Asymptotic freedom | EPFL Graph Search

In quantum field theory, asymptotic freedom is a property of some gauge theories that causes interactions between particles to become asymptotically weaker as the energy scale increases and the corresponding length scale decreases. (Alternatively, and perhaps contrarily, in applying an S-matrix, asymptotically free refers to free particles states in the distant past or the distant future.) Asymptotic freedom is a feature of quantum chromodynamics (QCD), the quantum field theory of the strong interaction between quarks and gluons, the fundamental constituents of nuclear matter. Quarks interact weakly at high energies, allowing perturbative calculations. At low energies, the interaction becomes strong, leading to the confinement of quarks and gluons within composite hadrons. The asymptotic freedom of QCD was discovered in 1973 by David Gross and Frank Wilczek,
and independently by David Politzer in the same year. For this work all three shared the 2004 Nobel Prize in Physics.

Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains

Samuel Gozel

In this thesis we study various one-dimensional quantum spin systems with SU(2) and SU(N) symmetry. We investigate the short-distance behavior of the SU(2) Heisenberg model in the limit of large spin and show that there exists an extended regime where perturbation theory, in the form of spin-wave theory, can be successfully applied. The reason for this perturbative regime stems from the asymptotic freedom of the nonlinear sigma model onto which the Heisenberg model can be mapped. When considering observables which respect the rotational invariance of the model, we observe a cancellation of infrared divergences in the perturbative expansions, leading to a meaningful description of correlation functions. We then turn to the study of SU(N) models. Building on the representation theory of the SU(N) group and on the matrix product state (MPS) formalism, we introduce a generic method to construct Affleck-Kennedy-Lieb-Tasaki (AKLT) models having edge states described by any self-conjugate irreducible representation (irrep) of SU(N). A simple example is given by a spin-1 AKLT model having spin-1 edge states. The phase transition between this model and the original AKLT model is shown to be continuous and to correspond to a topological phase transition described by the SU(2) level-1 Wess-Zumino-Witten conformal field theory universality class. In addition we study an SU(3) AKLT model for the 3-box symmetric irrep at each site. We demonstrate that the edge states are adjoint edge irreps, we extract its correlation length and provide a useful construction as an optimal MPS. Finally, we develop a density matrix renormalization group algorithm based on standard Young tableaus and subduction coefficients to make full use of the non-abelian symmetry and to investigate the SU(3) Heisenberg model with 3-box symmetric irrep at each site. We show that the model has a finite gap above the singlet ground state, in agreement with an extension of the Haldane conjecture to SU(3) chains in the fully symmetric irreps. We also argue that there are five branches of elementary excitations living in four different irreps, each of which is gapped.

EPFL2020

Asymptotic Freedom and Large Spin Antiferromagnetic Chains

Samuel Gozel, Frédéric Mila

Building on the mapping of large-S spin chains onto the O(3) nonlinear sigma model with coupling constant 2/S, and on general properties of that model (asymptotic freedom, implying that perturbation theory is valid at high energy, and Elitzur's conjecture that rotationally invariant quantities are infrared finite in perturbation theory), we use the Holstein-Primakoff representation to derive analytic expressions for the equal-time and dynamical spin-spin correlations valid at distances smaller than S-1 exp(pi S) or at energies larger than JS(2) exp(-pi S), where J is the Heisenberg exchange coupling. This is supported by comparing the static correlations with quantum Monte Carlo simulations for S = 5/2.

AMER PHYSICAL SOC2019

Schwinger production of scalar particles during and after inflation from the first principles

Oleksandr Sobol

By using the first-principles approach, we derive a system of three quantum kinetic equations governing the production and evolution of charged scalar particles by an electric field in an expanding universe. Analyzing the ultraviolet asymptotic behavior of the kinetic functions, we found the divergent parts of the electric current and the energy-momentum tensor of the produced particles and determined the corresponding counterterms. The renormalized system of equations is used to study the generation of electromagnetic fields during and after inflation in the kinetic coupling model L-EM = -(1/4)f(2)(phi)F-mu nu F-mu nu with the Ratra coupling function f = exp(beta phi/M-p). It is found that the electric current of created particles is retarded with respect to the electric field. This leads to an oscillatory behavior of both quantities in agreement with the results obtained previously in phenomenological kinetic and hydrodynamical approaches.

2020

Asymptotic freedom, Haldane gap and edge states of SU(N) spin chains

Samuel Gozel

EPFL2020