Efficient non-Markovian quantum dynamics using time-evolving matrix product operators
Tóm tắt
Từ khóa
Tài liệu tham khảo
Breuer, H. -P. & Petruccione, F. The Theory of Open Quantum Systems (Oxford University Press, Oxford, 2002).
de Vega, I. & Alonso, D. Dynamics of non-Markovian open quantum systems. Rev. Mod. Phys. 89, 015001 (2017).
Gröblacher, S. et al. Observation of non-Markovian micromechanical brownian motion. Nat. Commun. 6, 7606 (2015).
Madsen, K. H. et al. Observation of non-Markovian dynamics of a single quantum dot in a micropillar cavity. Phys. Rev. Lett. 106, 233601 (2011).
Mi, X., Cady, J. V., Zajac, D. M., Deelman, P. W. & Petta, J. R. Strong coupling of a single electron in silicon to a microwave photon. Science 355, 156–158 (2017).
Potočnik, A. et al. Studying light-harvesting models with superconducting circuits. Nat. Commun. 9, 904 (2018).
Aharonovich, I., Englund, D. & Toth, M. Solid-state single-photon emitters. Nat. Photon. 10, 631–641 (2016).
Chin, A. W. et al. The role of non-equilibrium vibrational structures in electronic coherence and recoherence in pigment–protein complexes. Nat. Phys. 9, 113–118 (2013).
Lee, M. K., Huo, P. & Coker, D. F. Semiclassical path integral dynamics: photosynthetic energy transfer with realistic environment interactions. Annu. Rev. Phys. Chem. 67, 639–668 (2016).
Barford, W. Electronic and Optical Properties of Conjugated Polymers (Oxford University Press, Oxford, 2013).
McCutcheon, D. P. S., Dattani, N. S., Gauger, E. M., Lovett, B. W. & Nazir, A. A general approach to quantum dynamics using a variational master equation: application to phonon-damped rabi rotations in quantum dots. Phys. Rev. B 84, 081305 (2011).
McCutcheon, D. P. S. & Nazir, A. Coherent and incoherent dynamics in excitonic energy transfer: correlated fluctuations and off-resonance effects. Phys. Rev. B 83, 165101 (2011).
Kaer, P., Nielsen, T. R., Lodahl, P., Jauho, A.-P. & Mørk, J. Non-Markovian model of photon-assisted dephasing by electron–phonon interactions in a coupled quantum-dot–cavity system. Phys. Rev. Lett. 104, 157401 (2010).
Roy, C. & Hughes, S. Influence of electron–acoustic-phonon scattering on intensity power broadening in a coherently driven quantum-dot–cavity system. Phys. Rev. X 1, 021009 (2011).
Segal, D. & Agarwalla, B. K. Vibrational heat transport in molecular junctions. Annu. Rev. Phys. Chem. 67, 185–209 (2016).
Subotnik, J. E. et al. Understanding the surface hopping view of electronic transitions and decoherence. Annu. Rev. Phys. Chem. 67, 387–417 (2016).
Bylicka, B., Chruściński, D. & Maniscalco, S. Non-Markovianity and reservoir memory of quantum channels: a quantum information theory perspective. Sci. Rep. 4, 5720 (2014).
Xiang, G.-Y. et al. Entanglement distribution in optical fibers assisted by nonlocal memory effects. Phys. Lett. 107, 54006 (2014).
Jang, S. Theory of coherent resonance energy transfer for coherent initial condition. J. Chem. Phys. 131, 164101 (2009).
Cohen, G., Gull, E., Reichman, D. R. & Millis, A. J. Taming the dynamical sign problem in real-time evolution of quantum many-body problems. Phys. Rev. Lett. 115, 266802 (2015).
Chen, H.-T., Cohen, G. & Reichman, D. R. Inchworm Monte Carlo for exact non-adiabatic dynamics. ii. Benchmarks and comparison with established methods. J. Chem. Phys. 146, 054106 (2017).
Yoshitaka, T. & Kubo, R. Time evolution of a quantum system in contact with a nearly Gaussian-Markoffian noise bath. J. Phys. Soc. Jpn. 58, 101–114 (1989).
Garraway, B. M. Non-perturbative decay of an atomic system in a cavity. Phys. Rev. A 55, 2290–2303 (1997).
Iles-Smith, J., Lambert, N. & Nazir, A. Environmental dynamics, correlations, and the emergence of noncanonical equilibrium states in open quantum systems. Phys. Rev. A 90, 032114 (2014).
Schröder, F. A. Y. N. et al. Multi-dimensional tensor network simulation of open quantum dynamics in singlet fission. Preprint at https://arxiv.org/abs/1710.01362 (2017).
Makri, N. & Makarov, D. E. Tensor propagator for iterative quantum time evolution of reduced density matrices. I. Theory. J. Chem. Phys. 102, 4600 (1995).
Makri, N. & Makarov, D.E. Tensor propagator for iterative quantum time evolution of reduced density matrices. II. Numerical methodology. J. Chem. Phys. 102, 4611 (1995).
Leggett, A. J. et al. Dynamics of the dissipative two-state system. Rev. Mod. Phys. 59, 1–85 (1987).
