Related papers: Boundary correlation functions of the six-vertex m…
We present some open problems in the field of exactly solvable models. Two of the problems are related to the correlation functions of the XXX spin chain and the XXZ spin chain, one to the entropy of subsystems and one to the six vertex…
We introduce one matrix model coupled to multi-flavor vectors. The two-flavor vector model is demonstrated to reproduce the two-point correlation numbers of boundary primary fields of two dimensional (2, 2p+1) minimal Liouville gravity on…
We explore systems with a large number of fermionic degrees of freedom subject to non-local interactions. We study both vector and matrix-like models with quartic interactions. The exact thermal partition function is expressed in terms of…
We study the influence of boundary conditions on the entropy of the six-vertex model. We consider the case of fixed boundary conditions in order to argue that the entropy of the six-vertex model vary continuously from its value for…
Belavin's $(\mathbb{Z}/n\mathbb{Z})$-symmetric model is considered on the basis of bosonization of vertex operators in the $A^{(1)}_{n-1}$ model and vertex-face transformation. The corner transfer matrix (CTM) Hamiltonian of…
We compute lattice correlation functions for the model of critical dense polymers on a semi-infinite cylinder of perimeter $n$. In the lattice loop model, contractible loops have a vanishing fugacity whereas non-contractible loops have a…
We consider path integration of a fermionic oscillator with a one-parameter family of boundary conditions with respect to the time coordinate. The dependence of the fermion determinant on these boundary conditions is derived in a closed…
A single-sided boundary is introduced in the three-dimensional Chern-Simons model. It is shown that only one boundary condition for the gauge fields is possible, which plays the twofold role of chirality condition and bosonization rule for…
The $s$-point correlation function of a Gaussian Hermitian random matrix theory, with an external source tuned to generate a multi-critical singularity, provides the intersection numbers of the moduli space for the $p$-th spin curves…
In this letter we study the negativity of one dimensional free fermions. We derive the general form of the $\mathbb{Z}_{N}$ symmetric term in moments of the partial transposed (reduced) density matrix, which is an algebraic function of the…
We construct embeddings of boundary algebras B into ZF algebras A. Since it is known that these algebras are the relevant ones for the study of quantum integrable systems (with boundaries for B and without for A), this connection allows to…
Motivated by conjectures about near-horizon dynamics in quantum gravity, we search for lines of perturbatively accessible fixed points emanating from models of $N$ free fermions. Through two loops we find a new class of models, apart from…
We consider the problem of correlation functions in the stationary states of one-dimensional stochastic models having conformal invariance. If one considers the space dependence of the correlators, the novel aspect is that although one…
At the beginning of the 70's, Baxter introduced a multiparametric generalization of the six-vertex model. This integrable system has been found to exhibit a remarkable variety of critical behaviors. The work is part of a series of papers…
We show that the emptiness formation probability of the six-vertex model with domain wall boundary conditions at its free-fermion point is a $\tau$-function of the sixth Painlev\'e equation. Using this fact we derive asymptotics of the…
We study non-relativistic conformal field theory on a flat space in the presence of a planar boundary. We compute correlation functions of primary operators and obtain the expression for the boundary conformal block. We also discuss the…
The $\alpha$-determinant is a one-parameter generalisation of the standard determinant, with $\alpha=-1$ corresponding to the determinant, and $\alpha=1$ corresponding to the permanent. In this paper a simple limit procedure to construct…
We study fermionic one-matrix, two-matrix and $D$-dimensional gauge invariant matrix models. In all cases we derive loop equations which unambiguously determine the large-$N$ solution. For the one-matrix case the solution is obtained for an…
Correlation factors are constructed that are consistent with the permutation symmetry group of N Fermions at given value of the filling factor.
We supplement the determinantal and Pfaffian bounds of Sims and Warzel (Commun Math Phys 347:903--931, 2016) for many-body localization of quasi-free fermions, by considering the high dimensional case and complex-time correlations. Our…