On time-step bounds in unitary quantum evolution using the Lanczos method

Mohankumar, N.; Auerbach, Scott M.

doi:10.1016/j.cpc.2006.07.005

Cited by 25 publications

(15 citation statements)

References 10 publications

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“…In the presence of the external field A(t), the Hamiltonian is time dependent, Ĥ → Ĥ(t), and hence we have to solve the time dependent Schrödinger equation to evolve the state |Ψ(t) in time. For this purpose, we employ the time dependent ED method based on the Lanczos algorithm, where the time evolution with a short time step δt is calculated in the corresponding Krylov subspace generated by M L Lanczos iterations [31,32]. In our calculation, we use the finite-size clusters of L sites with periodic boundary conditions (PBC).…”

Section: Methods and Correlation Functionsmentioning

confidence: 99%

Superconductivity and charge density wave under a time-dependent periodic field in the one-dimensional attractive Hubbard model

Fujiuchi,

Kaneko,

Sugimoto

et al. 2020

Preprint

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We investigate the competition between superconductivity (SC) and charge density wave (CDW) under a time-dependent periodic field in the attractive Hubbard model. By employing the timedependent exact diagonalization method, we show that the driving frequency and amplitude of the external field can control the enhancement of either superconducting pair or CDW correlations, which are degenerate in the ground state of the attractive Hubbard model in the absence of the field. In the strong-coupling limit of the attractive Hubbard interaction, the controllability is characterized by the anisotropic interaction of the effective model. The anisotropy is induced by the external field and lifts the degeneracy of SC and CDW. We find that the enhancement or suppression of the superconducting pair and CDW correlations in the periodically-driven attractive Hubbard model can be well interpreted by the quench dynamics of the effective model derived in the strong-coupling limit.

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Section: Methods and Correlation Functionsmentioning

confidence: 99%

Superconductivity and charge density wave under a time-dependent periodic field in the one-dimensional attractive Hubbard model

Fujiuchi,

Kaneko,

Sugimoto

et al. 2020

Preprint

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“…In Table 2, we compare results obtained choosing t according to Eq. (20) and with the Park and Light [6] and the Mohankumar and Auerbach (MA) [17] criteria, for the same test problem. Both the other methods are based on the Taylor expansion of the matrix exponential.…”

Section: Calculationsmentioning

confidence: 99%

“…In this communication we propose new ideas for using the short iterative Lanczos (SIL) approach. The SIL algorithm was proposed by Park and Light [6] and has been developed by other authors [11][12][13][14][15][16][17][18]. To solve Eq.…”

Section: Introductionmentioning

confidence: 99%

A new approach for determining the time step when propagating with the Lanczos algorithm

Mohankumar¹,

Carrington²

2010

Computer Physics Communications

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“…We assume that for t = 0 the system is in the Mott insulating ground state and evolve the state forward in time usingĤ(t ), which isĤ with the time-dependent hopping. We employ the time-dependent exact diagonalization (ED) method [30,31] for a finite-size cluster with periodic boundary conditions (PBC), and the state at time t is indicated by | (t ) . For t − t 0 σ p , the resulting state is projected onto the eigenstates |ψ m (eigenenergies ε m ) of the unperturbed Hubbard model, obtained by full (exact) diagonalization.…”

mentioning

confidence: 99%

Charge stiffness and long-range correlation in the optically induced η -pairing state of the one-dimensional Hubbard model

Kaneko

Yunoki

Millis

2020

Phys. Rev. Research

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We show that optical excitation of the Mott insulating phase of the one-dimensional Hubbard model can create a state possessing two of the hallmarks of superconductivity: a nonvanishing charge stiffness and longranged pairing correlation. By employing the exact diagonalization method, we find that the superposition of the η-pairing eigenstates induced by the optical pump exhibits a nonvanishing charge stiffness and a pairing correlation that decays very slowly with system size, in sharp contrast to the behavior of an ensemble of thermally excited eigenstates, which has a vanishing charge stiffness and no long-ranged pairing correlations. We show that the charge stiffness is indeed directly associated with the η-pairing correlation in the Hubbard model. Our finding demonstrates that optical pumping can actually lead to superconducting-like properties on the basis of the η-pairing states.

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On time-step bounds in unitary quantum evolution using the Lanczos method

Cited by 25 publications

References 10 publications

Superconductivity and charge density wave under a time-dependent periodic field in the one-dimensional attractive Hubbard model

Superconductivity and charge density wave under a time-dependent periodic field in the one-dimensional attractive Hubbard model

A new approach for determining the time step when propagating with the Lanczos algorithm

Charge stiffness and long-range correlation in the optically induced η -pairing state of the one-dimensional Hubbard model

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