389 research outputs found
Gaplessness protected by bulk-edge correspondence
After almost half a century of Laughlin's celebrated study of the
wavefunctions of integer and fractional quantum Hall effects, there have still
existed difficulties to prove whether the given wavefunction can describe
gapped phase or not in general. In this work, we show the FQH states
constructed from nonunitary conformal field theories (CFTs), such as Gaffiinian
and Haldane-Rezayi states have a difficulty gapping out under preserving
bulk-edge correspondence in the cylinder geometry. Contrary to the common
understandings of the condensed matter communities, the gaplessness for these
systems seems not to come from the negative conformal dimensions of nonunitary
CFTs in this setting at least directly. We propose the difficulty is coming
from the mismatch of monodromy charge and simple charge of underlying CFTs,
known as Galois shuffle. In the Haldane-Rezayi state, this corresponds to the
conjugate operation of the Neveu-Schwartz and Ramond sectors for unitary Weyl
fermion and symplectic fermion. In the Gaffinian state, besides Galois shuffle
structure, the anomalous conformal dimension of the simple current
results in the cylinder partition functions outside of the existing local
quantum field theory. This indicates the existing gapless fractional quantum
Hall states have similar nonlocal structures, similar to deconfined quantum
criticality. Our work opens up a new paradigm which gives a criterion to
predict whether the candidate of topological ordered states are gapped or not,
and local or nonlocal, by revisiting the problem of anomaly and the duality of
symplectic and Dirac fermion
Composing parafermions: a construction of fractional quantum Hall systems and a modern understanding of confinement and duality
In this work, we propose a modern view of the integer spin simple currents
which have played a central role in discrete torsion. We reintroduce them as
nonanomalous composite particles constructed from parafermionic field
theories. These composite particles have an analogy with the Cooper pair in the
Bardeen-Cooper-Schrieffer theory and can be interpreted as a typical example of
anyon condensation. Based on these anomaly free composite particles, we
propose a systematic construction of the cylinder partition function of
fractional quantum Hall effects (FQHEs). One can expect realizations of a class
of general topological ordered systems by breaking the bulk-edge correspondence
of the bosonic parts of these FQH models. We also give a brief overview of
various phenomena in contemporary condensed matter physics, such as
Haldane conjecture, general gapless and gapped topological order with respect
to the quantum anomaly of simple currents and bulk and boundary renormalization
group flow. Moreover, we point out an analogy with the FQHE and the 2d quantum
gravity coupled to matter, and propose a generalization of
supersymmetry known as "fractional supersymmetry" in the composite
parafermionic theory and study its analogy with quark confinement. Our analysis
gives a simple but general understanding of the contemporary physics of
topological phases in the form of the partition functions derived from the
operator formalism
Protected edge modes based on the bulk and boundary renormalization group: A relationship between duality and generalized symmetry
We propose a theoretical formulation of protected edge modes in the language
of quantum field theories based on the contemporary understanding of the
renormalization group. We use bulk and boundary renormalization arguments which
have never captured enough attention in condensed matter physics and related
fields. We revisit various exotic bulk and boundary phenomena in contemporary
physics, and one can see the conciseness of our formulations. Moreover, in the
systems with open boundaries in general space-time dimensions, we also analyze
their implications under general duality implemented by the shift of defects
corresponding to generalized symmetries, including higher-form, non-invertible
symmetries, in principle. Our formulation opens up a new paradigm to explore
the systems with protected edge modes in the established language of the
renormalization group.Comment: Typos are corrected, references are adde
Fermionic fractional quantum Hall states: A modern approach of systems with bulk-boundary correspondence
In contemporary physics, especially in condensed matter physics, fermionic
topological order and its protected edge modes are one of the most important
objects. In this work, we propose a systematic construction of the cylinder
partition corresponding to the fermionic or electric fractional quantum Hall
effect (FQHE) and a general mechanism to obtain the candidates of protected
edge modes. In our construction, when the underlying conformal field theory has
the duality defect corresponding to the fermionic electric
particle, we show that the FQH partition function has a fermionic T duality.
This duality is analogous to (hopefully the same as) the dualities in the dual
resonance models, typically known as supersymmetry and gives a renormalization
group (RG) theoretic understanding of topological phases. We also introduce a
modern understanding of the bulk topological degeneracies and the topological
entanglement entropy. This understanding is based on the traditional tunnel
problem and the recent conjecture of correspondence between bulk
renormalization group flow and boundary conformal field theory. Our formalism
gives an intuitive understanding of modern physics of topological ordered
systems in the traditional language of RG and fermionization
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