Obtaining the two-body density matrix in the density matrix renormalization group method.

We present an approach that allows to produce the two-body density matrix during the density matrix renormalization group (DMRG) run without an additional increase in the current disk and memory requirements. The computational cost of producing the two-body density matrix is proportional to O(M3k2+M2k4). The method is based on the assumption that different elements of the two-body density matrix can be calculated during different steps of a sweep. Hence, it is desirable that the wave function at the convergence does not change during a sweep. We discuss the theoretical structure of the wave function ansatz used in DMRG, concluding that during the one-site DMRG procedure, the energy and the wave function are converging monotonically at every step of the sweep. Thus, the one-site algorithm provides an opportunity to obtain the two-body density matrix free from the N-representability problem. We explain the problem of local minima that may be encountered in the DMRG calculations. We discuss theoretically why and when the one- and two-site DMRG procedures may get stuck in a metastable solution, and we list practical solutions helping the minimization to avoid the local minima.

[1]  David Yaron,et al.  COMPARISON OF DENSITY MATRIX RENORMALIZATION GROUP CALCULATIONS WITH ELECTRON-HOLE MODELS OF EXCITON BINDING IN CONJUGATED POLYMERS , 1998 .

[2]  Markus Reiher,et al.  Construction of environment states in quantum-chemical density-matrix renormalization group calculations. , 2006, The Journal of chemical physics.

[3]  Yuansheng Jiang,et al.  Spin distribution in neutral polyene radicals: Pariser-Parr-Pople model studied with the density matrix renormalization group method. , 2005, The Journal of chemical physics.

[4]  Steven R. White.  Numerical canonical transformation approach to quantum many-body problems , 2002 .

[5]  White,et al.  Density-matrix algorithms for quantum renormalization groups. , 1993, Physical review. B, Condensed matter.

[6]  T. H. Dunning.  Gaussian basis sets for use in correlated molecular calculations. I. The atoms boron through neon and hydrogen , 1989 .

[7]  B. Roos.  The Complete Active Space Self‐Consistent Field Method and its Applications in Electronic Structure Calculations , 2007 .

[8]  S. Rommer,et al.  CLASS OF ANSATZ WAVE FUNCTIONS FOR ONE-DIMENSIONAL SPIN SYSTEMS AND THEIR RELATION TO THE DENSITY MATRIX RENORMALIZATION GROUP , 1997 .

[9]  White,et al.  Density matrix formulation for quantum renormalization groups. , 1992, Physical review letters.

[10]  M. Reiher,et al.  Decomposition of density matrix renormalization group states into a Slater determinant basis. , 2007, The Journal of chemical physics.

[11]  Richard L. Martin,et al.  Ab initio quantum chemistry using the density matrix renormalization group , 1998 .

[12]  Guido Fano,et al.  Quantum chemistry using the density matrix renormalization group , 2001 .

[13]  M. Reiher,et al.  Density matrix renormalization group calculations on relative energies of transition metal complexes and clusters. , 2008, The Journal of chemical physics.

[14]  Marcel Nooijen,et al.  On the spin and symmetry adaptation of the density matrix renormalization group method. , 2008, The Journal of chemical physics.

[15]  Yuansheng Jiang,et al.  "Triplet-excited region" in polyene oligomers revisited: Pariser-Parr-Pople model studied with the density matrix renormalization group method. , 2004, The Journal of chemical physics.

[16]  J. I. Cirac,et al.  Variational study of hard-core bosons in a two-dimensional optical lattice using projected entangled pair states , 2007 .

[17]  Markus Reiher,et al.  Relativistic DMRG calculations on the curve crossing of cesium hydride. , 2005, The Journal of chemical physics.

[18]  Garnet Kin-Lic Chan,et al.  Density-matrix renormalization-group algorithms with nonorthogonal orbitals and non-Hermitian operators, and applications to polyenes. , 2005, The Journal of chemical physics.

[19]  G. Fano,et al.  The density matrix renormalization group method. Application to the PPP model of a cyclic polyene chain. , 1998, cond-mat/9803071.

[20]  M. Head‐Gordon,et al.  Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group , 2002 .

[21]  B. A. Hess,et al.  QC-DMRG study of the ionic-neutral curve crossing of LiF , 2002 .

[22]  Markus Reiher,et al.  Convergence behavior of the density-matrix renormalization group algorithm for optimized orbital orderings. , 2005, The Journal of chemical physics.

[23]  Garnet Kin-Lic Chan,et al.  Canonical transformation theory for multireference problems. , 2006, The Journal of chemical physics.

[24]  Östlund,et al.  Thermodynamic limit of density matrix renormalization. , 1995, Physical review letters.

[25]  J. Sólyom,et al.  Optimizing the density-matrix renormalization group method using quantum information entropy , 2003 .

[26]  David Pérez-García,et al.  PROJECTED ENTANGLED STATES: PROPERTIES AND APPLICATIONS , 2006 .

[27]  S. White.  Density matrix renormalization group algorithms with a single center site , 2005, cond-mat/0508709.

[28]  F. Verstraete,et al.  Matrix product density operators: simulation of finite-temperature and dissipative systems. , 2004, Physical review letters.

[29]  Jürgen Gauss,et al.  State-of-the-art density matrix renormalization group and coupled cluster theory studies of the nitrogen binding curve. , 2004, The Journal of chemical physics.

[30]  Garnet Kin-Lic Chan,et al.  An algorithm for large scale density matrix renormalization group calculations. , 2004, The Journal of chemical physics.

[31]  Garnet Kin-Lic Chan,et al.  Exact solution (within a triple-zeta, double polarization basis set) of the electronic Schrödinger equation for water , 2003 .

[32]  Yuansheng Jiang,et al.  Theoretical study of the lowest π →π* excitation energies for neutral and doped polyenes , 2005 .

[33]  Paul W. Ayers,et al.  On the Distribution of Eigenvalues of Grand Canonical Density Matrices , 2002 .

[34]  Guido Fano,et al.  Quantum chemistry using the density matrix renormalization group II , 2003 .

[35]  S. Evangelisti,et al.  Density matrix renormalization group study of dimerization of the Pariser–Parr–Pople model of polyacetilene , 1999 .

[36]  B. A. Hess,et al.  Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach , 2002, cond-mat/0204602.

[37]  C. Daul,et al.  Full‐CI quantum chemistry using the density matrix renormalization group , 1999 .