相关论文: On the Mutual Information in Conformal Field Theor…

Quantifying the dependence between high-dimensional random variables is central to statistical learning and inference. Two classical methods are canonical correlation analysis (CCA), which identifies maximally correlated projected versions…

In this paper, we try to establish a connection between a quantum information concept, i.e. the mutual information, and the conventional order parameter in condensed matter physics. We show that a non-vanishing mutual information at a long…

We study general perturbations of two-dimensional conformal field theories by holomorphic fields. It is shown that the genus one partition function is controlled by a contact term (pre-Lie) algebra given in terms of the operator product…

The explicit computation of higher-point conformal blocks in any dimension is usually a challenging task. For two-dimensional conformal field theories in Euclidean signature, the oscillator formalism proves to be very efficient. We…

We show that the four-point functions in conformal field theory are defined as distributions on the boundary of the region of convergence of the conformal block expansion. The conformal block expansion converges in the sense of…

Quantum many-body systems realise many different phases of matter characterised by their exotic emergent phenomena. While some simple versions of these properties can occur in systems of free fermions, their occurrence generally implies…

We consider conformal perturbation theory for $n$-point functions on the sphere in general 2D CFTs to first order in coupling constant. We regulate perturbation integrals using canonical hard disk excisions of size $\epsilon$ around the…

Federated learning (FL) is a widely adopted privacy-preserving distributed learning framework, yet its generalization performance remains less explored compared to centralized learning. In FL, the generalization error consists of two…

Mutual information between two random variables is a well-studied notion, whose understanding is fairly complete. Mutual information between one random variable and a pair of other random variables, however, is a far more involved notion.…

Because of the kinematic reversibility of the Stokes equation, fluid mixing at the microscale requires an interplay between advection and diffusion. Here we introduce mutual information between particle positions before and after mixing as…

We consider possible conformal field theory (CFT) descriptions of the various inertial ranges that exist in $2d$ duality invariant Magnetohydrodynamics. Such models arise as effective theories of dyonic plasmas in 3 dimensions in which all…

This thesis uses a quantity that is defined and justified by information theory -- mutual information -- to examine models of condensed matter systems. More precisely, it studies models which are made up out of ferromagnetically interacting…

We describe in detail a counterexample to the topological classification of free fermion systems. We deal with a one dimensional chain of Majorana fermions with an unusual T symmetry. The topological invariant for the free fermion…

Conformal field theory (CFT) is an extremely powerful tool for explicitly computing critical exponents and correlation functions of statistical mechanics systems at a second order phase transition, or of condensed matter systems at a…

Multimodal image alignment is the process of finding spatial correspondences between images formed by different imaging techniques or under different conditions, to facilitate heterogeneous data fusion and correlative analysis. The…

For a given conformal field theory (CFT), one can deform it via the addition of a marginal operator to the spectrum. In two dimensions, when the added operator has conformal weights $h=\bar{h}=1$, conformal symmetry is not broken and the…

We rigorously derive a single-letter variational expression for the mutual information of the asymmetric two-groups stochastic block model in the dense graph regime. Existing proofs in the literature are indirect, as they involve mapping…

We propose a generalization of the collective field theory hamiltonian, including interactions between the original bosonic collective field $w_0 (z)$ and supplementary fields ${\bar w}_j (z)$ realizing classically a $w_\infty$ algebra. The…

We study an exactly solvable quantum field theory (QFT) model describing interacting fermions in 2+1 dimensions. This model is motivated by physical arguments suggesting that it provides an effective description of spinless fermions on a…

This is an invited contribution to the 2nd edition of the Encyclopedia of Mathematical Physics. We review the following algebraic structures which appear in two-dimensional conformal field theory (CFT): The symmetries of two-dimensional…