Ground-state two-particle reduced density matrices (2-RDMs) are used to calculate excited-state energy spectra. Solving the Schrodinger equation for excited states dominated by single excitations from the ground-state wavefunction requires the ground-state 2- and 3-RDMs. The excited states, however, can be obtained without a knowledge of the ground-state 3-RDM by two methods: (i) cumulant expansion methods which build the 3-RDM from the 2-RDM, and (ii) double commutator methods which eliminate the 3-RDM. Previous work [Mazziotti, Phys. Rev. A 68, 052501 (2003)] examined the accuracy of excited states extracted from ground-state 2-RDMs, which were calculated by full configuration interaction or the variational 2-RDM method. In this work we employ (i) advances in semidefinite programming to treat the excited states of water and hydrogen fluoride and chains of hydrogen atoms, and (ii) the addition of partial three-particle N-representability conditions to compute more accurate ground-state 2-RDMs. With the hydrogen chains we examine the metal-to-insulator transition as measured by the band gap (the difference between the ground-state and the first excited-state energies), which is difficult for excited-state methods to capture.Ground-state two-particle reduced density matrices (2-RDMs) are used to calculate excited-state energy spectra. Solving the Schrodinger equation for excited states dominated by single excitations from the ground-state wavefunction requires the ground-state 2- and 3-RDMs. The excited states, however, can be obtained without a knowledge of the ground-state 3-RDM by two methods: (i) cumulant expansion methods which build the 3-RDM from the 2-RDM, and (ii) double commutator methods which eliminate the 3-RDM. Previous work [Mazziotti, Phys. Rev. A 68, 052501 (2003)] examined the accuracy of excited states extracted from ground-state 2-RDMs, which were calculated by full configuration interaction or the variational 2-RDM method. In this work we employ (i) advances in semidefinite programming to treat the excited states of water and hydrogen fluoride and chains of hydrogen atoms, and (ii) the addition of partial three-particle N-representability conditions to compute more accurate ground-state 2-RDMs. With the hydrogen chains we examine the metal-to-insulator transition as measured by the band gap (the difference between the ground-state and the first excited-state energies), which is difficult for excited-state methods to capture.

The Journal of Chemical PhysicsMar 20, 200828 citations

Excitations as ground state variational parameters

Miodrag V. Mihailović, Mitja Rosina

Nuclear Physics AJun 1, 196933 citations

Variational calculation of 4 He tetramer ground and excited states using a realistic pair potential

Emiko Hiyama, M. Kamimura

We calculated the ${}^{4}$ He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method for ab initio variational calculations of few-body systems. The method has been extensively used for a variety of three-, four-, and five-body systems in nuclear physics and exotic atomic and molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three- (four-) body Gaussian basis functions, ranging from very compact to very diffuse, without assumption of any pair correlation function. The calculated results for the trimer ground and excited states are in excellent agreement with values reported in the literature. The binding energies of the tetramer ground and excited states are obtained as 558.98 and 127.33 mK (0.93 mK below the trimer ground state), respectively. We found that precisely the same shape of the short-range correlation (${r}_{ij}\ensuremath{\lesssim}4$ \AA{}) in the dimer appears in the ground and excited states of the trimer and tetramer. The overlap function between the trimer excited state and the dimer ground state and that between the tetramer excited state and the trimer ground state are almost proportional to the dimer wave function in the asymptotic region (up to $\ensuremath{\sim}$1000 \AA{}). Also, the pair correlation functions of trimer and tetramer excited states are almost proportional to the squared dimer wave function. We then propose a model which predicts the binding energy of the first excited state of ${}^{4}$ He ${}_{N}$ ($N\ensuremath{\ge}3$) measured from the ${}^{4}$ He${}_{N\ensuremath{-}1}$ ground state to be nearly $\frac{N}{2(N\ensuremath{-}1)}{B}_{2}$ where ${B}_{2}$ is the dimer binding energy.We calculated the ${}^{4}$He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method for ab initio variational calculations of few-body systems. The method has been extensively used for a variety of three-, four-, and five-body systems in nuclear physics and exotic atomic and molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three- (four-) body Gaussian basis functions, ranging from very compact to very diffuse, without assumption of any pair correlation function. The calculated results for the trimer ground and excited states are in excellent agreement with values reported in the literature. The binding energies of the tetramer ground and excited states are obtained as 558.98 and 127.33 mK (0.93 mK below the trimer ground state), respectively. We found that precisely the same shape of the short-range correlation (${r}_{ij}\ensuremath{\lesssim}4$ \AA{}) in the dimer appears in the ground and excited states of the trimer and tetramer. The overlap function between the trimer excited state and the dimer ground state and that between the tetramer excited state and the trimer ground state are almost proportional to the dimer wave function in the asymptotic region (up to $\ensuremath{\sim}$1000 \AA{}). Also, the pair correlation functions of trimer and tetramer excited states are almost proportional to the squared dimer wave function. We then propose a model which predicts the binding energy of the first excited state of ${}^{4}$He${}_{N}$ ($N\ensuremath{\ge}3$) measured from the ${}^{4}$He${}_{N\ensuremath{-}1}$ ground state to be nearly $\frac{N}{2(N\ensuremath{-}1)}{B}_{2}$ where ${B}_{2}$ is the dimer binding energy.

