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Register a new userQuantum Link Models with Many Rishon Flavors and with Many Colors
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Quantum link models are a novel formulation of gauge theories in terms of discrete degrees of freedom. These degrees of freedom are described by quantum operators acting in a finite-dimensional Hilbert space. We show that for certain representations of the operator algebra, the usual Yang-Mills action is recovered in the continuum limit. The quantum operators can be expressed as bilinears of fermionic creation and annihilation operators called rishons. Using the rishon representation the quantum link Hamiltonian can be expressed entirely in terms of color-neutral operators. This allows us to study the large N_c limit of this model. In the t Hooft limit we find an area law for the Wilson loop and a mass gap. Furthermore, the strong coupling expansion is a topological expansion in which graphs with handles and boundaries are suppressed.
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This note is based on our recent results on QCD with varying number of flavors of fundamental fermions. Topics include unusual, strong dynamics in the preconformal, confining phase, the physics of the conformal window and the role of ab-initio lattice simulations in establishing our current knowledge of the phases of many flavor QCD
Information of the phase structure of many flavor SU(3) gauge theory is of great interest for finding a theory which dynamically breaks the electro-weak symmetry. We study the SU(3) gauge theory with fermions for $N_f=12$ and 16 in fundamental representation. Both of them, through perturbation theory, reside in the conformal phase. We try to determine the phase of each theory non-perturbatively with lattice simulation and to find the characteristic behavior of the physical quantities in the phase. HISQ type staggered fermions are used to reduce the discretization error which could compromise the behavior of the physical quantity to determine the phase structure at non-zero lattice spacings. Spectral quantities such as bound state masses of meson channel and meson decay constants are investigated with careful finite volume analysis. Our data favor the conformal over chiral symmetry breaking scenario for both $N_f=12$ and 16.
We discuss the phases of QCD in the parameter space spanned by the number of light flavours and the temperature with respect to the realisation of chiral and conformal symmetries. The intriguing interplay of these symmetries is best studied by means of lattice simulations, and some selected results from our recent work are presented here.
Recently, there has been significant progress in solving quantum many-particle problem via machine learning based on the restricted Boltzmann machine. However, it is still highly challenging to solve frustrated models via machine learning, which has not been demonstrated so far. In this work, we design a brand new convolutional neural network (CNN) to solve such quantum many-particle problems. We demonstrate, for the first time, of solving the highly frustrated spin-1/2 J$_1$-J$_2$ antiferromagnetic Heisenberg model on square lattices via CNN. The energy per site achieved by the CNN is even better than previous string-bond-state calculations. Our work therefore opens up a new routine to solve challenging frustrated quantum many-particle problems using machine learning.
We present our result of the many-flavor QCD. Information of the phase structure of many-flavor SU(3) gauge theory is of great interest, since the gauge theories with the walking behavior near the infrared fixed point are candidates of new physics for the origin of the dynamical electroweak symmetry breaking. We study the SU(3) gauge theories with 12 and 16 fundamental fermions. Utilizing the HISQ type action which is useful to study the continuum physics, we analyze the lattice data of the mass and the decay constant of the pseudoscalar meson and the mass of the vector meson as well at several values of lattice spacing and fermion mass. The finite size scaling test in the conformal hypothesis is also performed. Our data is consistent with the conformal scenario for Nf=12. We obtain the mass anomalous dimension $gamma_m sim 0.4-0.5$. An update of $N_f=16$ study is also shown.
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