56 research outputs found
Renormalization group flows for the second parafermionic field theory for even
Extending the results obtained in the case odd, the effect of slightly
relevant perturbations of the second parafermionic field theory with the
symmetry , for even, are studied. The renormalization group
equations, and their infra red fixed points exhibit the same structure in both
cases. In addition to the standard flow from the -th to the -th
model, another fixed point corresponding to the -th model is found
Entanglement entropies of minimal models from null-vectors
We present a new method to compute R\'enyi entropies in one-dimensional
critical systems. The null-vector conditions on the twist fields in the cyclic
orbifold allow us to derive a differential equation for their correlation
functions. The latter are then determined by standard bootstrap techniques. We
apply this method to the calculation of various R\'enyi entropies in the
non-unitary Yang-Lee model.Comment: 43 pages, 7 figure
Variational Ansatz for an Abelian to non-Abelian Topological Phase Transition in Bilayers
We propose a one-parameter variational ansatz to describe the
tunneling-driven Abelian to non-Abelian transition in bosonic
fractional quantum Hall bilayers. This ansatz, based on exact matrix product
states, captures the low-energy physics all along the transition and allows to
probe its characteristic features. The transition is continuous, characterized
by the decoupling of antisymmetric degrees of freedom. We futhermore determine
the tunneling strength above which non-Abelian statistics should be observed
experimentally. Finally, we propose to engineer the inter-layer tunneling to
create an interface trapping a neutral chiral Majorana. We microscopically
characterize such an interface using a slightly modified model wavefunction.Comment: 5 pages, 4 Figures and Supplementary Materials. Comments are welcome
Adiabatic Deformations of Quantum Hall Droplets
We consider area-preserving deformations of the plane, acting on electronic
wavefunctions through "quantomorphisms" that change both the underlying metric
and the confining potential. We show that adiabatic sequences of such
transformations produce Berry phases that can be written in closed form in
terms of the many-body current and density, even in the presence of
interactions. For a large class of deformations that generalize squeezing and
shearing, the leading piece of the phase is a super-extensive Aharonov-Bohm
term (proportional to N for N electrons) in the thermodynamic limit. Its
gauge-invariant subleading partner only measures the current, whose dominant
contribution to the phase stems from a jump at the edge in the limit of strong
magnetic fields. This results in a finite Berry curvature per unit area,
reminiscent of the Hall viscosity. We show that the latter is in fact included
in our formalism, bypassing its standard derivation on a torus and suggesting
realistic experimental setups for its observation in quantum simulators.Comment: 40 pages, 10 figure
Matrix Product State description of the Halperin States
Many fractional quantum Hall states can be expressed as a correlator of a
given conformal field theory used to describe their edge physics. As a
consequence, these states admit an economical representation as an exact Matrix
Product States (MPS) that was extensively studied for the systems without any
spin or any other internal degrees of freedom. In that case, the correlators
are built from a single electronic operator, which is primary with respect to
the underlying conformal field theory. We generalize this construction to the
archetype of Abelian multicomponent fractional quantum Hall wavefunctions, the
Halperin states. These latest can be written as conformal blocks involving
multiple electronic operators and we explicitly derive their exact MPS
representation. In particular, we deal with the caveat of the full wavefunction
symmetry and show that any additional SU(2) symmetry is preserved by the
natural MPS truncation scheme provided by the conformal dimension. We use our
method to characterize the topological order of the Halperin states by
extracting the topological entanglement entropy. We also evaluate their bulk
correlation length which are compared to plasma analogy arguments.Comment: 23 pages, 16 figure
Finite-size corrections in critical symmetry-resolved entanglement
In the presence of a conserved quantity, symmetry-resolved entanglement
entropies are a refinement of the usual notion of entanglement entropy of a
subsystem. For critical 1d quantum systems, it was recently shown in various
contexts that these quantities generally obey entropy equipartition in the
scaling limit, i.e. they become independent of the symmetry sector.
In this paper, we examine the finite-size corrections to the entropy
equipartition phenomenon, and show that the nature of the symmetry group plays
a crucial role. In the case of a discrete symmetry group, the corrections decay
algebraically with system size, with exponents related to the operators'
scaling dimensions. In contrast, in the case of a U(1) symmetry group, the
corrections only decay logarithmically with system size, with model-dependent
prefactors. We show that the determination of these prefactors boils down to
the computation of twisted overlaps.Comment: 19 pages + Appendix, 5 figure
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