Adaptive Time-dependent Density Matrix Renormalization Research Articles

Full Quantum Dynamics Simulation of a Realistic Molecular System Using the Adaptive Time-Dependent Density Matrix Renormalization Group Method.

The accurate theoretical interpretation of ultrafast time-resolved spectroscopy experiments relies on full quantum dynamics simulations for the investigated system, which is nevertheless computationally prohibitive for realistic molecular systems with a large number of electronic and/or vibrational degrees of freedom. In this work, we propose a unitary transformation approach for realistic vibronic Hamiltonians, which can be coped with using the adaptive time-dependent density matrix renormalization group (t-DMRG) method to efficiently evolve the nonadiabatic dynamics of a large molecular system. We demonstrate the accuracy and efficiency of this approach with an example of simulating the exciton dissociation process within an oligothiophene/fullerene heterojunction, indicating that t-DMRG can be a promising method for full quantum dynamics simulation in large chemical systems. Moreover, it is also shown that the proper vibronic features in the ultrafast electronic process can be obtained by simulating the two-dimensional (2D) electronic spectrum by virtue of the high computational efficiency of the t-DMRG method.

Spinon and bound-state excitation light cones in Heisenberg XXZ chains

We investigate the out-of-equilibrium dynamics after a local quench that connects two spin-1/2 XXZ chains prepared in the ground state of the Hamiltonian in different phases, one in the ferromagnetic phase and the other in the critical phase. We analyze the time evolution of the on-site magnetization and bipartite entanglement entropy via adaptive time-dependent density matrix renormalization group. In systems with short-range inter- actions, such as the one we consider, the velocity of information transfer is expected to be bounded, giving rise to a light-cone effect. Interestingly, our results show that, when the anisotropy parameter of the critical chain is sufficiently close to that of the isotropic ferromagnet, the light cone is determined by the velocity of spin-wave bound states that propagate faster than single-particle ("spinon") excitations. Furthermore, we investigate how the system approaches equilibrium in the inhomogeneous ground state of the connected system, in which the ferromagnetic chain induces a nonzero magnetization in the critical chain in the vicinity of the interface.

Unifying time evolution and optimization with matrix product states

We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for studying time-evolution, which can cope with arbitrary Hamiltonians, including those with long-range interactions. Rather than a Suzuki-Trotter splitting of the Hamiltonian, which is the idea behind the adaptive time-dependent density matrix renormalization group method or time-evolving block decimation, our method is based on splitting the projector onto the matrix product state tangent space as it appears in the Dirac-Frenkel time-dependent variational principle. We discuss how the resulting algorithm resembles the density matrix renormalization group (DMRG) algorithm for finding ground states so closely that it can be implemented by changing just a few lines of code and it inherits the same stability and efficiency. In particular, our method is compatible with any Hamiltonian for which DMRG can be implemented efficiently and DMRG is obtained as a special case of imaginary time evolution with infinite time step.

Expansion dynamics in a one-dimensional hard-core boson model with three-body interactions.

Using the adaptive time-dependent density matrix renormalization group method, we numerically investigate the expansion dynamics of bosons in a one-dimensional hard-core boson model with three-body interactions. It is found that the bosons expand ballistically with weak interaction, which are obtained by local density and the radius Rn. It is shown that the expansion velocity V, obtained from Rn = Vt, is dependent on the number of bosons. As a prominent result, the expansion velocity decreases with the enhancement of three-body interaction. We further study the dynamics of the system, which quenches from the ground state with two-thirds filling, the results indicate the expansion is also ballistic in the gapless phase regime. It could help us detect the phase transition in the system.

Quench of non-Markovian coherence in the deep sub-Ohmic spin–boson model: A unitary equilibration scheme

The deep sub-Ohmic spin–boson model shows a longstanding non-Markovian coherence at low temperature. Motivating to quench this robust coherence, the thermal effect is unitarily incorporated into the time evolution of the model, which is calculated by the adaptive time-dependent density matrix renormalization group algorithm combined with the orthogonal polynomials theory. Via introducing a unitary heating operator to the bosonic bath, the bath is heated up so that a majority portion of the bosonic excited states is occupied. It is found in this situation the coherence of the spin is quickly quenched even in the coherent regime, in which the non-Markovian feature dominates. With this finding we come up with a novel way to implement the unitary equilibration, the essential term of the eigenstate-thermalization hypothesis, through a short-time evolution of the model.

