Impact of Parallel Computing on Study of Time Evolution of a Quantum Impurity System in Response to a Quench
Main Article Content
Abstract
In an arbitrary system subjected to a quench or an external field that varies the system parameters, the degrees of freedom increase double in comparison to that of an isolated system. In this study, we consider the quantum impurity system subjected to a quench, and measure the corresponding time-evolution of the spectral function, which is originated from the time-resolved photoemission spectroscopy. Due to the large number of degrees of freedom, the expression of the time-dependent spectral function is twice much more complicated than that of the time-independent spectral function, and therefore the calculation is extremely time-consuming. In this paper, we estimate the scale of time consumption of such calculation in comparison to that of time-independent calculation, and present our solution to the problem by using parallel computing as implementing both MPI and OpenMP to the calculation. We also discuss the possibility to exploit parallel computing with GPU in the near future, and the preliminary results of time-dependent spectral function.
References
https://doi.org/10.1103/PhysRev.124.41.
[2] J. Kondo, Resistance Minimum in Dilute Magnetic Alloys, Progress of Theoretical Physics. 32 (1964) 37–49.
https://doi.org/10.1143/PTP.32.37.
[3] K. Wilson, The renormalization group: Critical phenomena and the Kondo problem, Reviews of Modern Physics. 47 (1975) 773. https://doi.org/10.1103/RevModPhys.47.773.
[4] D.L. Cox, A. Zawadowski, Exotic Kondo Effects in Metals: Magnetic Ions in a Crystalline Electric Field and Tunneling Centers, Advances in Physics 47 (1998) 599-942. https://doi.org/10.1080/000187398243500.
[5] D. Pesin, L. Balent, Mott physics and band topology in materials with strong spin–orbit interaction, Nature Physics 6 (2010) 376–381. https://doi.org/10.1038/nphys1606.
[6] H. Aoki, N. Tsuji, M. Eckstein, M. Kollar, T. Oka, P. Werner, Nonequilibrium dynamical mean-field theory and its applications, Reviews of Modern Physics 86 (2014) 779. https://doi.org/10.1103/RevModPhys.86.779.
[7] J.K. Freericks, H.R. Krishnamurthy, T. Pruschke, Theoretical Description of Time-Resolved Photoemission Spectroscopy: Application to Pump-Probe Experiments, Physical Review Letters 83 (2009) 808. https://doi.org/10.1103/PhysRevLett.102.136401.
[8] F. Randi, D. Fausti, M. Eckstein, Bypassing the energy-time uncertainty in time-resolved photoemission, Physical Review B 95 (2017) 115132. https://doi.org/10.1103/PhysRevB.95.115132.
[9] H.T.M. Nghiem, T.A. Costi, Generalization of the time-dependent numerical renormalization group method to finite temperatures and general pulses, Physical Review B 89 (2014) 075118.
https://doi.org/10.1103/PhysRevB.89.075118.
[10] H.T.M. Nghiem, T.A. Costi, Time evolution of the Kondo resonance in response to a quench. Physical Review Letters 119 (2017) 156601. https://doi.org/10.1103/PhysRevLett.119.156601.
[11] H.T.M Nghiem, H.T. Dang, T.A. Costi, Time-dependent spectral functions of the Anderson impurity model in response to a quench and application to time-resolved photoemission spectroscopy, arXiv:1912.08474. https://arxiv.org/abs/1912.08474.
[12] A. Weichselbaum, J. von Delft, Sum-rule conserving spectral functions from the numerical renormalization group, Physical Review Letters 99 (2007) 076402. https://doi.org/10.1103/PhysRevLett.99.076402.
[13] T.A. Costi, V. Zlatić, Thermoelectric transport through strongly correlated quantum dots, Physical Review B 81 (2010) 235127. https://doi.org/10.1103/PhysRevB.81.235127.
[14] G.M. Amdahl, Validity of the single processor approach to achieving large scale computing capabilities. Proceedings of the April 18-20, 1967, Spring joint computer conference. ACM, 1967, 483-485. https://doi.org/10.1145/1465482.1465560.