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The staircase model (SM) is a simple generalization of the sinh-Gordon model, obtained by complexifying the coupling constant. This produces a new theory with many interesting features. Chief among them is the fact that scaling functions such as Zamolodchikov's c-function display 'roaming' behaviour, that is, they visit the vicinity of an infinite number of conformal fixed points, the unitary minimal models of conformal field theory. This rich structure also makes the model an interesting candidate for study using the generalized hydrodynamic approach to integrable quantum field theory (IQFT). By studying hydrodynamic quantities such as the effective velocities of quasiparticles we can develop a more physical picture of interaction in the theory, both at and away from equilibrium. Indeed, we find that in the SM the effective velocity displays monotonicity features not found in any other IQFT. These admit a natural interpretation when investigated in the context of the massless theories known as models, which provide an effective description of massless flows between consecutive unitary minimal models. Consequently, we find that the effective velocity in the SM can be reconstructed by a 'cut and paste' procedure involving the equivalent functions associated to the massless excitations of suitable models. We also investigate the average currents and densities of higher spin conserved quantities in the partitioning protocol. [ABSTRACT FROM AUTHOR]

Abstract: We obtain the exact expression for the Von Neumann entropy for an infinite bipartition of the XYZ model, by connecting its reduced density matrix to the corner transfer matrix of the eight vertex model. Then we consider the anisotropic scaling limit of the XYZ chain that yields the -dimensional sine-Gordon model. We present the formula for the entanglement entropy of the latter, which has the structure of a dominant logarithmic term plus a constant, in agreement with what is generally expected for a massive quantum field theory. [Copyright &y& Elsevier]

Abstract: The generalized non-linear Schrödinger (NLS) theory with particular integrable boundary conditions is considered. More precisely, two distinct types of boundary conditions, known as soliton preserving (SP) and soliton non-preserving (SNP), are implemented into the classical NLS model. Based on this choice of boundaries the relevant conserved quantities are computed and the corresponding equations of motion are derived. A suitable quantum lattice version of the boundary generalized NLS model is also investigated. The first non-trivial local integral of motion is explicitly computed, and the spectrum and Bethe ansatz equations are derived for the soliton non-preserving boundary conditions. [Copyright &y& Elsevier]

We investigate various excited states of sine-Gordon model on a strip with Dirichlet boundary conditions on both boundaries using a non-linear integral equation (NLIE) approach. [Copyright &y& Elsevier]

We consider the tricritical Ising model on a strip or cylinder under the integrable perturbation by the thermal ϕ1,3 boundary field. This perturbation induces five distinct renormalization group (RG) flows between Cardy type boundary conditions labelled by the Kac labels (r,s). We study these boundary RG flows in detail for all excitations. Exact thermodynamic Bethe ansatz (TBA) equations are derived using the lattice approach by considering the continuum scaling limit of the A4 lattice model with integrable boundary conditions. Fixing the bulk weights to their critical values, the integrable boundary weights admit a thermodynamic boundary field ξ which induces the flow and, in the continuum scaling limit, plays the role of the perturbing boundary field ϕ1,3. The excitations are completely classified, in terms of string content, by (m,n) systems and quantum numbers but the string content changes by either two or three well-defined mechanisms along the flow. We identify these mechanisms and obtain the induced maps between the relevant finitized Virasoro characters. We also solve the TBA equations numerically to determine the boundary flows for the leading excitations. [Copyright &y& Elsevier]

We show how a lattice approach can be used to derive Thermodynamic Bethe Ansatz (TBA) equations describing all excitations for boundary flows. The method is illustrated for a prototypical flow of the tricritical Ising model by considering the continuum scaling limit of the A4 lattice model with integrable boundaries. Fixing the bulk weights to their critical values, the integrable boundary weights admit two boundary fields ξ and η which play the role of the perturbing boundary fields ϕ1,3 and ϕ1,2 inducing the renormalization group flow between boundary fixed points. The excitations are completely classified in terms of (m,n) systems and quantum numbers but the string content changes by certain mechanisms along the flow. For our prototypical example, we identify these mechanisms and the induced map between the relevant finitized Virasoro characters. We also solve the boundary TBA equations numerically to determine the flows for the leading excitations. [Copyright &y& Elsevier]

We show that the elliptic parametrization of the coupling constants of the quantum XYZ spin chain can be analytically extended outside of their natural domain, to cover the whole phase diagram of the model, which is composed of 12 adjacent regions, related to one another by a spin rotation. This extension is based on the modular properties of the elliptic functions and we show how rotations in parameter space correspond to the double covering PGL(2,Z) of the modular group, implying that the partition function of the XYZ chain is invariant under this group in parameter space, in the same way as a conformal field theory partition function is invariant under the modular group acting in real space. The encoding of the symmetries of the model into the modular properties of the partition function could shed light on the general structure of integrable models [ABSTRACT FROM AUTHOR]

We study analytically the corrections to the leading terms in the Rényi entropy of a massive lattice theory, showing significant deviations from naive expectations. In particular, we show that finite size and finite mass effects give rise to different contributions (with different exponents) and thus violate a simple scaling argument. In the specific, we look at the entanglement entropy of a bipartite XYZ spin-1/2 chain in its ground state. When the system is divided into two semi-infinite half-chains, we have an analytical expression of the Rényi entropy as a function of a single mass parameter. In the scaling limit, we show that the entropy as a function of the correlation length formally coincides with that of a bulk Ising model. This should be compared with the fact that, at criticality, the model is described by ac = 1 conformai field theory and the corrections to the entropy due to finite size effects show exponents depending on the compactification radius of the theory. We will argue that there is no contradiction between these statements. If the lattice spacing is retained finite, the relation between the mass parameter and the correlation length generates new subleading terms in the entropy, whose form is path dependent in phase space and whose interpretation within a field theory is not available yet. These contributions arise as a consequence of the existence of stable bound states and are thus a distinctive feature of truly interacting theories, such as the XYZ chain. [ABSTRACT FROM AUTHOR]

We study the Renyi entropy of the one-dimensional X YZ spin-i /2 chain in the entirety of its phase diagram. The model has several quantum critical lines corresponding to rotated XXZ chains in their paramagnetic phase, and four tricritical points where these phases join. Two of these points are described by a conformal field theory and close to them the entropy scales as the logarithm of its mass gap. The other two points are not conformal and the entropy has a peculiar singular behavior in their neighbors, characteristic of an essential singularity. At these nonconformal points the model undergoes a discontinuous transition, with a level crossing in the ground state and a quadratic excitation spectrum. We propose the entropy as an efficient tool to determine the discontinuous or continuous nature of a phase transition also in more complicated models. [ABSTRACT FROM AUTHOR]

Abstract: We investigate boundary bound states of sine-Gordon model on the finite-size strip with Dirichlet boundary conditions. For the purpose we derive the nonlinear integral equation (NLIE) for the boundary excited states from the Bethe ansatz equation of the inhomogeneous XXZ spin 1/2 chain with boundary imaginary roots discovered by Saleur and Skorik. Taking a large volume (IR) limit we calculate boundary energies, boundary reflection factors and boundary Lüscher corrections and compare with the excited boundary states of the Dirichlet sine-Gordon model first considered by Dorey and Mattsson. We also consider the short distance limit and relate the IR scattering data with that of the UV conformal field theory. [Copyright &y& Elsevier]