Statistical localization: From strong fragmentation to strong edge modes

By Tibor Rakovszky, Pablo Sala, R. Verresen, Michael Jason Knap, Frank Pollmann. Physical review B, 2019

149 citations recorded by the source corpus.

Certain disorder-free Hamiltonians can be non-ergodic due to a \emph{strong fragmentation} of the Hilbert space into disconnected sectors. Here, we characterize such systems by introducing the notion of `statistically localized integrals of motion' (SLIOM), whose eigenvalues label the connected components of the Hilbert space. SLIOMs are not spatially localized in the operator sense, but appear localized to sub-extensive regions when their expectation value is taken in typical states with a finite density of particles. We illustrate this general concept on several Hamiltonians, both with and without dipole conservation. Furthermore, we demonstrate that there exist perturbations which destroy these integrals of motion in the bulk of the system, while keeping them on the boundary. This results in statistically localized \emph{strong zero modes}, leading to infinitely long-lived edge magnetizations along with a thermalizing bulk, constituting the first example of such strong edge modes in a non-integrable model. We also show that in a particular example, these edge modes lead to the appearance of topological string order in a certain subset of highly excited eigenstates. Some of our suggested models can be realized in Rydberg quantum simulators.

Subfields: Atomic and Molecular Physics, and Optics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/430671ec7e5bdb18c6e477b81ca8a5d283e38bd8

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

In Statistical and Nonlinear Physics

Citations in the corpus

Fracton phases of matter (2020, background): “[114] Tibor Rakovszky, Pablo Sala, Ruben Verresen, Michael Knap, and Frank Pollmann, “Statistical localization: from strong fragmentation to strong edge modes,” (2019), arXiv:1910.”
Quantum simulation and computing with Rydberg-interacting qubits (2020, background): “Related work has highlighted the potential for Rydberg QCA for studying non-equilibrium universality and criticality 278 , simulating lattice gauge theories 279 , and non-ergodic dynamics 280,281 .”
Hilbert Space Fragmentation and Commutant Algebras (2021, methodology): “[43] along with the 1 operator form a set of generators for the full commutant algebra, similar to the SLIOMs in the t − Jz model discussed in Sec.”
Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “In systems with Hilbert space fragmentation, there are exponentially many such integrals of motion that need not be sums of local operators (105, 106).”