Gradient-based stochastic estimation of the density matrix

Wang, Zhentao; Chern, Gia-Wei; Batista, Cristian D.; Barros, Kipton

doi:10.1063/1.5017741

Cited by 39 publications

(40 citation statements)

References 62 publications

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“…Note that QLLD requires solution of the equilibrium density matrixρ (0) at every timestep, in analogy to Born-Oppenheimer quantum molecular dynamics [45]. Rather than direct diagonalization of H BdG , we use the kernel polynomial method [46,47] with gradient-based probing [48,49] to estimateρ (0) , and thus effective forces, at a cost that scales linearly with system size.…”

mentioning

confidence: 99%

Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Chern

Barros

2019

Phys. Rev. B

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We present a framework of semiclassical superconductivity (SC) dynamics that properly includes effects of spatial fluctuations for the attractive Hubbard model. We consider both coherent and adiabatic limits. To model the coherent SC dynamics, we develop a real-space von Neumann equation based on the time-dependent Hartree-Fock-Bogoliubov theory. Applying our method to interaction quenches in the negative-U Hubbard model, we show that the relaxation of SC order at weak coupling is dominated by Landau-damping. At strong coupling, we find a two-stage relaxation of the pairing field: a collapse of the synchronized oscillation of Cooper pairs due to spatial inhomogeneity, followed by a slow relaxation to a quasi-stationary state. SC dynamics in adiabatic limit is described by a quantum Landau-Lifshitz equation with Ginzburg-Landau relaxation. Numerical simulations of the pump-probe process show that long time recovery of the pairing field is dominated by defects dynamics. Our results demonstrate the important role of spatial fluctuations in both limits.The nonequilibrium dynamics of superconductivity (SC) subject to an external stimulation has been intensively studied for some time [1][2][3][4][5][6][7][8]. This interest has recently been renewed by remarkable pump-probe experiments reporting the observation of the collective amplitude mode [9,10]. Prior work largely studies two physical limits determined by the relation between the quasiparticle relaxation time τ and the relaxation time τ ∆ of SC order parameter. The SC dynamics in the collisionless limit, τ τ ∆ , can be described using a timedependent self-consistent field approach. An interesting phenomenon in this regime is the collective Rabi oscillations of the order parameter [3,4]. In the opposite, adiabatic limit, τ τ ∆ , the dynamics of the pairing field is usually described by time-dependent Ginzburg-Landau (TDGL) equation [11,12]. TDGL has recently been employed to simulate the out-of-equilibrium dynamics of superconductors in pump-probe experiments [13,14].Numerical simulations based on TDGL also provide useful insights on the dynamical inhomogeneity of nonequilibrium superconductivity [15,16], for example, the formation of topological defects by rapid thermal quenches as described in the Kibble-Zurek scenario [17,18]. However, contrary to numerous large-scale TDGL simulation studies, effects of spatial fluctuations in the collisionless limit are rarely addressed in most numerical studies, even though earlier calculations [19,20] have demonstrated dramatic effects of spatial inhomogeneity in out-of-equilibrium superconductivity.In this paper, we present a theoretical framework for SC dynamics that properly includes the effects of spatial fluctuations in both the collisionless and adiabatic limits. To model the collisionless (coherent) limit, we develop a real-space formulation of the time-dependent Hartree-Fock-Bogoliubov (TDHFB) theory, which is particularly suitable for the negative-U Hubbard model. Numerical solution shows two distinct dynamical regim...

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confidence: 99%

Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Chern

Barros

2019

Phys. Rev. B

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“…Here F (ε − µ) is the free energy of the system, and ρ(ε, {S i }) is the density of state of conduction electrons for a given set of the local magnetizations {S i }. To calculate Ω and its magnetization-derivatives ∂Ω/∂S i , we adopt the kernel polynomial method, which is based on the Chebyshev polynomial expansion of Ω and the automatic differentiation [89][90][91][92][93][94][95].…”

Section: Methodsmentioning

confidence: 99%

“…For the simulations, a lattice with N = 36 2 sites, on which periodic boundary conditions are imposed, is adopted. We use 324 correlated random vectors [95,96] for simulating relaxation dynamics to obtain initial magnetic configurations through minimizing the energy, whereas we adopt complete orthonormal basis states for the simulations of microwave-induced dynamics. We use Chebyshev polynomials up to the 2000th-order for the expansion of Ω and adopt the fourthorder Runge-Kutta method with a time slice of ∆t = 4 to solve the LLG equation in Eq.…”

Section: Methodsmentioning

confidence: 99%

Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet

Eto,

Mochizuki

2021

Preprint

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We theoretically demonstrate microwave-induced dynamical switching of magnetic topology in centrosymmetric itinerant magnets by taking the Kondo-lattice model on a triangular lattice, which is known to exhibit two types of skyrmion lattices with different magnetic topological charges of |N sk |=1 and |N sk |=2. Our numerical simulations reveal that intense excitation of a resonance mode with circularly polarized microwave field can switch the magnetic topology, i.e., from the skyrmion lattice with |N sk |=1 to another skyrmion lattice with |N sk |=2 or to a nontopological magnetic order with |N sk |=0 depending on the microwave frequency. This magnetic-topology switching shows various distinct behaviors, that is, deterministic irreversible switching, probabilistic irreversible switching, and temporally random fluctuation depending on the microwave frequency and the strength of external magnetic field, variety of which is attributable to different energy landscapes in the dynamical regime. The obtained results are also discussed in the light of time-evolution equations based on an effective model derived using perturbation expansions.

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“…This analysis suggests that increasing accuracy requirements will cause local calculations to be more efficient than random calculations, especially at high temperatures or for insulators. However, this outcome depends on R i , and there are efficient alternatives to the random-phase vector ensemble [21].…”

Section: Random Approximationmentioning

confidence: 99%

Assessment of localized and randomized algorithms for electronic structure

Moussa

Baczewski

2019

Electron. Struct.

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As electronic structure simulations continue to grow in size, the system-size scaling of computational costs increases in importance relative to cost prefactors. Presently, linear-scaling costs for three-dimensional systems are only attained by localized or randomized algorithms that have large cost prefactors in the difficult regime of low-temperature metals. Using large copper clusters in a minimal-basis semiempirical model as our reference system, we study the costs of these algorithms relative to a conventional cubic-scaling algorithm using matrix diagonalization and a recent quadratic-scaling algorithm using sparse matrix factorization and rational function approximation. The linear-scaling algorithms are competitive at the high temperatures relevant for warm dense matter, but their cost prefactors are prohibitive near ambient temperatures. To further reduce costs, we consider hybridized algorithms that combine localized and randomized algorithms. While simple hybridized algorithms do not improve performance, more sophisticated algorithms using recent concepts from structured linear algebra show promising initial performance results on a simple-cubic orthogonal tight-binding model.

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Gradient-based stochastic estimation of the density matrix

Cited by 39 publications

References 62 publications

Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Nonequilibrium dynamics of superconductivity in the attractive Hubbard model

Dynamical Switching of Magnetic Topology in Microwave-Driven Itinerant Magnet

Assessment of localized and randomized algorithms for electronic structure

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