Correlation function diagnostics for type-I fracton phases

Fracton phases are recent entrants to the roster of topological phases in three dimensions. They are characterized by subextensively divergent topological degeneracy and excitations that are constrained to move along lower dimensional subspaces, including the eponymous fractons that are immobile in isolation. We develop correlation function diagnostics to characterize Type I fracton phases which build on their exhibiting {\it partial deconfinement}. These are inspired by similar diagnostics from standard gauge theories and utilize a generalized gauging procedure that links fracton phases to classical Ising models with subsystem symmetries. En route, we explicitly construct the spacetime partition function for the plaquette Ising model which, under such gauging, maps into the X-cube fracton topological phase. We numerically verify our results for this model via Monte Carlo calculations

A Bionic Coulomb Phase on the Pyrochlore Lattice

A class of three dimensional classical lattice systems with macroscopic ground state degeneracies, most famously the spin ice system, are known to exhibit "Coulomb" phases wherein long wavelength correlations within the ground state manifold are described by an emergent Maxwell electrodynamics. We discuss a new example of this phenomenon-the four state Potts model on the pyrochlore lattice-where the long wavelength description now involves three independent gauge fields as we confirm via simulation. The excitations above the ground state manifold are bions, defects that are simultaneously charged under two of the three gauge fields, and exhibit an entropic interaction dictated by these charges. We also show that the distribution of flux loops shows a scaling with loop length and system size previously identified as characteristic of Coulomb phases

Topology- and symmetry-protected domain wall conduction in quantum Hall nematics

We consider domain walls in nematic quantum Hall ferromagnets predicted to form in multivalley semiconductors, recently probed by scanning tunnelling microscopy experiments on Bi(111) surfaces. We show that the domain wall properties depend sensitively on the filling factor $\nu$ of the underlying (integer) quantum Hall states. For $\nu=1$ and in the absence of impurity scattering we argue that the wall hosts a single-channel Luttinger liquid whose gaplessness is a consequence of valley and charge conservation. For $\nu=2$, it supports a two-channel Luttinger liquid, which for sufficiently strong interactions enters a symmetry-preserving thermal metal phase with a charge gap coexisting with gapless neutral intervalley modes. The domain wall physics in this state is identical to that of a bosonic topological insulator protected by $U(1)\times U(1)$ symmetry, and we provide a formal mapping between these problems. We discuss other unusual properties and experimental signatures of these `anomalous' one-dimensional systems.Comment: 11 pages, 3 figures, published versio

The Renormalization Group and the Superconducting Susceptibility of a Fermi Liquid

A free Fermi gas has, famously, a superconducting susceptibility that diverges logarithmically at zero temperature. In this paper we ask whether this is still true for a Fermi liquid and find that the answer is that it does {\it not}. From the perspective of the renormalization group for interacting fermions, the question arises because a repulsive interaction in the Cooper channel is a marginally irrelevant operator at the Fermi liquid fixed point and thus is also expected to infect various physical quantities with logarithms. Somewhat surprisingly, at least from the renormalization group viewpoint, the result for the superconducting susceptibility is that two logarithms are not better than one. In the course of this investigation we derive a Callan-Symanzik equation for the repulsive Fermi liquid using the momentum-shell renormalization group, and use it to compute the long-wavelength behavior of the superconducting correlation function in the emergent low-energy theory. We expect this technique to be of broader interest.Comment: 9 pages, 2 figure

Order and Disorder in AKLT Antiferromagnets in Three Dimensions

The models constructed by Affleck, Kennedy, Lieb, and Tasaki describe a family of quantum antiferromagnets on arbitrary lattices, where the local spin S is an integer multiple M of half the lattice coordination number. The equal time quantum correlations in their ground states may be computed as finite temperature correlations of a classical O(3) model on the same lattice, where the temperature is given by T=1/M. In dimensions d=1 and d=2 this mapping implies that all AKLT states are quantum disordered. We consider AKLT states in d=3 where the nature of the AKLT states is now a question of detail depending upon the choice of lattice and spin; for sufficiently large S some form of Neel order is almost inevitable. On the unfrustrated cubic lattice, we find that all AKLT states are ordered while for the unfrustrated diamond lattice the minimal S=2 state is disordered while all other states are ordered. On the frustrated pyrochlore lattice, we find (conservatively) that several states starting with the minimal S=3 state are disordered. The disordered AKLT models we report here are a significant addition to the catalog of magnetic Hamiltonians in d=3 with ground states known to lack order on account of strong quantum fluctuations.Comment: 7 pages, 2 figure

Accidental SUSY: Enhanced Bulk Supersymmetry from Brane Back-reaction

We compute how bulk loops renormalize both bulk and brane effective interactions for codimension-two branes in 6D gauged chiral supergravity, as functions of the brane tension and brane-localized flux. We do so by explicitly integrating out hyper- and gauge-multiplets in 6D gauged chiral supergravity compactified to 4D on a flux-stabilized 2D rugby-ball geometry, specializing the results of a companion paper, arXiv:1210.3753, to the supersymmetric case. While the brane back-reaction generically breaks supersymmetry, we show that the bulk supersymmetry can be preserved if the amount of brane-localized flux is related in a specific BPS-like way to the brane tension, and verify that the loop corrections to the brane curvature vanish in this special case. In these systems it is the brane-bulk couplings that fix the size of the extra dimensions, and we show that in some circumstances the bulk geometry dynamically adjusts to ensure the supersymmetric BPS-like condition is automatically satisfied. We investigate the robustness of this residual supersymmetry to loops of non-supersymmetric matter on the branes, and show that supersymmetry-breaking effects can enter only through effective brane-bulk interactions involving at least two derivatives. We comment on the relevance of this calculation to proposed applications of codimension-two 6D models to solutions of the hierarchy and cosmological constant problems.Comment: 49 pages + appendices. This is the final version to appear in JHE