643 research outputs found
Towards classification of Fracton phases: the multipole algebra
We present an effective field theory approach to the Fracton phases. The
approach is based the notion of a multipole algebra. It is an extension of
space(-time) symmetries of a charge-conserving matter that includes global
symmetries responsible for the conservation of various components of the
multipole moments of the charge density. We explain how to construct field
theories invariant under the action of the algebra. These field theories
generally break rotational invariance and exhibit anisotropic scaling. We
further explain how to partially gauge the multipole algebra. Such gauging
makes the symmetries responsible for the conservation of multipole moments
local, while keeping rotation and translations symmetries global. It is shown
that upon such gauging one finds the symmetric tensor gauge theories, as well
as the generalized gauge theories discussed recently in the literature. The
outcome of the gauging procedure depends on the choice of the multipole
algebra. In particular, we show how to construct an effective theory for the
version of the Haah code based on the principles of symmetry and provide
a two dimensional example with operators supported on a Sierpinski triangle. We
show that upon condensation of charged excitations Fracton phases of both types
as well as various SPTs emerge. Finally, the relation between the present
approach and the formalism based on polynomials over finite fields is
discussed.Comment: 17 pages, 8 figure
Bimetric Theory of Fractional Quantum Hall States
We present a bimetric low-energy effective theory of fractional quantum Hall
(FQH) states that describes the topological properties and a gapped collective
excitation, known as Girvin-Macdonald-Platzman (GMP) mode. The theory consist
of a topological Chern-Simons action, coupled to a symmetric rank two tensor,
and an action \`a la bimetric gravity, describing the gapped dynamics of the
spin- GMP mode. The theory is formulated in curved ambient space and is
spatially covariant, which allows to restrict the form of the effective action
and the values of phenomenological coefficients. Using the bimetric theory we
calculate the projected static structure factor up to the order in the
momentum expansion. To provide further support for the theory, we derive the
long wave limit of the GMP algebra, the dispersion relation of the GMP mode,
and the Hall viscosity of FQH states. We also comment on the possible
applications to fractional Chern insulators, where closely related structures
arise. Finally, it is shown that the familiar FQH observables acquire a curious
geometric interpretation within the bimetric formalism.Comment: 14 pages, v2: Acknowledgments updated, v3: A few presentation
improvements, Published versio
Entanglement Entropy in 2D Non-abelian Pure Gauge Theory
We compute the Entanglement Entropy (EE) of a bipartition in 2D pure
non-abelian gauge theory. We obtain a general expression for EE on an
arbitrary Riemann surface. We find that due to area-preserving diffeomorphism
symmetry EE does not depend on the size of the subsystem, but only on the
number of disjoint intervals defining the bipartition. In the strong coupling
limit on a torus we find that the scaling of the EE at small temperature is
given by ,
which is similar to the scaling for the matter fields recently derived in
literature. In the large limit we compute all of the Renyi entropies and
identify the Douglas-Kazakov phase transition.Comment: 6 page
- β¦