Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength $W$ increases, such a system undergoes two transitions. It first changes from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder ${W}_{c,1}$ . Another transition from the marginal metal to an insulator occurs at a stronger disorder ${W}_{c,2}$ . Through highly accurate numerical procedures based on the recursive Green's function and the exact diagonalization methods, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The conductance is described by an unorthodox one-parameter scaling law: Conductance of various system sizes and disorders collapse into two branches of a scaling curve corresponding to diffusive metal and insulating phases with an exponentially diverging correlation length, $\ensuremath{\xi}\ensuremath{\propto}exp[\ensuremath{\alpha}/\sqrt{|W\ensuremath{-}{W}_{c}|}]$, near transition points. Finite-size scaling analysis of the inverse participation ratio reveals that the states of the marginal metal are fractals of a universal fractal dimension $D=1.90\ifmmode\pm\else\textpm\fi{}0.02$, while those of the diffusive metal spread over the whole system with $D=2$ and states in the insulating phase are localized with $D=0$ . The phase diagram for diffusive metals, marginal metals, and the Anderson insulators is plotted in the disorder-magnetic-coupling plane.Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength $W$ increases, such a system undergoes two transitions. It first changes from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder ${W}_{c,1}$. Another transition from the marginal metal to an insulator occurs at a stronger disorder ${W}_{c,2}$. Through highly accurate numerical procedures based on the recursive Green's function and the exact diagonalization methods, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The conductance is described by an unorthodox one-parameter scaling law: Conductance of various system sizes and disorders collapse into two branches of a scaling curve corresponding to diffusive metal and insulating phases with an exponentially diverging correlation length, $\ensuremath{\xi}\ensuremath{\propto}exp[\ensuremath{\alpha}/\sqrt{|W\ensuremath{-}{W}_{c}|}]$, near transition points. Finite-size scaling analysis of the inverse participation ratio reveals that the states of the marginal metal are fractals of a universal fractal dimension $D=1.90\ifmmode\pm\else\textpm\fi{}0.02$, while those of the diffusive metal spread over the whole system with $D=2$ and states in the insulating phase are localized with $D=0$. The phase diagram for diffusive metals, marginal metals, and the Anderson insulators is plotted in the disorder-magnetic-coupling plane.

arXiv:1907.02213Physical review. B./Physical review. BDec 3, 201913 citations

Unconventional quantum criticality in insulators and metals

T. Senthil

Bulletin of the American Physical SocietyMar 19, 20100 citations

Quantum criticality around metal-insulator transitions of strongly correlated electron systems

Takahiro Misawa, Masatoshi Imada

Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical ``opalescence.'' The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in ${(\mathrm{V},\mathrm{Cr})}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{ET}$-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.Quantum criticality of metal-insulator transitions in correlated electron systems is shown to belong to an unconventional universality class with violation of the Ginzburg-Landau-Wilson (GLW) scheme formulated for symmetry breaking transitions. This unconventionality arises from an emergent character of the quantum critical point, which appears at the marginal point between the Ising-type symmetry breaking at nonzero temperatures and the topological transition of the Fermi surface at zero temperature. We show that Hartree-Fock approximations of an extended Hubbard model on square lattices are capable of such metal-insulator transitions with unusual criticality under a preexisting symmetry breaking. The obtained universality is consistent with the scaling theory formulated for Mott transitions and with a number of numerical results beyond the mean-field level, implying that preexisting symmetry breaking is not necessarily required for the emergence of this unconventional universality. Examinations of fluctuation effects indicate that the obtained critical exponents remain essentially exact beyond the mean-field level. It further clarifies the whole structure of singularities by a unified treatment of the bandwidth-control and filling-control transitions. Detailed analyses of the criticality, containing diverging carrier density fluctuations around the marginal quantum critical point, are presented from microscopic calculations and reveal the nature as quantum critical ``opalescence.'' The mechanism of emerging marginal quantum critical point is ascribed to a positive feedback and interplay between the preexisting gap formation present even in metals and kinetic energy gain (loss) of the metallic carrier. Analyses of crossovers between GLW type at nonzero temperature and topological type at zero temperature show that the critical exponents observed in ${(\mathrm{V},\mathrm{Cr})}_{2}{\mathrm{O}}_{3}$ and $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{ET}$-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.

arXiv:cond-mat/0612632Physical Review BMar 21, 200754 citations

Two-dimensional ferromagnetic electron gases subject to random scalar potentials and Rashba spin-orbit interactions exhibit a striking quantum criticality. As disorder strength

W

increases, such a system undergoes two transitions. It first changes from a normal diffusive metal consisting of extended states to a marginal metal consisting of critical states at a critical disorder

{W}_{c,1}

. Another transition from the marginal metal to an insulator occurs at a stronger disorder

{W}_{c,2}

. Through highly accurate numerical procedures based on the recursive Green's function and the exact diagonalization methods, we elucidate the nature of the quantum criticality and the properties of the pertinent states. The conductance is described by an unorthodox one-parameter scaling law: Conductance of various system sizes and disorders collapse into two branches of a scaling curve corresponding to diffusive metal and insulating phases with an exponentially diverging correlation length, $\ensuremath{\xi}\ensuremath{\propto}exp[\ensuremath{\alpha}/\sqrt{|W\ensuremath{-}{W}_{c}|}]$, near transition points. Finite-size scaling analysis of the inverse participation ratio reveals that the states of the marginal metal are fractals of a universal fractal dimension $D=1.90\ifmmode\pm\else\textpm\fi{}0.02$, while those of the diffusive metal spread over the whole system with

D=2

and states in the insulating phase are localized with

D=0

. The phase diagram for diffusive metals, marginal metals, and the Anderson insulators is plotted in the disorder-magnetic-coupling plane.

{(\mathrm{V},\mathrm{Cr})}_{2}{\mathrm{O}}_{3}

and $\ensuremath{\kappa}\text{\ensuremath{-}}\mathrm{ET}$-type organic conductors provide us with evidence for the existence of the present marginal quantum criticality.