Iterative blip-summed path integral for quantum dynamics in strongly dissipative environments

Improved memory truncation scheme for quasi-adiabatic propagator path integral via influence functional renormalization

Accurately simulating non-Markovian quantum dynamics in system-bath coupled problems remains challenging. In this work, we present a novel memory truncation scheme for the iterative quasi-adiabatic propagator path integral (iQuAPI) method to improve accuracy. Conventional memory truncation in iQuAPI discards all influence functional beyond a certain time interval, which is not effective for problems with a long memory time. Our proposed scheme selectively retains the most significant parts of the influence functional using the density matrix renormalization group algorithm. We validate the effectiveness of our scheme through simulations of the spin-boson model across various parameter sets, demonstrating faster convergence and improved accuracy compared to the conventional scheme. Our findings suggest that the new memory truncation scheme significantly advances the capabilities of iQuAPI for problems with a long memory time.

Small Matrix Quantum-Classical Path Integral

The quantum-classical path integral (QCPI) is a rigorous formulation of nonadiabatic dynamics, where the dynamical interaction between a quantum system and its environment is captured consistently through classical trajectories driven by forces along quantum paths of the system. In this Letter, we develop a small matrix decomposition (SMatQCPI) that eliminates the tensor storage requirements of the iterative QCPI algorithm. In the case of a system coupled to a harmonic bath, SMatQCPI provides fully quantum mechanical propagation, which also reduces the computational cost to that of a single QCPI step. Further, the SMatQCPI matrices only need to account for quantum contributions to decoherence, allowing high efficiency in challenging regimes of incoherent dynamics. Overall, this new composite algorithm combines the best features of two powerful path integral formulations and offers a versatile tool for simulating condensed phase quantum dynamics.

Intramolecular Vibrations in Excitation Energy Transfer: Insights from Real-Time Path Integral Calculations

Excitation energy transfer (EET) is fundamental to many processes in chemical and biological systems and carries significant implications for the design of materials suitable for efficient solar energy harvest and transport. This review discusses the role of intramolecular vibrations on the dynamics of EET in nonbonded molecular aggregates of bacteriochlorophyll, a perylene bisimide, and a model system, based on insights obtained from fully quantum mechanical real-time path integral results for a Frenkel exciton Hamiltonian that includes all vibrational modes of each molecular unit at finite temperature. Generic trends, as well as features specific to the vibrational characteristics of the molecules, are identified. Weak exciton-vibration (EV) interaction leads to compact, near-Gaussian densities on each electronic state, whose peak follows primarily a classical trajectory on a torus, while noncompact densities and nonlinear peak evolution are observed with strong EV coupling. Interaction with many intramolecular modes and increasing aggregate size smear, shift, and damp these dynamical features. Expected final online publication date for the Annual Review of Physical Chemistry, Volume 73 is April 2022. Please see http://www.annualreviews.org/page/journal/pubdates for revised estimates.

A multisite decomposition of the tensor network path integrals

Tensor network decompositions of path integrals for simulating open quantum systems have recently been proven to be useful. However, these methods scale exponentially with the system size. This makes it challenging to simulate the non-equilibrium dynamics of extended quantum systems coupled with local dissipative environments. In this work, we extend the tensor network path integral (TNPI) framework to efficiently simulate such extended systems. The Feynman-Vernon influence functional is a popular approach used to account for the effect of environments on the dynamics of the system. In order to facilitate the incorporation of the influence functional into a multisite framework (MS-TNPI), we combine a matrix product state (MPS) decomposition of the reduced density tensor of the system along the sites with a corresponding tensor network representation of the time axis to construct an efficient 2D tensor network. The 2D MS-TNPI network, when contracted, yields the time-dependent reduced density tensor of the extended system as an MPS. The algorithm presented is independent of the system Hamiltonian. We outline an iteration scheme to take the simulation beyond the non-Markovian memory introduced by solvents. Applications to spin chains coupled to local harmonic baths are presented; we consider the Ising, XXZ, and Heisenberg models, demonstrating that the presence of local environments can often dissipate the entanglement between the sites. We discuss three factors causing the system to transition from a coherent oscillatory dynamics to a fully incoherent dynamics. The MS-TNPI method is useful for studying a variety of extended quantum systems coupled with solvents.