Nalbach, P., Ishizaki, A., Fleming, G. R. & Thorwart, M. Iterative path-integral algorithm versus cumulant time-nonlocal master equation approach for dissipative biomolecular exciton transport. N. J. Phys. 13, 063040 (2011).
Thorwart, M., Eckel, J. & Mucciolo, E. R. Non-Markovian dynamics of double quantum dot charge qubits due to acoustic phonons. Phys. Rev. B 72, 235320 (2005).
Sim, E. Quantum dynamics for a system coupled to slow baths: on-the-fly filtered propagator method. J. Chem. Phys. 115, 4450–4456 (2001).
Lambert, R. & Makri, N. Memory propagator matrix for long-time dissipative charge transfer dynamics. Mol. Phys. 110, 1967–1975 (2012).
Schollwöck, U. The density-matrix renormalization group in the age of matrix product states. Ann. Phys. (NY) 326, 96–192 (2011).
Orús, R. A practical introduction to tensor networks: matrix product states and projected entangled pair states. Ann. Phys. (NY) 349, 117–158 (2014).
White, S. R. Density matrix formulation for quantum renormalization groups. Phys. Rev. Lett. 69, 2863–2866 (1992).
Derrida, B., Evans, M. R., Hakim, V. & Pasquier, V. Exact solution of a 1d asymmetric exclusion model using a matrix formulation. J. Phys. A 26, 1493 (1993).
Vidal, G. Efficient classical simulation of slightly entangled quantum computations. Phys. Rev. Lett. 91, 147902 (2003).
Florens, S., Venturelli, D. & Narayanan, R. in Quantum Quenching, Annealing and Computation (eds Chandra, A. K., et al.) 145–162 (Springer, Berlin, Heidelberg, 2010).
Le Hur, K. in Understanding Quantum Phase Transitions (ed. Carr, L.) (CRC Press, New York, 2010)
Bulla, R., Tong, N.-H. & Vojta, M. Numerical renormalization group for bosonic systems and application to the sub-ohmic spin-boson model. Phys. Rev. Lett. 91, 170601 (2003).
Kessler, E. M. et al. Dissipative phase transition in a central spin system. Phys. Rev. A 86, 012116 (2012).
Orth, P. P., Roosen, D., Hofstetter, W. & Le Hur, K. Dynamics, synchronization, and quantum phase transitions of two dissipative spins. Phys. Rev. B 82, 144423 (2010).
Winter, A. & Rieger, H. Quantum phase transition and correlations in the multi-spin-boson model. Phys. Rev. B 90, 224401 (2014).
McCutcheon, D. P. S., Nazir, A., Bose, S. & Fisher, A.J. Separation-dependent localization in a two-impurity spin-boson model. Phys. Rev. B 81, 235321 (2010).
Nalbach, P., Eckel, J. & Thorwart, M. Quantum coherent biomolecular energy transfer with spatially correlated fluctuations. N. J. Phys. 12, 065043 (2010).
Johnson, T. H., Elliott, T. J., Clark, S. R. & Jaksch, D. Capturing exponential variance using polynomial resources: applying tensor networks to non-equilibrium stochastic processes. Phys. Rev. Lett. 114, 090602 (2015).
Oseledets, I. V. Tensor-train decomposition. J. Sci. Comput. 33, 2295–2317 (2011).
Stoudenmire, E. & Schwab, D. J. in Advances in Neural Information Processing Systems 29 (eds. Lee, D. D. et al.) 4799–4807 (Curran Associates, Red Hook, 2016).
Ferris, A. J. & Vidal, G. Perfect sampling with unitary tensor networks. Phys. Rev. B 85, 165146 (2012).
Guo, C., Weichselbaum, A., von Delft, J. & Vojta, M. Critical and strong-coupling phases in one- and two-bath spin-boson models. Phys. Rev. Lett. 108, 160401 (2012).
Cerrillo, J. & Cao, J. Non-Markovian dynamical maps: numerical processing of open quantum trajectories. Phys. Rev. Lett. 112, 110401 (2014).
Barth, A. M., Vagov, A. & Axt, V. M. Path-integral description of combined Hamiltonian and non-Hamiltonian dynamics in quantum dissipative systems. Phys. Rev. B 94, 125439 (2016).
Suzuki, M. Generalized Trotter’s formula and systematic approximants of exponential operators and inner derivations with applications to many-body problems. Comm. Math. Phys. 51, 183–190 (1976).
Stoudenmire, E. M. & White, S. R. Minimally entangled typical thermal state algorithms. N. J. Phys. 12, 055026 (2010).
Cygorek, M., Barth, A. M., Ungar, F., Vagov, A. & Axt, V. M. Nonlinear cavity feeding and unconventional photon statistics in solid-state cavity QED revealed by many-level real-time path-integral calculations. Phys. Rev. B 96, 201201 (2017).
Vagov, A., Croitoru, M. D., Glässl, M., Axt, V. M. & Kuhn, T. Real-time path integrals for quantum dots: quantum dissipative dynamics with superohmic environment coupling. Phys. Rev. B 83, 094303 (2011).
Strathearn, A., Lovett, B. W. & Kirton, P. Efficient real-time path integrals for non-Markovian spin-boson models. N. J. Phys. 19, 093009 (2017).