Physics (Internal)

Local constraints can globally shatter Hilbert space

This event is part of the Biophysics/Condensed Matter Seminar Series.

The dynamics of constrained systems is a subject of much recent interest. In this talk, I will 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. I will 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. I will prove that exponentially large localized subspaces exist for any one dimensional fractonic circuit with finite spatial range, providing a potentially new route for the robust storage of quantum information. 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. I will discuss the detailed pattern of fracturing and its implications.