Small Matrix Path Integral for Driven Dissipative Dynamics

The small matrix decomposition of the quasi-adiabatic propagator path integral (SMatPI) for a system coupled to a harmonic bath, which accounts for multitime memory correlations in the influence functional without the use of tensors, is extended to include a time-dependent term that drives the system. In the case of a periodic field, the algorithm requires the construction of SMatPI matrices initialized over a short time interval. The SMatPI algorithm circumvents the large array storage of tensor-based iterative path integral decompositions and, in the case of a periodic field, also eliminates the demanding tensor multiplication at each time step, leading to dramatic savings which allow the fully quantum mechanical treatment of multistate systems and long-memory environments.

Time Evolution of Bath Properties in Spin-Boson Dynamics

The dynamical behaviors of a two-level system (TLS) coupled to a harmonic dissipative bath has been studied extensively using a variety of analytical and numerical methods. The focus of the vast majority of these studies has been on the properties of the TLS, averaged with respect to the bath degrees of freedom. In this work, we use real-time path integral methods to probe the behavior of select bath degrees of freedom during the dynamics of a symmetric two-level system (TLS) coupled to a dissipative bath by calculating system-bath densities (SBD) and coordinate expectation values. Overall, the SBD motion on each diabatic state is simpler than the motion of the total density. In the weak coupling regime, which characterizes the parameters of oscillators that comprise such a bath, the SBD on each TLS state remains primarily compact and Gaussian-like, such that its peak is well characterized by the mode expectation value. In the absence of a dissipative environment, nonadiabatic density depletion leads to spikes in coordinate expectation values. The evolution of the SBD peak trajectory for two discrete modes exhibits Lissajous patterns with frequency-dependent shapes that strongly resemble classical trajectory motion on a torus. These patterns become more complex when the coupling of the mode to the TLS is increased outside of this regime, leading to persistent small amplitude oscillations in the TLS populations characterized by a very slow decay and SBD trajectories that exhibit behaviors reminiscent of chaotic classical systems. Indirect coupling to a dissipative bath has a stabilizing effect on the dynamics, eliminating spikes, synchronizing the SBD motion on the two diabatic states and regularizing the SBD trajectory to simple rectangular Lissajous-like shapes with a slowly shrinking boundary, regardless of the mode frequencies.

Density matrix and purity evolution in dissipative two-level systems: I. Theory and path integral results for tunneling dynamics

The time evolution of the purity (the trace of the square of the reduced density matrix) and von Neumann entropy in a symmetric two-level system coupled to a dissipative harmonic bath is investigated through analytical arguments and accurate path integral calculations on simple models and the singly excited bacteriochlorophyll dimer. A simple theoretical analysis establishes bounds and limiting behaviors. The contributions to purity from a purely incoherent term obtained from the diagonal elements of the reduced density matrix, a term associated with the difference of the two eigenstate populations, and a third term related to the square of the time derivative of a site population, are discussed in various regimes. In the case of tunneling dynamics from a localized initial condition, the complex interplay among these contributions leads to the recovery of purity under low-temperature, weakly dissipative conditions. Memory effects from the bath are found to play a critical role to the dynamics of purity. It is shown that the strictly quantum mechanical decoherence process associated with spontaneous phonon emission is responsible for the long-time recovery of purity. These analytical and numerical results show clearly that the loss of quantum coherence during the evolution toward equilibrium does not necessarily imply the decay of purity, and that the time scales relevant to these two processes may be entirely different.

