923 research outputs found
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 of the underlying
(integer) quantum Hall states. For 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 , 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
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
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