Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport

Schiró, Marco; Fabrizio, Michele

doi:10.1103/physrevb.79.153302

Cited by 168 publications

(199 citation statements)

References 34 publications

(34 reference statements)

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“…The interaction expansion based on Eq. (148) is equivalent to the auxiliary field algorithms described by Gull et al (2008) and Werner, Oka, and Millis (2009), as was shown by Mikelsons, Macridin, and Jarrell (2009 (Mühlbacher and Rabani, 2008;Schiró and Fabrizio, 2009;Werner, Oka, and Millis, 2009). We sketch here the derivation for the general impurity model defined in Eq.…”

Section: B Weak-coupling Ctqmcmentioning

confidence: 99%

“…This sharp crossover was unexpected because the corresponding equilibrium temperature T eff after the quench is much higher than the critical end point of the Mott metal-insulator transition in equilibrium [T c ≈ 0.055 (Georges et al, 1996), but T eff ¼ 0.84 for U ¼ 3.3]. Interestingly, a good approximation for the critical interaction U dyn c ≈ 3.4 is obtained from a timedependent variational theory using the Gutzwiller approximation Fabrizio, 2010, 2011). A similar strong dependence on the quenched interaction was observed in Heisenberg chains (Barmettler et al, 2009).…”

Section: Interaction Quench In the Hubbard Model Prethermalizatiomentioning

confidence: 99%

“…correlated Mott and charge-transfer insulators (Ogasawara et al, 2000;Iwai et al, 2003;Perfetti et al, 2006;Kübler et al, 2007;Okamoto et al, , 2008, the pump-induced melting and recovery of charge density waves (Schmitt et al, 2008;Hellmann et al, 2010;Petersen et al, 2011) with studies combining structural and electronic dynamics (Eichberger et al, 2010), and ultrafast dynamics induced in ferromagnets (Beaurepaire et al, 1996) or antiferromagnets (Ehrke et al, 2011), to name only a few.…”

Section: B Physical Backgroundmentioning

confidence: 99%

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Nonequilibrium dynamical mean-field theory and its applications

et al. 2014

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The study of nonequilibrium phenomena in correlated lattice systems has developed into one of the most active and exciting branches of condensed matter physics. This research field provides rich new insights that could not be obtained from the study of equilibrium situations, and the theoretical understanding of the physics often requires the development of new concepts and methods. On the experimental side, ultrafast pump-probe spectroscopies enable studies of excitation and relaxation phenomena in correlated electron systems, while ultracold atoms in optical lattices provide a new way to control and measure the time evolution of interacting lattice systems with a vastly different characteristic time scale compared to electron systems. A theoretical description of these phenomena is challenging because, first, the quantum-mechanical time evolution of many-body systems out of equilibrium must be computed and second, strong-correlation effects which can be of a nonperturbative nature must be addressed. This review discusses the nonequilibrium extension of the dynamical mean field theory (DMFT), which treats quantum fluctuations in the time domain and works directly in the thermodynamic limit. The method reduces the complexity of the calculation via a mapping to a selfconsistent impurity problem, which becomes exact in infinite dimensions. Particular emphasis is placed on a detailed derivation of the formalism, and on a discussion of numerical techniques, which enable solutions of the effective nonequilibrium DMFT impurity problem. Insights gained into the properties of the infinite-dimensional Hubbard model under strong nonequilibrium conditions are summarized. These examples illustrate the current ability of the theoretical framework to reproduce and understand fundamental nonequilibrium phenomena, such as the dielectric breakdown of Mott insulators, photodoping, and collapse-and-revival oscillations in quenched systems. Furthermore, remarkable novel phenomena have been predicted by the nonequilibrium DMFT simulations of correlated lattice systems, including dynamical phase transitions and field-induced repulsion-to-attraction conversions.

