arXiv subjects

Benedikt R. Graswald

Publications and source records attributed to Benedikt R. Graswald.

4 recordsLinked to original sources

arXiv2022

Exact matrix product state representation and convergence of a fully correlated electronic wavefunction in the infinite basis limit

In this article we present the exact representation of a fully correlated electronic wavefunction as the single-particle basis approaches completeness. It consists of a half-infinite chain of matrices of exponentially increasing size. The complete basis limit is illustrated numerically using the density matrix renormalization group method by computing the core-valence entanglement in the C$_2$ ground state in increasing subsets of cc-pVTZ and pVQZ bases until convergence is reached.

quant-ph↗

arXiv2021

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

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.

quant-ph↗

arXiv2021

Dissociation limit in Kohn-Sham density functional theory

We consider the dissociation limit for molecules of the type $X_2$ in the Kohn-Sham density functional theory setting, where $X$ can be any element with $N$ electrons. We prove that when the two atoms in the system are torn infinitely far apart, the energy of the system convergences to $\min \limits_{α\in [0,N]} \big( I^{X}_α + I^{X}_{2N-α} \big)$, where $I^{X}_α$ denotes the energy of the atom with $α$ electrons surrounding it. Depending on the "strength" of the exchange this minimum might not be equal to the symmetric splitting $2I^{X}_{N}$. We show numerically that for the $H_2$-molecule with Dirac exchange this gives the expected result of twice the energy of a H-atom $2 I^{H}_1$.

math-ph↗

arXiv2021

Electronic wavefunction with maximally entangled MPS representation

We present an example of an electronic wavefunction with maximally entangled MPS representation, in the sense that the bond dimension is maximal and cannot be lowered by any re-ordering of the underlying one-body basis. Our construction works for any number of electrons and orbitals.

quant-ph↗