In order to investigate photoinduced insulator-metal transitions observed in correlated electron systems, we propose a new theoretical method, where we combine a Floquet-matrix method for AC-driven systems with the dynamical mean-field theory. The method can treat nonequilibrium steady states exactly beyond the linear-response regime. We have applied the method to the Falicov-Kimball model coupled to AC electric fields, and numerically obtained the spectral function, the nonequilibrium distribution function and the current-voltage characteristic. The results show that intense AC fields indeed drive Mott-like insulating states into photoinduced metallic states in a nonlinear way.In order to investigate photoinduced insulator-metal transitions observed in correlated electron systems, we propose a new theoretical method, where we combine a Floquet-matrix method for AC-driven systems with the dynamical mean-field theory. The method can treat nonequilibrium steady states exactly beyond the linear-response regime. We have applied the method to the Falicov-Kimball model coupled to AC electric fields, and numerically obtained the spectral function, the nonequilibrium distribution function and the current-voltage characteristic. The results show that intense AC fields indeed drive Mott-like insulating states into photoinduced metallic states in a nonlinear way.

arXiv:0907.1027Journal of Physics Conference SeriesMar 1, 20090 citations

Numerical Simulations of Quantum Many-Body Systems with Applications to Superfluid-Insulator and Metal-Insulator Transitions

Parhat Niyaz

Jun 1, 19930 citations

Anderson metal-insulator transitions with classical magnetic impurities

Daniel Jung, Stefan Kettemann, Keith Slevin

We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude ${W}_{\mathrm{c}}$ with increasing exchange coupling strength $J$ . The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.We study numerically the effects of classical magnetic impurities on the Anderson metal-insulator transition. We find that a small concentration of Heisenberg impurities enhances the critical disorder amplitude ${W}_{\mathrm{c}}$ with increasing exchange coupling strength $J$. The resulting scaling with $J$ is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.

arXiv:1507.03374Physical review. B./Physical review. BApr 5, 20164 citations

Level statistics for quantum k -core percolation

L. Cao, Jennifer M. Schwarz

Quantum $k$ -core percolation is the study of quantum transport on $k$ -core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. As the bond occupation probability $p$ is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder ${l}_{d}$ is much greater than the coherence length ${l}_{c}$ , earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for $k=3$ the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability $p$ and system size on a Bethe-like lattice. The level spacing analysis suggests that for $k=0$ , ${p}_{q}$ , the quantum percolation critical probability, is greater than ${p}_{c}$ , the geometrical percolation critical probability, and the transition is continuous. In contrast, for $k=3$ , ${p}_{q}={p}_{c}$ , and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.Quantum $k$-core percolation is the study of quantum transport on $k$-core percolation clusters where each occupied bond must have at least $k$ occupied neighboring bonds. As the bond occupation probability $p$ is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder ${l}_{d}$ is much greater than the coherence length ${l}_{c}$, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for $k=3$ the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability $p$ and system size on a Bethe-like lattice. The level spacing analysis suggests that for $k=0$, ${p}_{q}$, the quantum percolation critical probability, is greater than ${p}_{c}$, the geometrical percolation critical probability, and the transition is continuous. In contrast, for $k=3$, ${p}_{q}={p}_{c}$, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.

arXiv:1203.4599Physical Review BAug 24, 20121 citation

{W}_{\mathrm{c}}

with increasing exchange coupling strength

J

. The resulting scaling with

J

is analyzed which supports an anomalous scaling prediction by Wegner due to the combined breaking of time-reversal and spin-rotational symmetry. Moreover, we find that the presence of magnetic impurities lowers the critical correlation length exponent $\ensuremath{\nu}$ and enhances the multifractality parameter ${\ensuremath{\alpha}}_{0}$. The new value of $\ensuremath{\nu}$ improves the agreement with the value measured in experiments on the metal-insulator transition (MIT) in doped semiconductors like phosphor-doped silicon, where a finite density of magnetic moments is known to exist in the vicinity of the MIT. The results are obtained by a finite-size scaling analysis of the geometric mean of the local density of states which is calculated by means of the kernel polynomial method. We establish this combination of numerical techniques as a method to obtain critical properties of disordered systems quantitatively.

Quantum

k

-core percolation is the study of quantum transport on

k

-core percolation clusters where each occupied bond must have at least

k

occupied neighboring bonds. As the bond occupation probability

p

is increased from zero to unity, the system undergoes a transition from an insulating phase to a metallic phase. When the length scale for the disorder

{l}_{d}

is much greater than the coherence length

{l}_{c}

, earlier analytical calculations of quantum conduction on the Bethe lattice demonstrated that for

k=3

the metal-insulator transition (MIT) is discontinuous, suggesting a new type of disorder-driven quantum MITs. Here, we numerically compute the level spacing distribution as a function of bond occupation probability

p

and system size on a Bethe-like lattice. The level spacing analysis suggests that for

k=0

{p}_{q}

, the quantum percolation critical probability, is greater than

{p}_{c}

, the geometrical percolation critical probability, and the transition is continuous. In contrast, for

k=3

{p}_{q}={p}_{c}

, and the transition is discontinuous such that these numerical findings are consistent with our previous work to reiterate a new random first-order phase transition and therefore a new universality class of disorder-driven quantum MITs.