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Section: B Weak-coupling Ctqmcmentioning

confidence: 99%

Section: Interaction Quench In the Hubbard Model Prethermalizatiomentioning

confidence: 99%

Section: B Physical Backgroundmentioning

confidence: 99%

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Nonequilibrium dynamical mean-field theory and its applications

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“…These shortcomings have motivated us to develop a systematic, numerically exact methodology to study quantum dynamics and quantum transport including many-body effects, in particular, correlated electronic-nuclear dynamics-the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory in second quantization representation (SQR). 79 Other efforts along the same direction include the numerical path integral approach, [80][81][82] real-time quantum Monte Carlo simulations, 83,84 the numerical renormalization group approach, 85 and the time-dependent density matrix renormalization group approach. 86 For a comparison and an overview of various different methods in the related problem of nonequilibrium transport with electron-electron interaction, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

Wang

Pshenichnyuk

Härtle

et al. 2011

The Journal of Chemical Physics

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The multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) theory within second quantization representation of the Fock space, a novel numerically exact methodology to treat manybody quantum dynamics for systems containing identical particles, is applied to study the effect of vibrational motion on electron transport in a generic model for single-molecule junctions. The results demonstrate the importance of electronic-vibrational coupling for the transport characteristics. For situations where the energy of the bridge state is located close to the Fermi energy, the simulations show the time-dependent formation of a polaron state that results in a pronounced suppression of the current corresponding to the phenomenon of phonon blockade. We show that this phenomenon cannot be explained solely by the polaron shift of the energy but requires methods that incorporate the dynamical effect of the vibrations on the transport. The accurate results obtained with the ML-MCTDH in this parameter regime are compared to results of nonequilibrium Green's function theory.

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“…Though much is known for quantum impurity systems in equilibrium, understanding their properties in non-equilibrium steady-state is still limited. Nevertheless, significant progress has been made by different approaches, such as (1) analytical approximations: perturbative renormalization group method (RG) 27,28 , Hamiltonian flow equations 29 , functional RG 30,31 , strong-coupling expansions 32 , master equations 33 ; (2) exact analytical solutions: field theory techniques 34 , the scattering Bethe Ansatz 35 , mapping of a steady-state non-equilibrium problem onto an effective equilibrium system [36][37][38][39] , non-linear response theory approach to current fluctuations 40 ; (3) numerical methods: time-dependent density matrix renormalization group (RG) 41 , time-dependent numerical RG 42 , diagrammatic Monte Carlo 43 , and imaginary-time nonequilibrium quantum Monte Carlo 44 .…”

Section: Introductionmentioning

confidence: 99%

Nonequilibrium quantum transport through a dissipative resonant level

Chung¹,

Hur

Finkelstein

et al. 2013

Phys. Rev. B

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The resonant-level model represents a paradigmatic quantum system which serves as a basis for many other quantum impurity models. We provide a comprehensive analysis of the non-equilibrium transport near a quantum phase transition in a spinless dissipative resonant-level model, extending earlier work [Phys. Rev. Lett. 102, 216803 (2009)]. A detailed derivation of a rigorous mapping of our system onto an effective Kondo model is presented. A controlled energy-dependent renormalization group approach is applied to compute the non-equilibrium current in the presence of a finite bias voltage V . In the linear response regime V → 0, the system exhibits as a function of the dissipative strength a localized-delocalized quantum transition of the Kosterlitz-Thouless (KT) type. We address fundamental issues of the non-equilibrium transport near the quantum phase transition: Does the bias voltage play the same role as temperature to smear out the transition? What is the scaling of the non-equilibrium conductance near the transition? At finite temperatures, we show that the conductance follows the equilibrium scaling for V < T , while it obeys a distinct non-equilibrium profile for V > T . We furthermore provide new signatures of the transition in the finite-frequency current noise and AC conductance via a recently developed functional renormalization group (FRG) approach. The generalization of our analysis to non-equilibrium transport through a resonant level coupled to two chiral Luttinger-liquid leads, generated by fractional quantum Hall edge states, is discussed. Our work on the dissipative resonant level has direct relevance to experiments on a quantum dot coupled to a resistive environment, such as H. Mebrahtu et al., Nature 488, 61, (2012).

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Real-time diagrammatic Monte Carlo for nonequilibrium quantum transport

Cited by 168 publications

References 34 publications

Nonequilibrium dynamical mean-field theory and its applications

Nonequilibrium dynamical mean-field theory and its applications

Numerically exact, time-dependent treatment of vibrationally coupled electron transport in single-molecule junctions

Nonequilibrium quantum transport through a dissipative resonant level

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