Unidirectional Subsystem Symmetry in a Hole-Doped Honeycomb-Lattice Ising Magnet.

We study a model of a hole-doped collinear Ising antiferromagnet on the honeycomb lattice as a route toward realization of subsystem symmetry. We find nearly exact conservation of dipole symmetry verified both numerically with exact diagonalization on finite clusters and analytically with perturbation theory. The emergent symmetry forbids the motion of single holes-or fractons-but allows hole pairs-or dipoles-to move freely along a one-dimensional line, the antiferromagnetic direction, of the system; in the transverse direction both fractons and dipoles are completely localized. This presents a realization of a "unidirectional" subsystem symmetry. By studying interactions between dipoles, we argue that the subsystem symmetry is likely to continue to persist up to finite (but probably small) hole concentrations.

Emergent Moments and Random Singlet Physics in a Majorana Spin Liquid.

We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).

Vacancy-Induced Low-Energy States in Undoped Graphene.

We demonstrate that a nonzero concentration n_{v} of static, randomly placed vacancies in graphene leads to a density w of zero-energy quasiparticle states at the band center ε=0 within a tight-binding description with nearest-neighbor hopping t on the honeycomb lattice. We show that w remains generically nonzero in the compensated case (exactly equal number of vacancies on the two sublattices) even in the presence of hopping disorder and depends sensitively on n_{v} and correlations between vacancy positions. For low, but not-too-low, |ε|/t in this compensated case, we show that the density of states ρ(ε) exhibits a strong divergence of the form ρ_{Dyson}(ε)∼|ε|^{-1}/[log(t/|ε|)]^{(y+1)}, which crosses over to the universal low-energy asymptotic form (modified Gade-Wegner scaling) expected on symmetry grounds ρ_{GW}(ε)∼|ε|^{-1}e^{-b[log(t/|ε|)]^{2/3}} below a crossover scale ε_{c}≪t. ε_{c} is found to decrease rapidly with decreasing n_{v}, while y decreases much more slowly.