arXiv:1111.4370Physical Review AFeb 2, 201258 citations

Collective excitations and ground state correlations

E. Heinz, H. Müther, Harry A. Mavromatis

arXiv:nucl-th/9408020Nuclear Physics AMay 1, 19957 citations

Particles and Elementary Excitations

G. Costa, F. Scaramuzzi, Livio Scarsi

NATO ASI series. Series B : PhysicsJan 1, 19910 citations

EFFECT OF PARTICLE-HOLE EXCITATIONS ON THE BCS GROUND STATE

J. D. Fan, Y. M. Malozovsky

We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.We show that the well-known BCS Hamiltonian in terms of the BCS ground state represents, in fact, the generator of the particle-hole pairs and that the BCS ground state describes both the particle-hole excitations and the pairing condensate. We calculate the contribution of particle-hole excitation to the ground state energy. We show that the particle-hole pairs in the case of attractive interaction significantly lower the ground state energy, which means that the BCS ground state is not really the superconducting ground state. In contrast, for the repulsive interaction the particle-hole excitations are just to renormalize the ground state energy. Thus, in the case of repulsive interaction the condensate of bound pairs would lead to the real superconducting ground state of the system as shown.

International Journal of Modern Physics BJan 30, 20050 citations

We calculated the

{}^{4}

He trimer and tetramer ground and excited states with the LM2M2 potential using our Gaussian expansion method for ab initio variational calculations of few-body systems. The method has been extensively used for a variety of three-, four-, and five-body systems in nuclear physics and exotic atomic and molecular physics. The trimer (tetramer) wave function is expanded in terms of symmetric three- (four-) body Gaussian basis functions, ranging from very compact to very diffuse, without assumption of any pair correlation function. The calculated results for the trimer ground and excited states are in excellent agreement with values reported in the literature. The binding energies of the tetramer ground and excited states are obtained as 558.98 and 127.33 mK (0.93 mK below the trimer ground state), respectively. We found that precisely the same shape of the short-range correlation (${r}_{ij}\ensuremath{\lesssim}4$ \AA{}) in the dimer appears in the ground and excited states of the trimer and tetramer. The overlap function between the trimer excited state and the dimer ground state and that between the tetramer excited state and the trimer ground state are almost proportional to the dimer wave function in the asymptotic region (up to $\ensuremath{\sim}$1000 \AA{}). Also, the pair correlation functions of trimer and tetramer excited states are almost proportional to the squared dimer wave function. We then propose a model which predicts the binding energy of the first excited state of

{}^{4}

{}_{N}

($N\ensuremath{\ge}3$) measured from the

{}^{4}

He${}_{N\ensuremath{-}1}$ ground state to be nearly $\frac{N}{2(N\ensuremath{-}1)}{B}_{2}$ where

{B}_{2}

is the dimer binding energy.