Corpus ID: 237581159

Two-electron wavefunctions are matrix product states with bond dimension Three

  title={Two-electron wavefunctions are matrix product states with bond dimension Three},
  author={G. Friesecke and Benedikt R. Graswald},
We prove the statement in the title, for a suitable (wavefunction-dependent) choice of the underlying orbitals, and show that Three is optimal. Thus for two-electron systems, the QC-DMRG method with bond dimension Three combined with fermionic mode optimization exactly recovers the FCI energy. 

Figures from this paper


Rigorous results on valence-bond ground states in antiferromagnets.
A valence-bond solid is presented, which is simply constructed out of valence bonds, is nondegenerate, and breaks no symmetries, and there is an energy gap and an exponentially decaying correlation function. Expand
Quantum chemistry using the density matrix renormalization group
A new implementation of the density matrix renormalization group is presented for ab initio quantum chemistry. Test computations have been performed of the dissociation energies of the diatomics Be2,Expand
Ab initio quantum chemistry using the density matrix renormalization group
In this paper we describe how the density matrix renormalization group can be used for quantum chemical calculations for molecules, as an alternative to traditional methods, such as configurationExpand
Inversion symmetry of singular values and a new orbital ordering method in tensor train approximations for quantum chemistry
Optizing the invariants or their superposition thus provides a new ordering scheme for QC-DMRG, and numerical tests show that the new scheme reduces the tail of the singular values by several orders of magnitudes over existing methods, including the widely used Fiedler order. Expand
Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems with matrix-product states
C. Krumnow,1 L. Veis,2 J. Eisert,1, 3 and Ö. Legeza4 Dahlem Center for Complex Quantum Systems, Freie Universität Berlin, 14195 Berlin, Germany J. Heyrovský Institute of Physical Chemistry, AcademyExpand
Controlling the accuracy of the density-matrix renormalization-group method: The dynamical block state selection approach
We have applied the momentum space version of the density-matrix renormalization-group method (k-DMRG) in quantum chemistry in order to study the accuracy of the algorithm in this new context. WeExpand
Quantum-information analysis of electronic states of different molecular structures
We have studied transition metal clusters from a quantum information theory perspective using the density-matrix renormalization group (DMRG) method. We demonstrate the competition betweenExpand
Fermionic Orbital Optimization in Tensor Network States.
The described algorithm generalizes basis changes in the spirit of the Hartree-Fock method to matrix-product states, and provides a black box tool for basis optimization in tensor network methods. Expand
The density-matrix renormalization group in the age of matrix product states
Abstract The density-matrix renormalization group method (DMRG) has established itself over the last decade as the leading method for the simulation of the statics and dynamics of one-dimensionalExpand
Highly correlated calculations with a polynomial cost algorithm: A study of the density matrix renormalization group
We study the recently developed Density Matrix Renormalization Group (DMRG) algorithm in the context of quantum chemistry. In contrast to traditional approaches, this algorithm is believed to yieldExpand