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Ergodicity Breaking Arising from Hilbert Space Fragmentation in Dipole-Conserving Hamiltonians
We show that the combination of charge and dipole conservation---characteristic of fracton systems---leads to an extensive fragmentation of the Hilbert space, which in turn can lead to a breakdown of
One-dimensional symmetry protected topological phases and their transitions
We present a unified perspective on symmetry protected topological (SPT) phases in one dimension and address the open question of what characterizes their phase transitions. In the first part of this
Gapless Topological Phases and Symmetry-Enriched Quantum Criticality
We introduce topological invariants for critical bosonic and fermionic chains. More generally, the symmetry properties of operators in the low-energy conformal field theory (CFT) provide discrete
Confined Phases of One-Dimensional Spinless Fermions Coupled to Z_{2} Gauge Theory.
TLDR
This work investigates a quantum many-body lattice system of one-dimensional spinless fermions interacting with a dynamical Z_{2} gauge field and develops an exactly solvable effective theory of bosonic dimers with emergent constraints at strong coupling.
Prediction of Toric Code Topological Order from Rydberg Blockade
The physical realization of $\mathbb Z_2$ topological order as encountered in the paradigmatic toric code has proven to be an elusive goal. We show that this phase of matter can be created in a
Intrinsically gapless topological phases
Topology in quantum matter is typically associated with gapped phases. For example, in symmetry protected topological (SPT) phases, the bulk energy gap localizes edge modes near the boundary. In this
Topology and edge states survive quantum criticality between topological insulators
It is often thought that emergent phenomena in topological phases of matter are destroyed when tuning to a critical point. In particular, topologically protected edge states supposedly delocalize
Dynamics of the Kitaev-Heisenberg Model.
TLDR
These results provide an example of a natural path for proximate spin liquid features to arise at high energies above a conventionally ordered state, as the diffuse remnants of spin-wave bands intersect to yield a broad peak at the Brillouin zone center.
Statistical localization: From strong fragmentation to strong edge modes
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
Topology and Edge Modes in Quantum Critical Chains.
TLDR
It is shown that topology can protect exponentially localized, zero energy edge modes at critical points between one-dimensional symmetry-protected topological phases and can be stable in the presence of interactions and disorder.
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