Many-body localization in a fragmented Hilbert space

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 manybody 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.

Glassy dynamics of the one-dimensional Mott insulator excited by a strong terahertz pulse

“…p=3 = 0, where P = k kn k is the dipole moment. Such conservation imposes kinetic constraints leading to the emergent fragmentation of the Hilbert space into exponentially many disconnected subspaces [41][42][43][44][45][46][47][48][49][50]. A representative system with restricted mobility is a fracton system [57][58][59][60][61][62][63][64], which is characterized by dipole-moment conservation [88] localizing charge excitations topologically.…”

“…In contrast, we find that strong electric fields inducing the Zener breakdown [40] strongly suppress σ D , even if we introduce a large number of carriers. We consider that the emergence of the Hilbert-space fragmentation [41][42][43][44][45][46][47][48][49][50] due to high fields leads to glassy dynamics [51][52][53][54][55][56] as seen in fracton systems [57][58][59][60][61][62][63][64].…”

Hilbert Space Fragmentation and Commutant Algebras

“…Strongly fragmented systems, on the other hand, do not have a dominant Krylov subspace, and hence violate weak ETH as well. Nevertheless, signatures of ETH within sufficiently large Krylov subspaces K α (referred to as Krylov-restricted thermalization [11,38]) were found in models exhibiting both strong and weak Hilbert space fragmentation [38,40,41], provided the Hamiltonian restricted to the studied Krylov subspace is non-integrable and not many-body localized [42]. Several examples of Hilbert space fragmentation that do not involve dipole-conserving models have been found in Refs.…”

Robustness of Stark many-body localization in the $J_1$-$J_2$ Heisenberg model

“…It was shown that in the strongly localized regime the domain walls (if at low density) do not melt as time evolves, a remarkable signature of quantum localization. The lack of thermalization of certain initial states in these system has been associated to the concept fragmentation of Hilbert space [27][28][29][30]. Under this concept, certain initial states avoid some region of the Hilbert states under time evolution, thus preventing the system from thermalization.…”