10,142 research outputs found
Higher particle form factors of branch point twist fields in integrable quantum field theories
In this paper we compute higher particle form factors of branch point twist
fields. These fields were first described in the context of massive
1+1-dimensional integrable quantum field theories and their correlation
functions are related to the bi-partite entanglement entropy. We find analytic
expressions for some form factors and check those expressions for consistency,
mainly by evaluating the conformal dimension of the corresponding twist field
in the underlying conformal field theory. We find that solutions to the form
factor equations are not unique so that various techniques need to be used to
identify those corresponding to the branch point twist field we are interested
in. The models for which we carry out our study are characterized by staircase
patterns of various physical quantities as functions of the energy scale. As
the latter is varied, the beta-function associated to these theories comes
close to vanishing at several points between the deep infrared and deep
ultraviolet regimes. In other words, renormalisation group flows approach the
vicinity of various critical points before ultimately reaching the ultraviolet
fixed point. This feature provides an optimal way of checking the consistency
of higher particle form factor solutions, as the changes on the conformal
dimension of the twist field at various energy scales can only be accounted for
by considering higher particle form factor contributions to the expansion of
certain correlation functions.Comment: 25 pages, 4 figures; v2 contains small correction
Vertically aligned carbon nanotubes for microelectrode arrays applications
In this work a methodology to fabricate carbon nanotube based electrodes using plasma enhanced chemical vapour deposition has been explored and defined. The final integrated microelectrode based devices should present specific properties that make them suitable for microelectrode arrays applications. The methodology studied has been focused on the preparation of highly regular and dense vertically aligned carbon nanotube (VACNT) mat compatible with the standard lithography used for microelectrode arrays technology
Minimum Conductivity and Evidence for Phase Transitions in Ultra-clean Bilayer Graphene
Bilayer graphene (BLG) at the charge neutrality point (CNP) is strongly
susceptible to electronic interactions, and expected to undergo a phase
transition into a state with spontaneous broken symmetries. By systematically
investigating a large number of singly- and doubly-gated bilayer graphene (BLG)
devices, we show that an insulating state appears only in devices with high
mobility and low extrinsic doping. This insulating state has an associated
transition temperature Tc~5K and an energy gap of ~3 meV, thus strongly
suggesting a gapped broken symmetry state that is destroyed by very weak
disorder. The transition to the intrinsic broken symmetry state can be tuned by
disorder, out-of-plane electric field, or carrier density
Bi-partite entanglement entropy in integrable models with backscattering
In this paper we generalise the main result of a recent work by J. L. Cardy
and the present authors concerning the bi-partite entanglement entropy between
a connected region and its complement. There the expression of the leading
order correction to saturation in the large distance regime was obtained for
integrable quantum field theories possessing diagonal scattering matrices. It
was observed to depend only on the mass spectrum of the model and not on the
specific structure of the diagonal scattering matrix. Here we extend that
result to integrable models with backscattering (i.e. with non-diagonal
scattering matrices). We use again the replica method, which connects the
entanglement entropy to partition functions on Riemann surfaces with two branch
points. Our main conclusion is that the mentioned infrared correction takes
exactly the same form for theories with and without backscattering. In order to
give further support to this result, we provide a detailed analysis in the
sine-Gordon model in the coupling regime in which no bound states (breathers)
occur. As a consequence, we obtain the leading correction to the sine-Gordon
partition function on a Riemann surface in the large distance regime.
