Alladi Ramakrishnan Hall

Many-body localisation: a tale of correlations and constraints on Fock space

Sthitadhi Roy

University of Oxford

Many-body localised phases of matter are naturally interesting as they fall outside the paradigm the conventional statistical mechanics and thermodynamics. To understand the essential features underlying the phenomenon, one can ask the question, what minimal and generic properties random many-body Hamiltonians must possess for them to stabilise a localised phase. In this talk, I will discuss two complementary answers to the question by treating the problem directly on the Fock space as any many-body Hamiltonian maps to a disordered hopping problem on the complex and correlated Fock-space graph. I will first show how strong correlations in the on-site energies on the Fock space leads to localisation; these correlations naturally arise since the exponentially large in system size number of Fock-space site energies are built out of polynomially large random numbers for local Hamiltonians. In the second part of the talk, I will discuss how constrained dynamics on the Fock space can also lead to localisation despite the Fock-space site energies being uncorrelated. The theory is rooted in analytic but approximate calculations of the propagators on the Fock space and supported by numerical results of spectral and dynamical properties of microscopic Hamiltonians.

Refs: arXiv:1911.12370 and arXiv:1912.06660