In electronic band structure of solid state material, two band touching points with linear dispersion appear in pair in the momentum space. When they annihilate with each other, the system undergoes a quantum phase transition from three-dimensional Weyl semimetal (WSM) phase to a band insulator phase such as Chern band insulator (CI) phase. The phase transition is described by a new critical theory with a 'magnetic dipole' like object in the momentum space. In this paper, we reveal that the critical theory hosts a novel disorder-driven quantum multicritical point, which is encompassed by three quantum phases, renormalized WSM phase, CI phase, and diffusive metal (DM) phase. Based on the renormalization group argument, we first clarify scaling properties around the band touching points at the quantum multicritical point as well as all phase boundaries among these three phases. Based on numerical calculations of localization length, density of states and critical conductance distribution, we next prove that a localization-delocalization transition between the CI phase with a finite zero-energy density of states (zDOS) and DM phase belongs to an ordinary 3D unitary class. Meanwhile, a localization-delocalization transition between the Chern insulator phase with zero zDOS and a renormalized Weyl semimetal (WSM) phase turns out to be a direct phase transition whose critical exponent ν = 0.80 ± 0.01. We interpret these numerical results by a renormalization group analysis on the critical theory.

Low-energy magnon bands in a two-dimensional spin ice model become integer quantum magnon Hall bands under an out-of-plane field. By calculating the localization length and the two-terminal conductance of magnon transport, we show that the magnon bands with disorders undergo a quantum phase transition from an integer quantum magnon Hall regime to a conventional magnon localized regime. Finite size scaling analysis as well as a critical conductance distribution shows that the quantum critical point belongs to the same universality class as that in the quantum Hall transition. We characterize thermal magnon Hall conductivity in disordered quantum magnon Hall system in terms of robust chiral edge magnon transport. PACS numbers:Bosonic analogue of integer quantum Hall states have been proposed in a number of quasi-particle boson systems with broken time-reversal symmetry such as photon, 1-6 phonon, 7 exciton, 8 exciton-polariton, 9 triplon, 10 magnon 11-19 and surface magnon-polariton. 20 Typically, their quasi-particle excitations have extended bulk bands with topological integers and topological edge modes whose chiral dispersions cross band gaps among these bulk bands. Due to its chiral (unidirectional) nature, a quasi-particle boson flow along the edge mode is believed to be robust against generic elastic backward scatters, fostering a rich prospect of their future applications. [1][2][3][4][5][6][7][8][9][11][12][13]20 On the one hand, these bosonic systems often break conservation of the quasi-particle number even at the level of respective quadratic Hamiltonian. 8,9,[11][12][13][14][15][16]19,[21][22][23][24][25][26][27] Thereby, one naturally wonders if the quasi-particle flow along the topological edge modes is still robust against such particle-number-nonconserving perturbations or not. In other words, one may raise a question whether two quantum Hall regimes with different Chern integers are topologically distinguishable even in the absence of the U(1) symmetry associated with the quasi-particle number conservation.In this rapid communication, we study effects of generic disorder potentials in a simplest spin model in a quantum magnon Hall regime. Our numerical results and the following argument clarify that, even without the explicit U(1) symmetry at the Hamiltonian level, the topological magnon edge mode provides a robust quantized magnon conductance and therefore quantum magnon Hall regimes with different topological integers are always distinguished by a quantum critical point with delocalized bulk magnon band. Thermal conductance distributions calculated at the critical point clearly shows that the quantum critical point belongs to the same universality class as the two-dimensional integer quantum Hall plateau-plateau transition. Based on these knowledge, we give a generic expression for the thermal Hall conductivity in disordered integer quantum bosonic Hall systems from edge transport picture.We study spin excitations in a square-lattice spin ice model 28-31 under out-of-plane Zeeman field H Z ;

From transfer-matrix calculation of localization lengths and their finite-size scaling analyses, we evaluate critical exponents of the Anderson metal-insulator transition in three dimensional (3D) orthogonal class with particle-hole symmetry, class CI, as ν = 1.16 ± 0.02. We further study disorder-driven quantum phase transitions in the 3D nodal line Dirac semimetal model, which belongs to class BDI, and estimate critical exponent as ν = 0.80 ± 0.02. From a comparison of the critical exponents, we conclude that a disorder-driven re-entrant insulator-metal transition from the topological insulator phase in the class BDI to the diffusive metal phase belongs to the same universality class as the Anderson transition in the 3D class BDI. We also argue that an infinitesimally small disorder drives the nodal line Dirac semimetal in the clean limit to the diffusive metal.arXiv:1910.10409v2 [cond-mat.dis-nn] 1 Nov 2019