Dynamics of the sub-Ohmic spin-boson model: A comparison of three numerical approaches

Dynamics of the sub-Ohmic spin-boson model is examined using three numerical approaches, namely the Dirac-Frenkel time-dependent variation with the Davydov D(1) ansatz, the adaptive time-dependent density matrix renormalization group method within the representation of orthogonal polynomials, and a perturbative approach based on a unitary transformation. In order to probe the validity regimes of the three approaches, we study the dynamics of a qubit coupled to a bosonic bath with and without a local field. Comparison of the up-state population evolution shows that the three approaches are in agreement in the weak-coupling regime but exhibit marked differences when the coupling strength is large. The Davydov D(1) ansatz and the time-dependent density matrix renormalization group can both be reliably employed in the weak-coupling regime, while the former is also valid in the strong-coupling regime as judged by how faithfully the trial state follows the Schrödinger equation. We further explore the bipartite entanglement dynamics between two qubits coupled with individual bosonic baths which reveals entanglement sudden death and revival.

Correlation effects on the scattering of soliton pairs in conjugated polymers

By employing an adaptive time-dependent density matrix renormalization group (t-DMRG) method, we investigate the electron-electron correlation effects on the inelastic-scattering processes of oppositely charged-soliton anti-soliton pairs in conjugated polymers under the influence of an external electric field. The simulations are performed based on the Su-Schrieffer-Heeger (SSH) model modified to include electron-electron interactions and an external electric field. The percent yield of product is numerically calculated by a projection method. Our results show that the on-site Coulomb interaction is of fundamental importance and favors the recombination between the pairs of soliton. Additionally, the effects of external electric field and nearest-neighbor electron-electron interaction on the collision processes are also discussed.

Quantum dynamics of solitons in strongly interacting systems on optical lattices

Mean-field dynamics of strongly interacting bosons described by hard-core bosons with nearest-neighbor attraction has been shown to support two species of solitons: one of Gross-Pitaevskii type (GP type) where the condensate fraction remains dark, and a non-Gross-Pitaevskii type (non-GP type) characterized by brightening of the condensate fraction. Here we study the effects of quantum fluctuations on these solitons using the adaptive time-dependent density matrix renormalization group method, which takes into account the effect of strong correlations. We use local observables as the density, condensate density, and correlation functions as well as the entanglement entropy to characterize the stability of the initial states. We find both species of solitons to be stable under quantum evolution for a finite duration, their tolerance to quantum fluctuations being enhanced as the width of the soliton increases. We describe possible experimental realizations in atomic Bose-Einstein condensates, polarized degenerate Fermi gases, and in systems of polar molecules on optical lattices.

Real-time energy dynamics in spin-12Heisenberg chains

We study the real-time dynamics of the local energy density in the spin-1/2 XXZ chain starting from initial states with an inhomogeneous profile of bond energies. Numerical simulations of the dynamics of the initial states are carried out using the adaptive time-dependent density matrix renormalization group method. We analyze the time dependence of the spatial variance associated with the local energy density to classify the dynamics as either ballistic or diffusive. Our results are consistent with ballistic behavior both in the massless and the massive phase. We also study the same problem within Luttinger Liquid theory and obtain that energy wave-packets propagate with the sound velocity. We recover this behavior in our numerical simulations in the limit of very weakly perturbed initial states.

Real-time dynamics of a spin chain with Dzyaloshinskii-Moriya interactions: Spiral formation and quantum spin oscillations

We studied the non-equilibrium short-time dynamics of a spin-1/2 chain with Dzyaloshinskii-Moriya interactions after a sudden quench by a transverse field. We found that inhomogeneous spin-spirals with opposite chiralities propagate from the edges towards the center of the chain. This propagation is accompanied by quantum spin oscillations which decay asymptotically with time. A theoretical description of this phenomenon is given to a good accuracy with the help of numerical calculations with the adaptive time-dependent density matrix renormalization group algorithm.

Emergence of non-equilibrium superconductivity originated from repulsive interaction: Demonstration using optical lattices and implication to solid-state matter system

We study the dynamical properties of ultracold fermions in one-dimensional optical superlattices by using the adaptive time-dependent density matrix renormalization group method. The system is repulsive Hubbard model with an two-site periodic superlattice potential. Owing to superlattice structure, the ground-state states become the Mott-type insulating state at quarter-filling and band-type insulating state at half-filling, respectively. We clarify the dynamical properties of time evolution when the system is non-adiabatically changed to another lattice structure (i.e., the superlattice potential is suddenly changed to a normal one). In the case of Mott-type insulating state at quarter-filling, the time evolution exhibits a profile similar to that expected for single atom. On the other hand, we clarify the dynamical properties of a band-type insulating state at half-filling. The strongly-correlated interaction an unusual pairing of fermions induced the pair hopping process. We further address the robustness of pair hopping process and possibility of superconductivity by using sudden change from superlattice structure to normal one.

