correlations. Numerical exact diagonalisation is then used to corroborate the theoretical predictions for the occurrence or otherwise of a stable many-body localised phase; with mutual agreement found in each case.
      Comment: 25 pages, 10 figures
    • Accession Number:
      edsarx.1911.12370
  • Citations
    • ABNT:
      ROY, S.; LOGAN, D. E. Fock-space correlations and the origins of many-body localisation. [s. l.], 2019. Disponível em: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580. Acesso em: 17 jan. 2020.
    • AMA:
      Roy S, Logan DE. Fock-space correlations and the origins of many-body localisation. 2019. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580. Accessed January 17, 2020.
    • APA:
      Roy, S., & Logan, D. E. (2019). Fock-space correlations and the origins of many-body localisation. Retrieved from http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580
    • Chicago/Turabian: Author-Date:
      Roy, Sthitadhi, and David E. Logan. 2019. “Fock-Space Correlations and the Origins of Many-Body Localisation.” http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580.
    • Harvard:
      Roy, S. and Logan, D. E. (2019) ‘Fock-space correlations and the origins of many-body localisation’. Available at: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580 (Accessed: 17 January 2020).
    • Harvard: Australian:
      Roy, S & Logan, DE 2019, ‘Fock-space correlations and the origins of many-body localisation’, viewed 17 January 2020, .
    • MLA:
      Roy, Sthitadhi, and David E. Logan. Fock-Space Correlations and the Origins of Many-Body Localisation. 2019. EBSCOhost, search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580.
    • Chicago/Turabian: Humanities:
      Roy, Sthitadhi, and David E. Logan. “Fock-Space Correlations and the Origins of Many-Body Localisation,” 2019. http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580.
    • Vancouver/ICMJE:
      Roy S, Logan DE. Fock-space correlations and the origins of many-body localisation. 2019 [cited 2020 Jan 17]; Available from: http://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=edsarx&AN=edsarx.1911.12370&custid=s6224580