First-principles path-integral renormalization-group method for Coulombic many-body systems

Kojo, Masashi; Hirose, Kikuji

doi:10.1103/physreva.80.042515

Cited by 4 publications

(6 citation statements)

References 38 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The auxiliary-field variable A j (τ ) is a real number and nothing but the electric scalar potential in the Coulomb gauge. For details on this auxiliary field, see the appendix of [22] and [57]. Strictly speaking, the problem still remains in the case of Coulombic systems, because the integral with respect to its auxiliary-field variable A j (τ ) in the range [−∞, +∞] is required.…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…See [45] and [46] for more detailed information. (The explicit formula of the kinetic operator in the imaginary-time propagator within the RSFD scheme is given in the appendix of [22] ). Here, we assume the Hamiltonian Ĥ is a sum of two parts: a one-body part Ĥ1 and a two-body part Ĥ2 .…”

Section: Theoretical Methodsmentioning

confidence: 99%

“…However, in recent decades, diverse reliable and practical methods, such as density matrix renormalization group (DMRG) methods [4][5][6][7][8][9][10][11][12][13][14][15] and auxiliary-field quantum Monte Carlo (AF QMC) methods were developed [16][17][18][19][20]. On another front, the path-integral renormalization group (PIRG) [21,22] and direct energy minimization (DEM) methods [23][24][25] have been formulated within the framework of the real-space finite-difference (RSFD) scheme [26][27][28][29][30][31][32][33][34][35][36][37][38][39][40][41][42], and some methodological techniques are developed in order to apply them to practical few-body systems. The key to the present methods is employing linear combinations of nonorthogonal and unnormalized Slater determinants (SDs) as multi-body wavefunctions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

Sasaki¹,

Kojo²,

Hirose³

et al. 2011

J. Phys.: Condens. Matter

Self Cite

View full text Add to dashboard Cite

The path-integral renormalization group and direct energy minimization method of practical first-principles electronic structure calculations for multi-body systems within the framework of the real-space finite-difference scheme are introduced. These two methods can handle higher dimensional systems with consideration of the correlation effect. Furthermore, they can be easily extended to the multicomponent quantum systems which contain more than two kinds of quantum particles. The key to the present methods is employing linear combinations of nonorthogonal Slater determinants (SDs) as multi-body wavefunctions. As one of the noticeable results, the same accuracy as the variational Monte Carlo method is achieved with a few SDs. This enables us to study the entire ground state consisting of electrons and nuclei without the need to use the Born-Oppenheimer approximation. Recent activities on methodological developments aiming towards practical calculations such as the implementation of auxiliary field for Coulombic interaction, the treatment of the kinetic operator in imaginary-time evolutions, the time-saving double-grid technique for bare-Coulomb atomic potentials and the optimization scheme for minimizing the total-energy functional are also introduced. As test examples, the total energy of the hydrogen molecule, the atomic configuration of the methylene and the electronic structures of two-dimensional quantum dots are calculated, and the accuracy, availability and possibility of the present methods are demonstrated.

show abstract

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Theoretical Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

Sasaki¹,

Kojo²,

Hirose³

et al. 2011

J. Phys.: Condens. Matter

Self Cite

View full text Add to dashboard Cite

show abstract

“…[32][33][34][35] The path-integral renormalization group method also uses this approach to stochastically add non-orthogonal CI determinants, and has been applied to chemical systems such as H 2 . 36,37 Our method differs from this approach in the manner in which new determinants are t, and the performance benets of our method can be inferred from the data on H 2 in the appendix of this work.…”

Section: Compressed Imaginary Time Evolutionmentioning

confidence: 99%

Compact wavefunctions from compressed imaginary time evolution

McClean

Aspuru‐Guzik

2015

RSC Adv.

View full text Add to dashboard Cite

Simulation of quantum systems promises to deliver physical and chemical predictions for the frontiers of technology. Unfortunately, the exact representation of these systems is plagued by the exponential growth of dimension with the number of particles, or colloquially, the curse of dimensionality. The success of approximation methods has hinged on the relative simplicity of physical systems with respect to the exponentially complex worst case. Exploiting this relative simplicity has required detailed knowledge of the physical system under study. In this work, we introduce a general and efficient black box method for many-body quantum systems that utilizes technology from compressed sensing to find the most compact wavefunction possible without detailed knowledge of the system. It is a Multicomponent Adaptive Greedy Iterative Compression (MAGIC) scheme. No knowledge is assumed in the structure of the problem other than correct particle statistics. This method can be applied to many quantum systems such as spins, qubits, oscillators, or electronic systems. As an application, we use this technique to compute ground state electronic wavefunctions of hydrogen fluoride and recover 98% of the basis set correlation energy or equivalently 99.996% of the total energy with 50 configurations out of a possible 10 7 . Building from this compactness, we introduce the idea of nuclear union configuration interaction for improving the description of reaction coordinates and use it to study the dissociation of hydrogen fluoride and the helium dimer.

show abstract

“…The resonating Hartree-Fock method proposed by Fukutome utilizes nonorthogonal SDs, and many noteworthy results have been reported [ 25 - 30 ]. Also, Imada and co-workers [ 31 - 33 ] and Kojo and Hirose [ 34 , 35 ] employed nonorthogonal SDs in path integral renormalization group calculations. Goto and co-workers developed the direct energy minimization method using nonorthogonal SDs [ 36 - 39 ] based on the real-space finite-difference formalism [ 40 , 41 ].…”

Section: Introductionmentioning

confidence: 99%

Essentially exact ground-state calculations by superpositions of nonorthogonal Slater determinants

et al. 2013

Self Cite

View full text Add to dashboard Cite

An essentially exact ground-state calculation algorithm for few-electron systems based on superposition of nonorthogonal Slater determinants (SDs) is described, and its convergence properties to ground states are examined. A linear combination of SDs is adopted as many-electron wave functions, and all one-electron wave functions are updated by employing linearly independent multiple correction vectors on the basis of the variational principle. The improvement of the convergence performance to the ground state given by the multi-direction search is shown through comparisons with the conventional steepest descent method. The accuracy and applicability of the proposed scheme are also demonstrated by calculations of the potential energy curves of few-electron molecular systems, compared with the conventional quantum chemistry calculation techniques.

show abstract

First-principles path-integral renormalization-group method for Coulombic many-body systems

Cited by 4 publications

References 38 publications

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

Real-space finite-difference approach for multi-body systems: path-integral renormalization group method and direct energy minimization method

Compact wavefunctions from compressed imaginary time evolution

Essentially exact ground-state calculations by superpositions of nonorthogonal Slater determinants

Contact Info

Product

Resources

About