Nonequilibrium Current in the One Dimensional Hubbard Model at Half-Filling

Nonlinear transport in the one dimensional Hubbard model at half-filling under a finite bias voltage is investigated by the adaptive time-dependent density matrix renormalization group method. For repulsive on-site interaction, dielectric breakdown of the Mott insulating ground state to a current-carrying nonequilibrium steady state is clearly observed when the voltage exceeds the charge gap. It is found that by increasing the voltage further the current-voltage characteristics are scaled only by the charge gap and the scaling curve exhibits almost linear dependence on the voltage whose slope is suppressed by the electron correlation. In the case of attractive interaction the linear conductance is the perfect one $2e^2/h$ which agrees with the prediction by the Luttinger liquid theory.

Double time window targeting technique: Real-time DMRG dynamics in the Pariser-Parr-Pople model

We present a generalized adaptive time-dependent density matrix renormalization group (DMRG) scheme, called the {\it double time window targeting} (DTWT) technique, which gives accurate results with nominal computational resources, within reasonable computational time. This procedure originates from the amalgamation of the features of pace keeping DMRG algorithm, first proposed by Luo {\it et. al}, [Phys.Rev. Lett. {\bf 91}, 049701 (2003)], and the time-step targeting (TST) algorithm by Feiguin and White [Phys. Rev. B {\bf 72}, 020404 (2005)]. Using the DTWT technique, we study the phenomena of spin-charge separation in conjugated polymers (materials for molecular electronics and spintronics), which have long-range electron-electron interactions and belong to the class of strongly correlated low-dimensional many-body systems. The issue of real time dynamics within the Pariser-Parr-Pople (PPP) model which includes long-range electron correlations has not been addressed in the literature so far. The present study on PPP chains has revealed that, (i) long-range electron correlations enable both the charge and spin degree of freedom of the electron, to propagate faster in the PPP model compared to Hubbard model, (ii) for standard parameters of the PPP model as applied to conjugated polymers, the charge velocity is almost twice that of the spin velocity and, (iii) the simplistic interpretation of long-range correlations by merely renormalizing the {\it U} value of the Hubbard model fails to explain the dynamics of doped holes/electrons in the PPP model.

Effect of Electron−Electron Interactions on the Charge Carrier Transitions intrans-Polyacetylene

By employing a newly developed nonadiabatic dynamical simulation method, which is a combination of classical molecular dynamics and the adaptive time-dependent density matrix renormalization group, we investigate the dynamics of charge carrier transitions in trans-polyacetylene (PA) with the inclusion of both electron-phonon and electron-electron interactions. The calculations are performed within a modified Su-Schrieffer-Heeger model in which electron-electron interactions are taken into account via the combination with extended Hubbard model (EHM). We find that removing an electron from a trans-PA chain bearing a positively charged polaron leads to the formation of a pair of charged solitons. Furthermore, we study the effect of electron-electron interactions on such charge carrier transitions in trans-PA. Our results show that increasing the on-site Coulomb interaction and the nearest-neighbor Coulomb repulsion will not change the qualitative behavior of the transition from a polaron to a soliton pair in the evolution process but will quantitatively reduce the moving velocities of the both formed solitons significantly and change the conditions for the soliton collisions.

Nonadiabatic Dynamics of Ultracold Fermions in Optical Superlattices

We study the time-dependent dynamical properties of two-component ultracold fermions in a one-dimensional optical superlattice by applying the adaptive time-dependent density matrix renormalization group to a repulsive Hubbard model with an alternating superlattice potential. We clarify how the time evolution of local quantities occurs when the superlattice potential is suddenly changed to a normal one. For a Mott-type insulating state at quarter filling, the time evolution exhibits a profile similar to that expected for bosonic atoms, where correlation effects are less important. On the other hand, for a band-type insulating state at half filling, the strong repulsive interaction induces an unusual pairing of fermions, resulting in some striking properties in time evolution, such as a paired fermion co-tunneling process and the suppression of local spin moments. We further address the effect of a confining potential, which causes spatial confinement of the paired fermions.

