Fractonlike phases from subsystem symmetries

Gauge symmetries in geometric phases

The analysis of geometric phases is briefly reviewed by emphasizing various gauge symmetries involved. The analysis of geometric phases associated with level crossing is reduced to the familiar diagonalization of the Hamiltonian in the second quantized formulation. A hidden local gauge symmetry becomes explicit in this formulation and specifies physical observables; the choice of a basis set wh...

Geometric phases , gauge symmetries and ray representation

The conventional formulation of the non-adiabatic (Aharonov-Anandan) phase is based on the equivalence class {eiα(t)ψ(t, ~x)} which is not a symmetry of the Schrödinger equation. This equivalence class when understood as defining generalized rays in the Hilbert space is not generally consistent with the superposition principle in interference and polarization phenomena. The hidden local gauge s...

Topological phases with generalized global symmetries

We present simple lattice realizations of symmetry-protected topological phases with q-form global symmetries where charged excitations have q spatial dimensions. Specifically, we construct d space-dimensional models supported on a (d + 1)-colorable graph by using a family of unitary phase gates, known as multiqubit control-Z gates in quantum information community. In our construction, charged ...

Geometrical phases and symmetries in dissipative systems.

Identification of phases, symmetries and defects through local crystallography

Advances in electron and probe microscopies allow 10 pm or higher precision in measurements of atomic positions. This level of fidelity is sufficient to correlate the length (and hence energy) of bonds, as well as bond angles to functional properties of materials. Traditionally, this relied on mapping locally measured parameters to macroscopic variables, for example, average unit cell. This des...