1,721,071 research outputs found
Hidden Bethe states in a partially integrable model
No full textWe present a one-dimensional multicomponent model, known to be partially integrable when restricted to the subspaces made of only two components. By constructing fully antisymmetrized bases, we find integrable excited eigenstates corresponding to the totally antisymmetric irreducible representation of the permutation operator in the otherwise nonintegrable subspaces. We establish rigorously the breakdown of integrability in those subspaces by showing explicitly the violation of the Yang-Baxter equation. We further solve the constraints from the Yang-Baxter equation to find exceptional momenta that allows Bethe ansatz solutions of solitonic bound states. These integrable eigenstates have distinct dynamical consequence from the embedded integrable subspaces previously known, as they do not span their separate Krylov subspaces, and a generic initial state can partly overlap with them and therefore have slow thermalization. However, this novel form of weak ergodicity breaking contrasts with that of quantum many-body scars in that the integrable eigenstates involved do not have necessarily low entanglement. Our approach provides a complementary route to arrive at exact excited states in nonintegrable models: instead of solving towers of single-mode excited states based on a solvable ground state in a nonintegrable model, we identify the integrable eigenstates that survive in a deformation of the Hamiltonian away from its integrable point
Two point correlation function in integrable QFT with anticrossing symmetry
No full textThe two-point correlation function of the stress-energy tensor for the massive deformation of the non-unitary model is computed. We compare the ultraviolet CFT perturbative expansion of this correlation function with its spectral representation given by a summation over matrix elements of the intermediate asymptotic massive particles. The fast rate of convergence of both approaches provides an explicit example of an accurate interpolation between the infrared and ultraviolet behaviours of a Quantum Field Theory
The spin-spin correlation function in the two-dimensional Ising model in a magnetic field at T=T_c
No full textThe form factor bootstrap approach is used to compute the exact contributions in the large distance expansion of the correlation function of the two-dimensional Ising model in a magnetic field at . The matrix elements of the magnetization operator present a rich analytic structure induced by the (multi) scattering processes of the eight massive particles of the model. The spectral representation series has a fast rate of convergence and perfectly agrees with the numerical determination of the correlation function
Effective potentials and kink spectra in non-integrable perturbed conformal field theories
Full text linkWe analyze the evolution of the eective potential and the particle spectrum of two- parameter families of non-integrable quantum eld theories. These theories are dened by deformations of conformal minimal models Mm by using the operators Φ1,3, Φ1,2 and Φ2,1. This study extends to all minimal models the analysis previously done for the classes of universality of the Ising, the Tricritical Ising and the RSOS models. We establish the sym- metry and the duality properties of the various models also identifying the limiting theories that emerge when m → ∞
Generalized Riemann hypothesis, time series and normal distributions
No full textL functions based on Dirichlet characters are natural generalizations of the Riexnann zeta (s) function: they both have series representations and satisfy an Euler product representation, i.e. an infinite product taken over prime numbers. In this paper we address the generalized Riemann hypothesis relative to the non-trivial complex zeros of the Dirichlet L functions by studying the possibility to enlarge the original domain of convergence of their Euler product. The feasibility of this analytic continuation is ruled by the asymptotic behavior in N of the series B-N = Sigma(N)(n=1) cos (t log p(n) - arg chi (p(n))) involving Dirichlet characters chi modulo q on primes p(n) . Although deterministic, these series have pronounced stochastic features which make them analogous to random time series. We show that the B-N's satisfy various normal law probability distributions. The study of their large asymptotic behavior poses an interesting problem of statistical physics equivalent to the single Brownian trajectory problem, here addressed by defining an appropriate ensemble epsilon involving intervals of primes. For non-principal characters, we show that the series B-N present a universal diffusive random walk behavior B-N = O(root N) in view of the Dirichlet theorem on the equidistribution of reduced residue classes modulo q and the Lemke Oliver-Soundararajan conjecture on the distribution of pairs of residues on consecutive primes. This purely diffusive behavior of B-N implies that the domain of convergence of the infinite product representation of the Dirichlet L-functions for non-principal characters can be extended from R(s) > 1 down to R(s)=1/2, without encountering any zeros before reaching this critical line
RAMOND SECTOR OF THE SUPERSYMMETRIC MINIMAL MODELS
No full textA Coulomb gas representation for the Ramond sectors of the N = 1 supersymmetric models is constructed. The fusion rules and the 4-point functions for the Ramond fields are calculated explicitly by this method and used to describe the Z2 odd sectors of the tricritical Ising model and of the critical Kosterlitz-Thouless XY model
Semiclassical energy levels of sine-Gordon model on a strip with Dirichlet boundary conditions
No full textWe derive analytic expressions of the semiclassical energy levels of Sine-Gordon model in a strip geometry with Dirichlet boundary condition at both edges. They are obtained by initially selecting the classical backgrounds relative to the vacuum or to the kink sectors, and then solving the Schodinger equations (of Lame' type) associated to the stability condition. Explicit formulas are presented for the classical solutions of both the vacuum and kink states and for the energy levels at arbitrary values of the size of the system. Their ultraviolet and infrared limits are also discussed
FUSION RULES, 4-POINT FUNCTIONS AND DISCRETE SYMMETRIES OF N=2 SUPERCONFORMAL MODELS
No full textFusion rules, structure constants and four-point functions for all the fields of N = 2 superconformal minimal models (c ≤ 3) are derived. It is shown that the additional Zp+2 symmetries of these models are generated by specific N = 2 superfields which close the N = 2 superparafermionic algebra. General results are applied to the four- and three-generation Gepner tensor product models and the allowed Yukawa couplings are found. © 1989
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