We study both noncentrosymmetric and time-reversal breaking Weyl semimetal systems under a strong magnetic field with the Coulomb interaction. The three-dimensional bulk system is reduced to many mutually interacting quasi-one-dimensional wires. Each strongly correlated wire can be approached within the Tomonaga-Luttinger liquid formalism. Including impurity scatterings, we inspect the localization effect and the temperature dependence of the electrical resistivity. The effect of a large number of Weyl points in real materials is also discussed.Introduction.-The realization of linear band crossings in three dimensions (3D) in the Weyl semimetals are sparking keen interests [1]. This lends credence to the concept of Weyl fermion [2] in the context of variou condensed matter systems [3,4]. In principle, any solid-state realization should bear time-reversal symmetry breaking (TRB) and/or inversion symmetry breaking (IB) [5][6][7][8][9] so as to lift the Kramers degeneracy and to generate nonzero Berry curvatures. The Weyl point is interesting as a 3D counterpart of the two-dimensional (2D) Dirac physics [10], which means topologically protected monopoles of the momentum-space Berry phase [11]. Among others, the chiral magnetic effect [12] as a result of the chiral anomaly [13][14][15][16] is observed as negative magnetoresistance in Dirac/Weyl semimetals [17,18] once the chiral imbalance of chemical potential is generated by parallel electric and magnetic fields.The intriguing facet of the magnetotransport in Dirac/Weyl semimetals mainly comes from the the unique Landau level formation dissimilar to that of quadratic electronic bands, where the lowest Landau level, a linearly dispersed chiral mode along the direction of the magnetic field, is well separated from the higher levels by a cyclotron gap ∝ √ B, whose 2D variant has been vastly explored in graphene [19]. A further stage is when the (ultra) quantum limit is achieved[20], enabling the lowest Landau level to play a major role in shaping the low-energy physics. In this limit, the magnetic length l B = 1/ √ eB (setting = 1) becomes shorter than the Fermi wavelength since the quantized orbit of electrons shrinks with an increasing B and the lowest Landau level possesses the majority of population [21]. Remarkably, it implies a field-induced dimensional reduction [22] that will strongly enhance correlations hence the advent of the (quasi-) 1D system without electron quasiparticle excitations. This connects to the long-lasting search or application of the Tomonaga-Luttinger liquid (TLL) physics [23], including semiconductor quantum wires [24,25], singlewalled carbon nanotubes [26,27], edge states in fractional quantum Hall states [28,29] and 2D topological insulators [30,31], and so on.Because of the large cyclotron gap, it is expected and confirmed that the Dirac/Weyl semimetals can be driven to the quantum limit at lower magnetic fields than semiconductors [20]. Due to the instability from electron correlations, one possibility is the gap-opening or dynamical m...