Localization from Hilbert space shattering: From theory to physical realizations

By V. Khemani, M. Hermele, R. Nandkishore. 2020

394 citations recorded by the source corpus.

We show how local constraints can globally "shatter" Hilbert space into subsectors, leading to an unexpected dynamics with features reminiscent of both many body localization and quantum scars. A crisp example of this phenomenon is provided by a "fractonic circuit" - a model of quantum circuit dynamics in one dimension constrained to conserve both charge and dipole moment. We show how the Hilbert space of the fractonic circuit dynamically fractures into disconnected emergent subsectors within a particular charge and dipole symmetry sector. A large number of the emergent subsectors, exponentially many in the size of the system, have dimension one and exhibit strictly localized quantum dynamics---even in the absence of spatial disorder and in the presence of temporal noise. Exponentially large localized subspaces can be proven to exist for any one dimensional fractonic circuit with finite spatial range, and provide a potentially new route for the robust storage of quantum information. Other emergent subsectors display non-trivial dynamics and may be constructed by embedding finite sized non-trivial blocks into the localized subspace. The shattering of a particular symmetry sector into a distribution of dynamical subsectors with varying sizes leads to the coexistence of high and low entanglement states, i.e. this provides a general mechanism for the production of quantum many body scars. We discuss the detailed pattern of fracturing and its implications. We also discuss other mechanisms for similarly shattering Hilbert space.

Subfields: Artificial Intelligence, Atomic and Molecular Physics, and Optics

View Paper: https://www.semanticscholar.org/paper/ec58b69fe44251f1b889d7a7cf35caca6b275ea0

How researchers see this paper

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

In Artificial Intelligence

1. A. Nahum
2. Matthew Fisher
3. V. Khemani
4. S. Vijay
5. Maksym Serbyn
6. Roderich Moessner
7. D. Abanin
8. Z. Papi'c

In Atomic and Molecular Physics, and Optics

1. V. Khemani
2. Matthew Fisher
3. A. Nahum
4. D. Abanin
5. Anushya Chandran
6. Maksym Serbyn
7. Roderich Moessner
8. Z. Papi'c

Citations in the corpus

• Random Quantum Circuits (2022, background): “This was found to lead to a novel form of ergodicity breaking via the “shattering” of Hilbert space into exponentially many dynamically decoupled sectors, with no dynamical path even between states with the same charge and dipole quantum numbers (192, 193) — a surprising result in light of the conve”
• Hilbert Space Fragmentation and Commutant Algebras (2021, background): “The Krylov subspaces {Kα} can have any dimension, ranging from one-dimensional “frozen” product states [27, 28] where all terms of the Hamiltonian act trivially, to ones with exponentially large dimension that can be studied in terms of a restricted effective Hamiltonian [38, 39].”
• Quantum Many-Body Scars: A Quasiparticle Perspective (2022, background): “A transparent manifestation of Hilbert space fragmentation occurs in local systems which conserve both a global U(1) charge and its dipole moment (107, 101, 102).”
• Quantum many-body scars and weak breaking of ergodicity (2020, background): “[66] Vedika Khemani, Michael Hermele, and Rahul Nandkishore,”