Quantum Fragmentation

TL;DR

This paper presents a systematic method to construct and analyze quantum Hamiltonians with fragmented Hilbert spaces, highlighting their unique entanglement structures and potential experimental verification.

Contribution

It introduces a protocol to generate quantum fragmented models from classical ones using Rokhsar-Kivelson construction, applicable even to non-fragmented inputs like Ising models.

Findings

Krylov sectors can be labeled and counted in 1D.

Quantum fragmentation has a distinct entanglement structure.

Construction extended to higher dimensions with explicit examples.

Abstract

We introduce a systematic protocol for constructing quantum Hilbert-space-fragmented Hamiltonians, whose Krylov-sector structure, unlike in classically fragmented models, can be fully resolved only in an entangled basis. The protocol takes as input a classically fragmented model and uses a Rokhsar-Kivelson type construction to promote it to a quantum fragmented model. Notably, the procedure also works with non-fragmented inputs (such as Ising models). We explain how the Krylov sectors of the resulting quantum fragmented model may be labeled and counted in one dimension, and outline experimentally accessible verification of quantum fragmentation, assuming the ability to prepare specific initial states and perform tomography on reduced density matrices. We further analyze the entanglement structure of the entangled basis underlying quantum fragmentation, which sharply distinguishes it from both classical fragmentation and the trivial "fragmentation" of generic Hamiltonians in their eigenbasis. We also extend the construction to higher dimensions, with an explicit proof of principle example in two dimensions. We expect these results to open a new route to the systematic exploration of quantum fragmentation.