Hilbert Space Fragmentation and Gauge Symmetry
Thea Budde, Marina Kristć Marinković, Joao C. Pinto Barros
TLDR
This paper reveals an emergent gauge symmetry in a fragmented spin chain, enabling exact quantum simulation of a gauge theory.
Key contributions
- Identifies an emergent gauge symmetry in a fragmented S=1 dipole-conserving spin chain.
- Shows these non-invertible symmetries label an exponential number of dynamically disconnected sectors.
- Proposes simulating this non-gauge-invariant Hamiltonian for exact quantum simulation of a gauge theory.
Why it matters
This paper offers a novel approach to quantum simulate gauge theories by leveraging emergent symmetries in fragmented systems. It provides a deeper understanding of Hilbert space fragmentation and its connection to gauge symmetries, crucial for future quantum computing.
Original Abstract
The Hamiltonian formulation of lattice gauge theories plays a central role in quantum simulations of gauge theories, and understanding their spectrum and other properties is expected to become crucial in the upcoming years. The relevant Hamiltonians in this framework possess local symmetry at each lattice site and may exhibit higher-form symmetries. There are then an exponentially large number of dynamically disconnected symmetry sectors, most of which are not translation-invariant. An exponential number of dynamically disconnected sectors, i.e., Hilbert space fragmentation, can also occur in systems in which no such symmetries have been identified. In this contribution, we describe an emergent gauge symmetry that is valid only in a subset of sectors of the fragmented $S=1$ dipole-conserving spin chain. These non-invertible symmetries can label exponentially many of the model's sectors. Simulating this Hamiltonian, which is not gauge-invariant, yields an exact quantum simulation of a gauge theory.
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