Related papers: Hidden Grassmann Structure in the XXZ Model IV: CF…

We study fermionic conformal field theories on surfaces with spin structure in the presence of boundaries, defects, and interfaces. We obtain the relevant crossing relations, taking particular care with parity signs and signs arising from…

In this work, we use the master function approach to describe the CFT limit of the six-vertex model at the free fermion point. Using the ODE/IM correspondence, we obtain an explicit form of the master function. This allows us to compute the…

We reconsider the moments of the reduced density matrix of two disjoint intervals and of its partial transpose with respect to one interval for critical free fermionic lattice models. It is known that these matrices are sums of either two…

We consider the XXZ spin chain in the scaling limit in the Matsubara direction. The main result of this paper is new representations for the functions $\Psi(l, \kappa)$ and $\Theta(l, m; \kappa, \alpha)$ associated with the function…

We consider the partial transpose of the spin reduced density matrix of two disjoint blocks in spin chains admitting a representation in terms of free fermions, such as XY chains. We exploit the solution of the model in terms of Majorana…

In this article we unveil a new structure in the space of operators of the XXZ chain. We consider the space of all quasi-local operators, which are products of the disorder field with arbitrary local operators. In analogy with CFT the…

Critical statistical mechanics and Conformal Field Theory (CFT) are conjecturally connected since the seminal work of Beliavin, Polyakov, and Zamolodchikov [BPZ84a]. Both exhibit exactly solvable structures in two dimensions. A…

We explain how to incorporate the action of local integrals of motion into the fermionic basis for the sine-Gordon model and its UV CFT. The examples up to the level 4 are presented. Numerical computation support the results. Possible…

We review here some general properties of antiferromagnetic Heisenberg spin chains, emphasizing and discussing the role of hidden symmetries in the classification of the various phases of the models. We present also some recent results that…

We address the problem of computing temperature correlation functions of the XXZ chain, within the approach developed in our previous works. In this paper we calculate the expected values of a fermionic basis of quasi-local operators, in…

The spin-1/2 XXZ Heisenberg chain with two types of boundary terms is considered. For the first type, the Hamiltonian is hermitian but not for the second type which includes the U_{q}[SU(2)] symmetric case. It is shown that for a certain…

We generalize the results of [Comm. Math. Phys. 299 (2010), 825-866, arXiv:0911.3731] (hidden Grassmann structure IV) to the case of excited states of the transfer matrix of the six-vertex model acting in the so-called Matsubara direction.…

We study one-point functions of the sine-Gordon model on a cylinder. Our approach is based on a fermionic description of the space of descendent fields, developed in our previous works for conformal field theory and the sine-Gordon model on…

We set up a strategy for studying large families of logarithmic conformal field theories by using the enlarged symmetries and non--semi-simple associative algebras appearing in their lattice regularizations (as discussed in a companion…

We introduce a set of gauge invariant fermion fields in fermionic coset models and show that they play a very central role in the description of several Conformal Field Theories (CFT's). In particular we discuss the explicit realization of…

This article aims to review a selection of central topics and examples in logarithmic conformal field theory. It begins with a pure Virasoro example, critical percolation, then continues with a detailed exposition of symplectic fermions,…

We present a construction of an integrable model as a projective type limit of spin Calogero-Sutherland model with $N$ fermionic particles, where $N$ tends to infinity. It is implemented in the multicomponent fermionic Fock space. Explicit…

We study the general structure of Fermi conformal nets of von Neumann algebras on the circle, consider a class of topological representations, the general representations, that we characterize as Neveu-Schwarz or Ramond representations, in…

The generating functional of correlation functions for the XXZ spin chain is considered in the thermodynamic limit. We derive a system of integro-difference equations that prescribe this functional. On the basis of this system we establish…

In this work we describe the mathematical foundations used in the construction of primary fields of minimal models of conformal field theory. The work contains two parts: In the first part we give a description of Verma and Fock modules for…