Challenges to observation of many-body localization

I will discuss numerical attempts to pin-point a many-body localization (MBL) transition in 1D interacting quantum spin-1/2 chains, highlighting the role of finite size and finite time effects. I will briefly introduce a polynomially filtered exact diagonalization method (POLFED) of computing eigenvectors of large sparse matrices at arbitrary energies and discuss its utility in studies of MBL transition as well as other problems of non-equilibrium many-body physics. I will demonstrate the potential of POLFED by examining finite size effects at MBL transition in 1D disordered Heisenberg spin-1/2 chain. Introducing two system size dependent disorder strengths that allow to distinguish ergodic, critical and MBL regimes, I will discuss possible scenarios regarding the MBL transition along with estimates for the critical disorder strength. Then, I will consider MBL in highly constrained one-dimensional quantum spin chains. The increase of Hilbert space dimension with system size in constrained systems is slower than in the usually considered spin-1/2 chains which allows to investigate considerably larger system sizes. Surprisingly, extensive numerical simulations show that the constrained spin chains remain ergodic even in presence strong disorder when large system size limit is considered. This can be understood as a result of an interplay between disorder and constraints that introduces long-range interactions in an effective representation of the system. I will argue that, in contrast to the aforementioned examples, finite size effects at MBL transition in disordered Floquet models are less severe allowing for a more convincing numerical demonstration of stability of MBL in the large system size limit. Finally, I will focus on time dynamics of 1D disordered Heisenberg spin-1/2 chain considering a regime of large system sizes and a long time evolution. Numerical simulations show that the regimeof decay of an imbalance (a quantity often employed in the experimental studies of MBL) persists to disorder strengths exceeding by at least a factor of 2 the current estimates of the critical disorder strength for MBL in the 1D disordered Heisenberg spin-1/2 chain. Even though time evolution is investigated up to few thousands tunneling times, there are no signs of the saturation of imbalance that would provide a smoking gun evidence of MBL. This identifies challenges in an unequivocal experimental observation of the phenomenon of MBL.

[1] P. Sierant, J. Zakrzewski, arXiv:2109.13608

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[5] P. Sierant, M. Lewenstein, A. Scardiccio, J. Zak