Time-Dependent Density Matrix Renormalization Group Coupled with n-Mode Representation Potentials for the Excited State Radiationless Decay Rate:Formalism and Application to Azulene

We propose a method for calculating the nonradiative decay rates for polyatomic molecules including anharmonic effects of the potential energy surface(PES)in the Franck-Condon region.The method combines the n-mode repre-sentation method to construct the ab initio PES and the nearly exact time-dependent density matrix renormalization group method(TD-DMRG)to simulate quantum dynamics.In addition,in the framework of TD-DMRG,we further develop an algorithm to calculate the final-state-resolved rate coefficient which is very useful to analyze the contribution from each vibrational mode to the transition process.We use this method to study the internal conversion(IC)process of azulene after taking into account the anharmonicity of the ground state PES.The results show that even for this semi-rigid molecule,the intramode anharmonicity enhances the IC rate significantly,and after considering the two-mode coupling effect,the rate increases even further.The reason is that the anharmonicity enables the C-H vibrations to receive electronic energy while C-H vibrations do not contribute on the harmonic PES as the Huang-Rhys factor is close to 0.

Real-space parallel density matrix renormalization group with adaptive boundaries

We propose an improved real-space parallel strategy for the density matrix renormalization group(DMRG)method,where boundaries of separate regions are adaptively distributed during DMRG sweeps.Our scheme greatly improves the parallel efficiency with shorter waiting time between two adjacent tasks,compared with the original real-space parallel DMRG with fixed boundaries.We implement our new strategy based on the message passing interface(MPI),and dynamically control the number of kept states according to the truncation error in each DMRG step.We study the performance of the new parallel strategy by calculating the ground state of a spin-cluster chain and a quantum chemical Hamiltonian of the water molecule.The maximum parallel efficiencies for these two models are 91%and 76%in 4 nodes,which are much higher than the real-space parallel DMRG with fixed boundaries.

Improved hybrid parallel strategy for density matrix renormalization group method

We propose a new heterogeneous parallel strategy for the density matrix renormalization group(DMRG)method in the hybrid architecture with both central processing unit(CPU)and graphics processing unit(GPU).Focusing on the two most time-consuming sections in the finite DMRG sweeps,i.e.,the diagonalization of superblock and the truncation of subblock,we optimize our previous hybrid algorithm to achieve better performance.For the former,we adopt OpenMP application programming interface on CPU and use our own subroutines with higher bandwidth on GPU.For the later,we use GPU to accelerate matrix and vector operations involving the reduced density matrix.Applying the parallel scheme to the Hubbard model with next-nearest hopping on the 4-leg ladder,we compute the ground state of the system and obtain the charge stripe pattern which is usually observed in high temperature superconductors.Based on simulations with different numbers of DMRG kept states,we show significant performance improvement and computational time reduction with the optimized parallel algorithm.Our hybrid parallel strategy with superiority in solving the ground state of quasi-two dimensional lattices is also expected to be useful for other DMRG applications with large numbers of kept states,e.g.,the time dependent DMRG algorithms.

Ground-state phase diagram of the dimerizedspin-1/2 two-leg ladder

Dimerized spin-1/2 ladders exhibit a variety of phase structures,which depend on the intra-chain and inter-chain spin exchange energies as well as on the dimerization pattern of the ladder.Using the density matrix renormalization group(DMRG)algorithm,we study critical properties of the bond-alternating two-leg Heisenberg spin ladder with diagonal interaction J_(×).Two types of spin systems,staggered dimerized antiferromagnetic ladder and columnar dimerized ferro-antiferromagnetic couplings ladder,are investigated.To clarify the phase transition behaviors,we simultaneously analyze the string order parameter(SOP),the twisted order parameter(TOP),as well as a measurement of the quantum information analysis.Based on measuring this different observables,we establish the phase diagram accurately and give the fitting functions of the phase boundaries.In addition,the phase transition of cross-coupled spin ladder(in the absence of intrinsic dimerization)is also discussed.

Off-site trimer superfluid on a one-dimensional optical lattice

The Bose-Hubbard model with an effective off-site three-body tunneling,characterized by jumps towards one another,between one atom on a site and a pair atoms on the neighborhood site,is studied systematically on a one-dimensional（1D） lattice,by using the density matrix renormalization group method.The off-site trimer superfluid,condensing at momentum k = 0,emerges in the softcore Bose-Hubbard model but it disappears in the hardcore Bose-Hubbard model.Our results numerically verify that the off-site trimer superfluid phase derived in the momentum space from[Phys.Rev.A81,011601（R）（2010）]is stable in the thermodynamic limit.The off-site trimer superfluid phase,the partially off-site trimer superfluid phase and the Mott insulator phase are found,as well as interesting phase transitions,such as the continuous or first-order phase transition from the trimer superfluid phase to the Mott insulator phase.Our results are helpful in realizing this novel off-site trimer superfluid phase by cold atom experiments.

Analytical and Numerical Studies of Quantum Plateau State in One Alternating Heisenberg Chain

By using the coupled duster method and the numerical density matrix renormalization group method, we investigate the properties of the quantum plateau state in an alternating Heisenberg spin chain. In the absence of a magnetic field, the results obtained from the coupled cluster method and density matrix renormalization group method both show that the ground state of the aiternating chain is a gapped dimerized state when the parameter a exceeds a critical point ac. The value of the critical points can be determined precisely by a detailed investigation of the behavior of the spin gap. The system therefore possesses an m = 0 plateau state in the presence of a magnetic field When a 〉 ac. In addition to the m = 0 plateau state, the results of density matrix renormaiization group indicate that there is an m = 1/4 plateau state that occurs between two critical fields in the alternating chain if a 〉 1. The mechanism for the m = 1/4 plateau state and the critical behavior of the magnetization as one approaches this plateau state are also discussed.

Zero Temperature Numerical Studies of Multiband Lattice Models of Strongly Correlated Electrons

Relative to single-band models,multiband models of strongly interacting electron systems are of growing interest because of their wider range of novel phenomena and their closer match to the electronic structure of real materials.In this brief review we discuss the physics of three multiband models(the three-band Hubbard,the periodic Anderson,and the Falicov-Kimball models)that was obtained by numerical simulations at zero temperature.We first give heuristic descriptions of the three principal numerical methods(the Lanczos,the density matrix renormalization group,and the constrainedpath Monte Carlo methods).We then present generalized versions of the models and discuss the measurables most often associated with them.Finally,we summarize the results of their ground state numerical studies.While each model was developed to study specific phenomena,unexpected phenomena,usually of a subtle quantum mechanical nature,are often exhibited.Just as often,the predictions of the numerical simulations differ from those of mean-field theories.