Non-diagonal open spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and matrix elements of some quasi-local operators

The integrable quantum models, associated to the transfer matrices of the 6-vertex reflection algebra for spin 1/2 representations, are studied in this paper. In the framework of Sklyanin's quantum separation of variables (SOV), we provide the complete characterization of the eigenvalues and eigenstates of the transfer matrix and the proof of the simplicity of the transfer matrix spectrum. Moreover, we use these integrable quantum models as further key examples for which to develop a method in the SOV framework to compute matrix elements of local operators. This method has been introduced first in [1] and then used also in [2], it is based on the resolution of the quantum inverse problem (i.e. the reconstruction of all local operators in terms of the quantum separate variables) plus the computation of the action of separate covectors on separate vectors. In particular, for these integrable quantum models, which in the homogeneous limit reproduce the open spin-1/2 XXZ quantum chains with non-diagonal boundary conditions, we have obtained the SOV-reconstructions for a class of quasi-local operators and determinant formulae for the covector-vector actions. As consequence of these findings we provide one determinant formulae for the matrix elements of this class of reconstructed quasi-local operators on transfer matrix eigenstates.Comment: 40 pages. Minor modifications in the text and some notations and some more reference adde

Form factors of descendant operators in the massive Lee-Yang model

The form factors of the descendant operators in the massive Lee-Yang model are determined up to level 7. This is first done by exploiting the conserved quantities of the integrable theory to generate the solutions for the descendants starting from the lowest non-trivial solutions in each operator family. We then show that the operator space generated in this way, which is isomorphic to the conformal one, coincides, level by level, with that implied by the $S$-matrix through the form factor bootstrap. The solutions we determine satisfy asymptotic conditions carrying the information about the level that we conjecture to hold for all the operators of the model.Comment: 23 page

Point-like topological defects in bilayer quantum Hall systems

Following a suggestion given in Phys. Lett. B 571 (2003) 250, we show how a bilayer Quantum Hall system at fillings nu =m/pm+2 can exhibit a point-like topological defect in its edge state structure. Indeed our CFT theory for such a system, the Twisted Model (TM), gives rise in a natural way to such a feature in the twisted sector. Our results are in agreement with recent experimental findings (cond-mat/0503478) which evidence the presence of a topological defect in the bilayer system.Comment: 9 pages, 3 figure

Topological order in Josephson junction ladders with Mobius boundary conditions

We propose a CFT description for a closed one-dimensional fully frustrated ladder of quantum Josephson junctions with Mobius boundary conditions, in particular we show how such a system can develop topological order. Such a property is crucial for its implementation as a "protected" solid state qubit.Comment: 14 pages, 3 figures, to appear in JSTA

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

CFT description of the Fully Frustrated XY model and phase diagram analysis

Following a suggestion given in Nucl. Phys. B 300 (1988)611,we show how the U(1)*Z_{2} symmetry of the fully frustrated XY (FFXY) model on a square lattice can be accounted for in the framework of the m-reduction procedure developed for a Quantum Hall system at "paired states" fillings nu =1 (cfr. Cristofano et al.,Mod. Phys. Lett. A 15 (2000)1679;Nucl. Phys. B 641 (2002)547). The resulting twisted conformal field theory (CFT) with central charge c=2 is shown to well describe the physical properties of the FFXY model. In particular the whole phase diagram is recovered by analyzing the flow from the Z_{2} degenerate vacuum of the c=2 CFT to the infrared fixed point unique vacuum of the c=3/2 CFT. The last theory is known to successfully describe the critical behavior of the system at the overlap temperature for the Ising and vortex-unbinding transitions.Comment: 18 pages, 1 figure, to appear in JSTA

Form factors and complete spectrum of XXX antiperiodic higher spin chains by quantum separation of variables

The antiperiodic transfer matrix associated to higher spin representations of the rational 6-vertex Yang-Baxter algebra is analyzed by generalizing the approach introduced recently in [1], for the cyclic representations, in [2], for the spin-1/2 highest weight representations, and in [3], for the spin 1/2 representations of the reflection algebra. Here, we derive the complete characterization of the transfer matrix spectrum and we prove its simplicity in the framework of Sklyanin's quantum separation of variables (SOV). Then, the characterization of local operators by Sklyanin's quantum separate variables and the expression of the scalar products of separates states by determinant formulae allow to compute the form factors of the local spin operators by one determinant formulae similar to the scalar product ones. Finally, let us comment that these results represent the SOV analogous in the antiperiodic higher spin XXX quantum chains of the results obtained for the periodic chains in [4] in the framework of the algebraic Bethe ansatz.Comment: 20 pages, introduction improved by taking into account some relevant references on the spectrum of the model under general boundary conditions, no further relevant modification

A monocarboxylate transporter rescues frontotemporal dementia and Alzheimer's disease models

Brains are highly metabolically active organs, consuming 20% of a person's energy at resting state. A decline in glucose metabolism is a common feature across a number of neurodegenerative diseases. Another common feature is the progressive accumulation of insoluble protein deposits, it's unclear if the two are linked. Glucose metabolism in the brain is highly coupled between neurons and glia, with glucose taken up by glia and metabolised to lactate, which is then shuttled via transporters to neurons, where it is converted back to pyruvate and fed into the TCA cycle for ATP production. Monocarboxylates are also involved in signalling, and play broad ranging roles in brain homeostasis and metabolic reprogramming. However, the role of monocarboxylates in dementia has not been tested. Here, we find that increasing pyruvate import in Drosophila neurons by over-expression of the transporter bumpel, leads to a rescue of lifespan and behavioural phenotypes in fly models of both frontotemporal dementia and Alzheimer's disease. The rescue is linked to a clearance of late stage autolysosomes, leading to degradation of toxic peptides associated with disease. We propose upregulation of pyruvate import into neurons as potentially a broad-scope therapeutic approach to increase neuronal autophagy, which could be beneficial for multiple dementias

Effects of relaxed lockdown on pediatric er visits during sars-cov-2 pandemic in Italy

Previously, we demonstrated an 81% reduction in pediatric Emergency Room (ER) visits in Italy during the strict lockdown due to the SARS-CoV-2 pandemic. Since May 2020, lockdown measures were relaxed until 6 November 2020, when a strict lockdown was patchily reintroduced. Our aim was to evaluate the impact of the relaxed lockdown on pediatric ER visits in Italy. We performed a retrospective multicenter study involving 14 Italian pediatric ERs. We compared total ER visits from 24 September 2020 to 6 November 2020 with those during the corresponding timeframe in 2019. We evaluated 17 ER specific diagnoses grouped in air communicable and non-air communicable diseases. We recognized four different triage categories: white, green, yellow and red. In 2020 total ER visits were reduced by 51% compared to 2019 (16,088 vs. 32,568, respectively). The decrease in air communicable diseases was significantly higher if compared to non-air communicable diseases (−64% vs. −42%, respectively). ER visits in each triage category decreased in 2020 compared to 2019, but in percentage, white and red codes remained stable, while yellow codes slightly increased and green codes slightly decreased. Our results suggest that preventive measures drastically reduced the circulation of air communicable diseases even during the reopening of social activities but to a lesser extent with regard to the strict lockdown period (March–May 2020)