281 research outputs found
Non-Liquid Cellular States
The existence of quantum non-liquid states and fracton orders, both gapped
and gapless states, challenges our understanding of phases of entangled matter.
We generalize Wen's cellular topological states to liquid or non-liquid
cellular states. We propose a mechanism to construct more general non-abelian
states by gluing gauge-symmetry-breaking vs gauge-symmetry-extension interfaces
as extended defects in a cellular network, including defects of
higher-symmetries. Our approach also includes the anyonic particle/string
condensation and composite string (p-string)/membrane condensations. This also
shows gluing the familiar extended topological quantum field theory or
conformal field theory data via topology, geometry, and renormalization
consistency criteria (via certain modified group cohomology or cobordism theory
data) in a tensor network can still guide us to analyze the non-liquid states.
(Part of the abelian construction can be understood from the K-matrix
Chern-Simons theory approach and coupled-layer-by-junction constructions.) This
may also lead us toward a unifying framework for quantum systems of both
higher-symmetries and sub-system/sub-dimensional symmetries.Comment: 42 pages. Subtitle: Gluing Gauge-(Higher)-Symmetry-Breaking vs
-Extension Interfacial Defect
Gene-Mating Dynamic Evolution Theory II: Global stability of N-gender-mating polyploid systems
Extending the previous 2-gender dioecious diploid gene-mating evolution model
[arXiv:1410.3456], we attempt to answer "whether the Hardy-Weinberg global
stability and the exact analytic dynamical solutions can be found in the
generalized N-gender N-polyploid gene-mating system with an arbitrary number of
alleles?" For a 2-gender gene-mating evolution model, a pair of male and female
determines the trait of their offspring. Each of the pair contributes one
inherited character, the allele, to combine into the genotype of their
offspring. Hence, for an N-gender N-polypoid gene-mating model, each of N
different genders contributes one allele to combine into the genotype of their
offspring. We exactly solve the analytic solution of N-gender-mating
-alleles governing highly-nonlinear coupled differential equations in
the genotype frequency parameter space for any positive integer N and . For
an analogy, the 2-gender to N-gender gene-mating equation generalization is
analogs to the 2-body collision to the N-body collision Boltzmann equations
with continuous distribution functions of "discretized" variables instead of
"continuous" variables. We find their globally stable solution as a continuous
manifold and find no chaos. Our solution implies that the Laws of Nature, under
our assumptions, provide no obstruction and no chaos to support an N-gender
gene-mating stable system.Comment: 11 pages. A sequel to arXiv:1410.3456. v2: Refs added, comments
welcome, to appear on Theory in Biosciences - Springe
Schrodinger Fermi Liquids
A class of strongly interacting many-body fermionic systems in 2+1D
non-relativistic conformal field theory is examined via the gauge-gravity
duality correspondence. The 5D charged black hole with asymptotic Schrodinger
isometry in the bulk gravity side introduces parameters of background density
and finite particle number into the boundary field theory. We propose the
holographic dictionary, and realize a quantum phase transition of this
fermionic liquid with fixed particle number by tuning the background density
at zero temperature. On the larger side, we find the signal of
a sharp quasiparticle pole on the spectral function A(k,w), indicating a
well-defined Fermi surface. On the smaller side, we find only a hump
with no sharp peak for A(k,w), indicating the disappearance of Fermi surface.
The dynamical exponent of quasiparticle dispersion goes from being
Fermi-liquid-like scaling at larger to a non-Fermi-liquid
scaling at smaller . By comparing the structure of Green's
function with Landau Fermi liquid theory and Senthil's scaling ansatz, we
further investigate the behavior of this quantum phase transition.Comment: 26 pages, many figures of spectral functions A(k,w). v2: add a new
Fig, several clarifications, and discussions about holographic
renormalization. Program code shared via a URL link in the manuscrip
Symmetry-protected topological phases with charge and spin symmetries: response theory and dynamical gauge theory in 2D, 3D and the surface of 3D
A large class of symmetry-protected topological phases (SPT) in boson / spin
systems have been recently predicted by the group cohomology theory. In this
work, we consider SPT states at least with charge symmetry (U(1) or Z) or
spin rotation symmetry (U(1) or Z) in 2D, 3D, and the surface of 3D.
If both are U(1), we apply external electromagnetic field / `spin gauge field'
to study the charge / spin response. For the SPT examples we consider (i.e.