Nonlinear transport through quantum dot studied by the time-dependent DMRG

Nonequilibrium transport properties of quantum dot under a finite bias voltage is investigated using the adaptive time-dependent density matrix renormalization group (TdDMRG) method. The validity of the authors’ previous study was limited for relatively weak coupling parameters because the small scale Kondo energy in the strong coupling regime caused a difficulty. By taking sufficiently long system size, keeping large number of states during the TdDMRG process and utilizing the fourth order Suzuki–Trotter decomposition, we can extend calculations of current–voltage characteristics in the strongly correlated region up to the Wilson ratio R W < 1.97 , close to the strong coupling limit. The wide domain of applicability suggests future applications of the method to various nonequilibrium and time-dependent problems.

Real-time simulations of nonequilibrium transport in the single-impurity Anderson model

One of the main open problems in the field of transport in strongly interacting nanostructures is the understanding of currents beyond the linear response regime. In this work, we consider the single-impurity Anderson model and use the adaptive time-dependent density matrix renormalization group method to compute real-time currents out of equilibrium. We first focus on the particle-hole symmetric point where Kondo correlations are the strongest and then extend the study of the nonequilibrium transport to the mixed-valence regime. As a main result, we present accurate data for the current-voltage characteristics of this model.

Real-time study of diffusive and ballistic transport in spin-12chains using the adaptive time-dependent density matrix renormalization group method

Using the adaptive time-dependent density matrix renormalization group method, we numerically study the spin dynamics and transport in one-dimensional spin-1/2 systems at zero temperature. Instead of computing transport coefficients from linear-response theory, we study the real-time evolution of the magnetization starting from spatially inhomogeneous initial states. In particular, we are able to analyze systems far away from equilibrium with this setup. By computing the time dependence of the variance of the magnetization, we can distinguish diffusive from ballistic regimes, depending on model parameters. For the example of the anisotropic spin-1/2 chain and at half filling, we find the expected ballistic behavior in the easy-plane phase, while in the massive regime the dynamics of the magnetization is diffusive. Our approach allows us to tune the deviation of the initial state from the ground state and the qualitative behavior of the dynamics turns out to be valid even for highly perturbed initial states in the case of easy-plane exchange anisotropies. We further cover two examples of nonintegrable models, the frustrated chain and the two-leg spin ladder, and we encounter diffusive transport in all massive phases. In the former system, our results indicate ballistic behavior in the critical phase. We propose that the study of the time dependence of the spatial variance of particle densities could be instrumental in the characterization of the expansion of ultracold atoms in optical lattices as well.

Density matrix renormalization group study of a quantum impurity model with Landau-Zener time-dependent Hamiltonian

We use the adaptive time-dependent density matrix renormalization group method (t-DMRG) to study the nonequilibrium dynamics of a benchmark quantum impurity system which has a time-dependent Hamiltonian. This model is a resonant-level model, obtained by a mapping from a certain Ohmic spin-boson model describing the dissipative Landau-Zener transition. We map the resonant-level model onto a Wilson chain, then calculate the time-dependent occupation n(d)(t) of the resonant level. We compare t-DMRG results with exact results at zero temperature and find very good agreement. We also give a physical interpretation of the numerical results.

Dynamical Simulations of Polaron Transport in Conjugated Polymers with the Inclusion of Electron−Electron Interactions

Dynamical simulations of polaron transport in conjugated polymers in the presence of an external time-dependent electric field have been performed within a combined extended Hubbard model (EHM) and Su-Schrieffer-Heeger (SSH) model. Nearly all relevant electron-phonon and electron-electron interactions are fully taken into account by solving the time-dependent Schrödinger equation for the pi electrons and the Newton's equation of motion for the backbone monomer displacements by virtue of the combination of the adaptive time-dependent density matrix renormalization group (TDDMRG) and classical molecular dynamics (MD). We find that after a smooth turn-on of the external electric field, the polaron is accelerated at first and then moves with a nearly constant velocity as one entity consisting of both the charge and the lattice deformation. An ohmic region (3 < or = E0 < or = 9 mV/A) where the stationary velocity increases linearly with the electric field strength is observed for the case of U = 2.0 eV and V = 1.0 eV. The maximal velocity is well above the speed of sound. Below 3 mV/A, the polaron velocity increases nonlinearly, and in high electric fields with strengths of E0 > or = 10.0 mV/A, the polaron will become unstable and dissociate. The relationship between electron-electron interaction strengths and polaron transport is also studied in detail. We find that the on-site Coulomb interactions U will suppress the polaron transport, and small nearest-neighbor interactions V values are also not beneficial to the polaronic motion while large V values favor the polaron transport.