8,985 research outputs found
Topological Crystalline Bose Insulator in Two Dimensions via Entanglement Spectrum
Strongly correlated analogues of topological insulators have been explored in
systems with purely on-site symmetries, such as time-reversal or charge
conservation. Here, we use recently developed tensor network tools to study a
quantum state of interacting bosons which is featureless in the bulk, but
distinguished from an atomic insulator in that it exhibits entanglement which
is protected by its spatial symmetries. These properties are encoded in a model
many-body wavefunction that describes a fully symmetric insulator of bosons on
the honeycomb lattice at half filling per site. While the resulting integer
unit cell filling allows the state to bypass `no-go' theorems that trigger
fractionalization at fractional filling, it nevertheless has nontrivial
entanglement, protected by symmetry. We demonstrate this by computing the
boundary entanglement spectra, finding a gapless entanglement edge described by
a conformal field theory as well as degeneracies protected by the non-trivial
action of combined charge-conservation and spatial symmetries on the edge.
Here, the tight-binding representation of the space group symmetries plays a
particular role in allowing certain entanglement cuts that are not allowed on
other lattices of the same symmetry, suggesting that the lattice representation
can serve as an additional symmetry ingredient in protecting an interacting
topological phase. Our results extend to a related insulating state of
electrons, with short-ranged entanglement and no band insulator analogue.Comment: 18 pages, 13 figures Added additional reference
Topology by dissipation
Topological states of fermionic matter can be induced by means of a suitably
engineered dissipative dynamics. Dissipation then does not occur as a
perturbation, but rather as the main resource for many-body dynamics, providing
a targeted cooling into a topological phase starting from an arbitrary initial
state. We explore the concept of topological order in this setting, developing
and applying a general theoretical framework based on the system density matrix
which replaces the wave function appropriate for the discussion of Hamiltonian
ground-state physics. We identify key analogies and differences to the more
conventional Hamiltonian scenario. Differences mainly arise from the fact that
the properties of the spectrum and of the state of the system are not as
tightly related as in a Hamiltonian context. We provide a symmetry-based
topological classification of bulk steady states and identify the classes that
are achievable by means of quasi-local dissipative processes driving into
superfluid paired states. We also explore the fate of the bulk-edge
correspondence in the dissipative setting, and demonstrate the emergence of
Majorana edge modes. We illustrate our findings in one- and two-dimensional
models that are experimentally realistic in the context of cold atoms.Comment: 61 pages, 8 figure
On convergence of generators of equilibrium dynamics of hopping particles to generator of a birth-and-death process in continuum
We deal with two following classes of equilibrium stochastic dynamics of
infinite particle systems in continuum: hopping particles (also called Kawasaki
dynamics), i.e., a dynamics where each particle randomly hops over the space,
and birth-and-death process in continuum (or Glauber dynamics), i.e., a
dynamics where there is no motion of particles, but rather particles die, or
are born at random. We prove that a wide class of Glauber dynamics can be
derived as a scaling limit of Kawasaki dynamics. More precisely, we prove the
convergence of respective generators on a set of cylinder functions, in the
-norm with respect to the invariant measure of the processes. The latter
measure is supposed to be a Gibbs measure corresponding to a potential of pair
interaction, in the low activity-high temperature regime. Our result
generalizes that of [Finkelshtein D.L. et al., to appear in Random Oper.
Stochastic Equations], which was proved for a special Glauber (Kawasaki,
respectively) dynamics
Gravitational waves and dragging effects
Linear and rotational dragging effects of gravitational waves on local
inertial frames are studied in purely vacuum spacetimes. First the linear
dragging caused by a simple cylindrical pulse is investigated. Surprisingly
strong transversal effects of the pulse are exhibited. The angular momentum in
cylindrically symmetric spacetimes is then defined and confronted with some
results in literature. In the main part, the general procedure is developed for
studying weak gravitational waves with translational but not axial symmetry
which can carry angular momentum. After a suitable averaging the rotation of
local inertial frames due to such rotating waves can be calculated explicitly
and illustrated graphically. This is done in detail in the accompanying paper.
Finally, the rotational dragging is given for strong cylindrical waves
interacting with a rotating cosmic string with a small angular momentum.Comment: Scheduled to appear in Class. Quantum Grav. July 200
Pacifying the Fermi-liquid: battling the devious fermion signs
The fermion sign problem is studied in the path integral formalism. The
standard picture of Fermi liquids is first critically analyzed, pointing out
some of its rather peculiar properties. The insightful work of Ceperley in
constructing fermionic path integrals in terms of constrained world-lines is
then reviewed. In this representation, the minus signs associated with
Fermi-Dirac statistics are self consistently translated into a geometrical
constraint structure (the {\em nodal hypersurface}) acting on an effective
bosonic dynamics. As an illustrative example we use this formalism to study
1+1-dimensional systems, where statistics are irrelevant, and hence the sign
problem can be circumvented. In this low-dimensional example, the structure of
the nodal constraints leads to a lucid picture of the entropic interaction
essential to one-dimensional physics. Working with the path integral in
momentum space, we then show that the Fermi gas can be understood by analogy to
a Mott insulator in a harmonic trap. Going back to real space, we discuss the
topological properties of the nodal cells, and suggest a new holographic
conjecture relating Fermi liquids in higher dimensions to soft-core bosons in
one dimension. We also discuss some possible connections between mixed
Bose/Fermi systems and supersymmetry.Comment: 28 pages, 5 figure
Charting Class Territory
We extend the investigation of the recently introduced class of
4d SCFTs, by considering a large family of quiver gauge
theories within it, which we denote . These theories admit a
realization in terms of orbifolds of Type IIA configurations of
D4-branes stretched among relatively rotated sets of NS-branes. This fact
permits a systematic investigation of the full family, which exhibits new
features such as non-trivial anomalous dimensions differing from free field
values and novel ways of gluing theories. We relate these ingredients to
properties of compactification of the 6d (1,0) superconformal
theories on spheres with different kinds of punctures. We describe the
structure of dualities in this class of theories upon exchange of punctures,
including transformations that correspond to Seiberg dualities, and exploit the
computation of the superconformal index to check the invariance of the theories
under them.Comment: 44 pages, 24 figure
Gibbs states over the cone of discrete measures
We construct Gibbs perturbations of the Gamma process on \mathbbm{R}^d,
which may be used in applications to model systems of densely distributed
particles. First we propose a definition of Gibbs measures over the cone of
discrete Radon measures on \mathbbm{R}^d and then analyze conditions for
their existence. Our approach works also for general L\'evy processes instead
of Gamma measures. To this end, we need only the assumption that the first two
moments of the involved L\'evy intensity measures are finite. Also uniform
moment estimates for the Gibbs distributions are obtained, which are essential
for the construction of related diffusions. Moreover, we prove a Mecke type
characterization for the Gamma measures on the cone and an FKG inequality for
them.Comment: Keywords: Gamma process, Poisson point process, discrete Radon
measures, Gibbs states, DLR equation, Mecke identity, FK
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