Concept

Conformal symmetry

Related publications (109)

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Excitation spectrum and density matrix renormalization group iterations

Frédéric Mila, Natalia Chepiga

We show that, in certain circumstances, exact excitation energies appear as locally site-independent (or flat) modes if one records the excitation spectrum of the effective Hamiltonian while sweeping through the lattice in the variational matrix-product-st ...

2017

Dimerization and exotic criticality in spin-S chains

Natalia Chepiga

In this thesis we have studied the emergence of spontaneously dimerized phases in frustrated spin-S chains, with emphasis on the nature of the critical lines between the dimerized and non-dimerized phases. The main numerical method used in this thesis is t ...

EPFL2017

Semiclassics, Goldstone bosons and CFT data

Riccardo Rattazzi, Alexander Monin, David Pirtskhalava, Fiona Katharina Seibold

Hellerman et al. (arXiv:1505.01537) have shown that in a generic CFT the spectrum of operators carrying a large U(1) charge can be analyzed semiclassically in an expansion in inverse powers of the charge. The key is the operator state correspondence by whi ...

Springer2017

Color Representation in Deep Neural Networks

Sabine Süsstrunk, Martin Pierre Engilberge, Edo Collins

Convolutional neural networks are top-performers on image classification tasks. Understanding how they make use of color information in images may be useful for various tasks. In this paper we analyze the representation learned by a popular CNN to detect a ...

2017

Conformal invariance of crossing probabilities for the Ising model with free boundary conditions

Clément Hongler

We prove that crossing probabilities for the critical planar Ising model with free boundary conditions are conformally invariant in the scaling limit, a phenomenon first investigated numerically by Langlands, Lewis and Saint-Aubin (J. Stat. Phys. 98 (2000) ...

Inst Mathematical Statistics2016

Weyl vs. conformal

Alexander Monin, Georgios Karananas

In this note we show that given a conformally invariant theory in flat space-time, it is not always possible to couple it to gravity in a Weyl invariant way. (C) 2016 The Authors. Published by Elsevier B.V. This is an open access article under the CC BY li ...

Elsevier2016

Perturbative and non-perturbative aspects of RG flows in quantum field theory

Lorenzo Vitale

This thesis explores two aspects of the renormalization group (RG) in quantum field theory (QFT). In the first part we study the structure of RG flows in general Poincaré-invariant, unitary QFTs, and in particular the irreversibility properties and the rel ...

EPFL2016

Constraints on perturbative RG flows in six dimensions

Lorenzo Vitale

When conformal field theories (CFTs) are perturbed by marginally relevant deformations, renormalization group (RG) flows ensue that can be studied with perturbative methods, at least as long as they remain close to the original CFT. In this work we study s ...

Springer2016

Poincaré, Scale and Conformal Symmetries

Georgios Karananas

Symmetries are omnipresent and play a fundamental role in the description of Nature. Thanks to them, we have at our disposal nontrivial selection rules that dictate how a theory should be constructed. This thesis, which is naturally divided into two parts, ...

EPFL2016

A variational investigation of the SU(N) Heisenberg model in antisymmetric irreducible representations

Jérôme Dufour

Motivated by recent experimental progress in the context of ultra-cold multi-colour fermionic atoms in optical lattices, this thesis investigates the properties of the antiferromagnetic SU(N) Heisenberg models with fully antisymmetric irreducible represent ...

EPFL2016