Abstract
We study many-body localization (MBL) in a pair-hopping model exhibiting strong fragmentation of the Hilbert space. We show that several Krylov subspaces have both ergodic statistics in the thermodynamic limit and a dimension that scales much slower than the full Hilbert space, but still exponentially. Such a property allows us to study the MBL phase transition in systems including more than $50$ spins. The different Krylov spaces that we consider show clear signatures of a many-body localization transition, both in the Kullback-Leibler divergence of the distribution of their level spacing ratio and their entanglement properties. But they also present distinct scalings with system size. Depending on the subspace, the critical disorder strength can be nearly independent of the system size or conversely show an approximately linear increase with the number of spins.
Highlights
Many-body localization (MBL) and its transition [1,2,3,4] have been the subjects of numerous studies over the recent decades
We show that our Krylov subspaces present all signs of the many-body localization (MBL) phase transitions
We introduce the notion of Krylov subspaces, vector subspaces of the symmetry-resolved Hilbert space which are stable under the application of the Hamiltonian
Summary
Many-body localization (MBL) and its transition [1,2,3,4] have been the subjects of numerous studies over the recent decades They are directly related to core physical concepts and properties of the physics of closed quantum systems, namely thermalization, transport, and the effects of disorder. Interacting systems at weak disorder thermalize and present ergodic features seemingly following the so-called strong eigenstate thermalization hypothesis (ETH) [5,6,7] It states that, at high energy, a generic closed quantum system has all its eigenstates display thermal values for all local observables. We identify sets of ergodic subspaces whose dimension grows much slower than the total Hilbert space dimension, albeit still in an exponentional fashion This gives us the possibility to investigate through exact (and full) diagonalization one-dimensional systems of unprecedented physical sizes. We carefully discuss the scaling of the vNEE with subsystem size which present unusual plateaus due to the strongly constrained nature of our model
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