Quantum Information and Algorithms for Correlated Quantum Matter

Discoveries in quantum materials, which are characterized by the strongly quantum-mechanical nature of electrons and atoms, have revealed exotic properties that arise from correlations. It is the promise of quantum materials for quantum information science superimposed with the potential of new computational quantum algorithms to discover new quantum materials that inspires this Review. We anticipate that quantum materials to be discovered and developed in the next years will transform the areas of quantum information processing including communication, storage, and computing. Simultaneously, efforts toward developing new quantum algorithmic approaches for quantum simulation and advanced calculation methods for many-body quantum systems enable major advances toward functional quantum materials and their deployment. The advent of quantum computing brings new possibilities for eliminating the exponential complexity that has stymied simulation of correlated quantum systems on high-performance classical computers. Here, we review new algorithms and computational approaches to predict and understand the behavior of correlated quantum matter. The strongly interdisciplinary nature of the topics covered necessitates a common language to integrate ideas from these fields. We aim to provide this common language while weaving together fields across electronic structure theory, quantum electrodynamics, algorithm design, and open quantum systems. Our Review is timely in presenting the state-of-the-art in the field toward algorithms with nonexponential complexity for correlated quantum matter with applications in grand-challenge problems. Looking to the future, at the intersection of quantum information science and algorithms for correlated quantum matter, we envision seminal advances in predicting many-body quantum states and describing excitonic quantum matter and large-scale entangled states, a better understanding of high-temperature superconductivity, and quantifying open quantum system dynamics.

Ultrafast Spectroscopy of Photoactive Molecular Systems from First Principles: Where We Stand Today and Where We Are Going

Computational spectroscopy is becoming a mandatory tool for the interpretation of the complex, and often congested, spectral maps delivered by modern non-linear multi-pulse techniques. The fields of Electronic Structure Methods, Non-Adiabatic Molecular Dynamics, and Theoretical Spectroscopy represent the three pillars of the virtual ultrafast optical spectrometer, able to deliver transient spectra in silico from first principles. A successful simulation strategy requires a synergistic approach that balances between the three fields, each one having its very own challenges and bottlenecks. The aim of this Perspective is to demonstrate that, despite these challenges, an impressive agreement between theory and experiment is achievable now regarding the modeling of ultrafast photoinduced processes in complex molecular architectures. Beyond that, some key recent developments in the three fields are presented that we believe will have major impacts on spectroscopic simulations in the very near future. Potential directions of development, pending challenges, and rising opportunities are illustrated.

A scalable algorithm of numerical real-time path integral for quantum dissipative systems

Numerical real-time path integration has been a practical method to study a quantum system under the influence of its environment. Performing the path integral computations, however, is a resource-demanding task in general, and implementing it is less straightforward with modern hardware architectures of massively parallel platforms. In this article, a numerical algorithm based on the quasiadiabatic propagator path integral scheme is proposed and shown to scale for systems with large size. As a case study of performance, the quantum dynamics of excitation energy transfer in the Fenna-Matthews-Olson complex is discussed, employing a vibronic model in which the system size can be varied simply by adding vibrational excitations.

Path-integral methodology and simulations of quantum thermal transport: Full counting statistics approach

We develop and test a computational framework to study heat exchange in interacting, nonequilibrium open quantum systems. Our iterative full counting statistics path integral (iFCSPI) approach extends a previously well-established influence functional path integral method, by going beyond reduced system dynamics to provide the cumulant generating function of heat exchange. The method is straightforward; we implement it for the nonequilibrium spin boson model to calculate transient and long-time observables, focusing on the steady-state heat current flowing through the system under a temperature difference. Results are compared to perturbative treatments and demonstrate good agreement in the appropriate limits. The challenge of converging nonequilibrium quantities, currents and high order cumulants, is discussed in detail. The iFCSPI, a numerically exact technique, naturally captures strong system-bath coupling and non-Markovian effects of the environment. As such, it is a promising tool for probing fundamental questions in quantum transport and quantum thermodynamics.