arXiv subjects
Publications and source records attributed to Jose Garre Rubio.
If a local Hamiltonian eigenstate is mapped to another state by local operators commuting with the Hamiltonian terms, the latter is also an eigenstate. This basic observation implies a no-go result for both being a unique ground state and having a degeneracy protected against local perturbations.
We introduce a modified 2D toric code Hamiltonian that exhibits explicit anyon confinement along a single spatial direction. By bounding the motion of these confined anyons, we obtain dipolar excitations with restricted mobility. We analyze the resulting logical operators, whose existence depends on the system size, as well as the structure of gapped boundaries and a tensor network representation of the ground state. Furthermore, when confinement is enforced in both directions, fractal-like excitations emerge, resulting in unpaired logical operators. We extend our construction to 3D models, such as the surface code and the X-cube model, leading to novel dipole-loop and dipole-planon excitations that arise from bounding confined excitations. These modifications are implemented through group cohomological twistings--projective representations of finite groups--with most examples based on Z2xZ2.
We study the statistics of domain wall excitations in quantum spin chains. We focus on systems with finite symmetry groups represented by matrix product unitaries (MPUs), i.e. finite depth quantum circuits. Such symmetries can be anomalous, in which case gapped phases which they support must break the symmetry. The lowest lying excitations of those systems are thus domain wall excitations. We investigate the behavior of these domain walls under exchange, and find that they can exhibit non-trivial exchange statistics. This statistics is completely determined by the anomaly of the symmetry, and we provide a direct relation between the known classification of MPU symmetry actions on ground states and the domain wall statistics. Already for the simplest case of a $\mathbb Z_2$ symmetry, we obtain that the presence of an anomalous MPU symmetry gives rise to domain wall excitations which behave neither as bosons nor as fermions, but rather exhibit fractional statistics. Finally, we show that the exchange statistics of domain walls is a physically accessible quantity, by devising explicit measurement operators through which it can be determined.
We consider the anyonic spin systems with a global symmetry, the so-called symmetry enriched topological (SET) phases. We introduce the phase characterizing the symmetry fractionalization of the anyons. Our assumptions on how the global symmetry acts prevents anyon permutation effects.
Gauging introduces gauge fields in order to localize an existing global symmetry, resulting in a dual global symmetry on the gauge fields that can be gauged again. By iterating the gauging process on spin chains with Abelian group symmetries and arranging the gauge fields in a 2D lattice, the local symmetries become the stabilizer of the $XZZX$-code for any Abelian group. By twisting the gauging map we obtain new codes that explicitly confine anyons, which violate an odd number of plaquette terms and whose fusion results in mobile dipole excitations. Our construction naturally realizes any gapped boundary by taking different quantum phases of the initial (1+1)D globally symmetric system. Our method establishes a new route to obtain higher dimensional topological codes from lower ones, to identify their gapped boundaries and their tensor network representations.
We consider the classification problem of quantum spin chains invariant under local decomposable group actions, covering matrix product unitaries (MPUs), using an operator algebraic approach. We focus on finite group symmetries hosting both symmetric and symmetry broken phases. The local-decomposable group actions we consider have a 3-cocycle class of the symmetry group associated to them. We derive invariants for our classification that naturally cover one-dimensional symmetry protected topological (SPT) phases. We prove that these invariants coincide with the ones of [J. Garre Rubio et al, Quantum 7, 927 (2023)] using matrix product states (MPSs) techniques, by explicitly working out the GNS representation of MPSs and MPUs, resulting in a useful dictionary between both approaches that could be of independent interest.