U(1)Z, U(1)Z,
U(1)[U(1)Z]; subscripts and are short for
charge and spin; Z and Z are time-reversal symmetry and
-rotation about , respectively), many variants of Witten effect in
the 3D SPT bulk and various versions of anomalous surface quantum Hall effect
are defined and systematically investigated. If charge or spin symmetry reduces
to Z by considering charge- or spin- condensate, instead of the
linear response approach, we gauge the charge/spin symmetry, leading to a
dynamical gauge theory with some remaining global symmetry. The 3D dynamical
gauge theory describes a symmetry-enriched topological phase (SET), i.e. a
topologically ordered state with global symmetry which admits nontrivial ground
state degeneracy depending on spatial manifold topology. For the SPT examples
we consider, the corresponding SET states are described by dynamical
topological gauge theory with topological BF term and axionic -term in
3D bulk. And the surface of SET is described by the chiral boson theory with
quantum anomaly.Comment: 23 pages, 1 figure, REVTeX; Table II and Table III for summary of
part of key result
Boundary Degeneracy of Topological Order
We introduce the concept of boundary degeneracy of topologically ordered
states on a compact orientable spatial manifold with boundaries, and emphasize
that the boundary degeneracy provides richer information than the bulk
degeneracy. Beyond the bulk-edge correspondence, we find the ground state
degeneracy of the fully gapped edge modes depends on boundary gapping
conditions. By associating different types of boundary gapping conditions as
different ways of particle or quasiparticle condensations on the boundary, we
develop an analytic theory of gapped boundaries. By Chern-Simons theory, this
allows us to derive the ground state degeneracy formula in terms of boundary
gapping conditions, which encodes more than the fusion algebra of
fractionalized quasiparticles. We apply our theory to Kitaev's toric code and
Levin-Wen string-net models. We predict that the toric code and
double-semion model (more generally, the gauge theory and the non-chiral fractional quantum Hall state at even integer )
can be numerically and experimentally distinguished, by measuring their
boundary degeneracy on an annulus or a cylinder.Comment: 15 pages, 4 figures. v3: the expanded version, add new tables for
clarification, with some new correction
Symmetry-protected many-body Aharonov-Bohm effect
It is known as a purely quantum effect that a magnetic flux affects the real
physics of a particle, such as the energy spectrum, even if the flux does not
interfere with the particle's path - the Aharonov-Bohm effect. Here we examine
an Aharonov-Bohm effect on a many-body wavefunction. Specifically, we study
this many-body effect on the gapless edge states of a bulk gapped phase
protected by a global symmetry (such as ) - the
symmetry-protected topological (SPT) states. The many-body analogue of spectral
shifts, the twisted wavefunction and the twisted boundary realization are
identified in this SPT state. An explicit lattice construction of SPT edge
states is derived, and a challenge of gauging its non-onsite symmetry is
overcome. Agreement is found in the twisted spectrum between a numerical
lattice calculation and a conformal field theory prediction.Comment: 5 pages main text + 8 pages appendix, 3 figures. v2: nearly PRB
versio
Non-Abelian String and Particle Braiding in Topological Order: Modular SL(3,Z) Representation and 3+1D Twisted Gauge Theory
String and particle braiding statistics are examined in a class of
topological orders described by discrete gauge theories with a gauge group
and a 4-cocycle twist of 's cohomology group
in 3 dimensional space and 1
dimensional time (3+1D). We establish the topological spin and the
spin-statistics relation for the closed strings, and their multi-string
braiding statistics. The 3+1D twisted gauge theory can be characterized by a
representation of a modular transformation group SL. We express
the SL generators and in
terms of the gauge group and the 4-cocycle . As we compactify one
of the spatial directions into a compact circle with a gauge flux
inserted, we can use the generators and of
an SL subgroup to study the dimensional reduction of the 3D
topological order to a direct sum of degenerate
states of 2D topological orders in different flux
sectors: .
The 2D topological orders are described by 2D gauge
theories of the group twisted by the 3-cocycles ,
dimensionally reduced from the 4-cocycle . We show that the
SL generators, and , fully
encode a particular type of three-string braiding statistics with a pattern
that is the connected sum of two Hopf links. With certain 4-cocycle twists, we
discover that, by threading a third string through two-string unlink into
three-string Hopf-link configuration, Abelian two-string braiding statistics is
promoted to non-Abelian three-string braiding statistics.Comment: 36 pages, many figures, 17 tables. v3: Accepted by Phys. Rev. B. Add
acknowledgements to Louis H. Kauffma
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