Observations are made concerning the limit of large number of sheets.Comment: 22 pages, 2 figure
Bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories
This paper is a review of the main results obtained in a series of papers involving the present authors and their collaborator J L Cardy over the last 2 years. In our work, we have developed and applied a new approach for the computation of the bi-partite entanglement entropy in massive (1+1)-dimensional quantum field theories. In most of our work we have also considered these theories to be integrable. Our approach combines two main ingredients: the 'replica trick' and form factors for integrable models and more generally for massive quantum field theory. Our basic idea for combining fruitfully these two ingredients is that of the branch-point twist field. By the replica trick, we obtained an alternative way of expressing the entanglement entropy as a function of the correlation functions of branch-point twist fields. On the other hand, a generalization of the form factor program has allowed us to study, and in integrable cases to obtain exact expressions for, form factors of such twist fields. By the usual decomposition of correlation functions in an infinite series involving form factors, we obtained exact results for the infrared behaviours of the bi-partite entanglement entropy, and studied both its infrared and ultraviolet behaviours for different kinds of models: with and without boundaries and backscattering, at and out of integrability
Transport Spectroscopy of Symmetry-Broken Insulating States in Bilayer Graphene
The flat bands in bilayer graphene(BLG) are sensitive to electric fields
E\bot directed between the layers, and magnify the electron-electron
interaction effects, thus making BLG an attractive platform for new
two-dimensional (2D) electron physics[1-5]. Theories[6-16] have suggested the
possibility of a variety of interesting broken symmetry states, some
characterized by spontaneous mass gaps, when the electron-density is at the
carrier neutrality point (CNP). The theoretically proposed gaps[6,7,10] in
bilayer graphene are analogous[17,18] to the masses generated by broken
symmetries in particle physics and give rise to large momentum-space Berry
curvatures[8,19] accompanied by spontaneous quantum Hall effects[7-9]. Though
recent experiments[20-23] have provided convincing evidence of strong
electronic correlations near the CNP in BLG, the presence of gaps is difficult
to establish because of the lack of direct spectroscopic measurements. Here we
present transport measurements in ultra-clean double-gated BLG, using
source-drain bias as a spectroscopic tool to resolve a gap of ~2 meV at the
CNP. The gap can be closed by an electric field E\bot \sim13 mV/nm but
increases monotonically with a magnetic field B, with an apparent particle-hole
asymmetry above the gap, thus providing the first mapping of the ground states
in BLG.Comment: 4 figure
Antiperiodic dynamical 6-vertex model I: Complete spectrum by SOV, matrix elements of the identity on separate states and connections to the periodic 8-vertex model
The spin-1/2 highest weight representations of the dynamical 6-vertex and the
standard 8-vertex Yang-Baxter algebra on a finite chain are considered in this
paper. For the antiperiodic dynamical 6-vertex transfer matrix defined on
chains with an odd number of sites, we adapt the Sklyanin's quantum separation
of variable (SOV) method and explicitly construct SOV representations from the
original space of representations. We provide the complete characterization of
eigenvalues and eigenstates proving also the simplicity of its spectrum.
Moreover, we characterize the matrix elements of the identity on separated
states by determinant formulae. The matrices entering in these determinants
have elements given by sums over the SOV spectrum of the product of the
coefficients of separate states. This SOV analysis is not reduced to the case
of the elliptic roots of unit and the results here derived define the required
setup to extend to the dynamical 6-vertex model the approach recently developed
in [1]-[5] to compute the form factors of the local operators in the SOV
framework, these results will be presented in a future publication. For the
periodic 8-vertex transfer matrix, we prove that its eigenvalues have to
satisfy a fixed system of equations. In the case of a chain with an odd number
of sites, this system of equations is the same entering in the SOV
characterization of the antiperiodic dynamical 6-vertex transfer matrix
spectrum. This implies that the set of the periodic 8-vertex eigenvalues is
contained in the set of the antiperiodic dynamical 6-vertex eigenvalues. A
criterion is introduced to find simultaneous eigenvalues of these two transfer
matrices and associate to any of such eigenvalues one nonzero eigenstate of the
periodic 8-vertex transfer matrix by using the SOV results. Moreover, a
preliminary discussion on the degeneracy of the periodic 8-vertex spectrum is
also presented.Comment: 36 pages, main modifications in section 3 and one appendix added, no
result modified for the dynamical 6-vertex transfer matrix spectrum and the
matrix elements of identity on separate states for chains with an odd number
of site
Form factors of integrable Heisenberg (higher) spin chains
We present determinant formulae for the form factors of spin operators of
general integrable XXX Heisenberg spin chains for arbitrary (finite
dimensional) spin representations. The results apply to any "mixed" spin
chains, such as alternating spin chains, or to spin chains with magnetic
impurities.Comment: 24 page
The nested SU(N) off-shell Bethe ansatz and exact form factors
The form factor equations are solved for an SU(N) invariant S-matrix under
the assumption that the anti-particle is identified with the bound state of N-1
particles. The solution is obtained explicitly in terms of the nested off-shell
Bethe ansatz where the contribution from each level is written in terms of
multiple contour integrals.Comment: This work is dedicated to the 75th anniversary of H. Bethe's
foundational work on the Heisenberg chai
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