Variational method with Quantum number projection and two dimensional Hubbard models

We apply a variational method devised for the nuclear many-body problem to the one-dimensional Hubbard model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single Hartree--Fock determinant mixing all the sites (or momenta) as well as the spin projections of the electrons. Total spin and linear momentum are restored by projection methods before the variation. It is demonstrated that this approach reproduces the results of exact diagonalizations for half-filled $N=12$ and $N=14$ lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of ten electrons in an $N=12$ lattice is investigated and, finally, an $N=30$ lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry-projected wave functions as well.We apply a variational method devised for the nuclear many-body problem to the one-dimensional Hubbard model with nearest neighbor hopping and periodic boundary conditions. The test wave function consist for each state out of a single Hartree--Fock determinant mixing all the sites (or momenta) as well as the spin projections of the electrons. Total spin and linear momentum are restored by projection methods before the variation. It is demonstrated that this approach reproduces the results of exact diagonalizations for half-filled $N=12$ and $N=14$ lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of ten electrons in an $N=12$ lattice is investigated and, finally, an $N=30$ lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry-projected wave functions as well.

arXiv:cond-mat/0409691Physical Review BAug 12, 200519 citations

Variational cluster approach to quasi-two-dimensional Hubbard model

俊彦吉川

Jan 1, 20100 citations

Symmetry-projected variational approach for ground and excited states of the two-dimensional Hubbard model

R. R. Rodríguez-Guzmán, K.W. Schmid, Carlos A. Jiménez-Hoyos +1 more

We present a symmetry-projected configuration mixing scheme to describe ground and excited states, with well defined quantum numbers, of the two-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Results for the half-filled $2\ifmmode\times\else\texttimes\fi{}4$, $4\ifmmode\times\else\texttimes\fi{}4$, and $6\ifmmode\times\else\texttimes\fi{}6$ lattices as well as doped $4\ifmmode\times\else\texttimes\fi{}4$ systems, compare well with available results, both exact and from other state-of-the-art approximations. We report spectral functions and density of states obtained from a well-controlled ansatz for the $({N}_{e}\ifmmode\pm\else\textpm\fi{}1)$-electron system. Symmetry projected methods have been widely used for the many-body nuclear physics problem but have received little attention in the solid state community. Given their relatively low (mean-field) computational cost and the high quality of results here reported, we believe that they deserve further scrutiny.We present a symmetry-projected configuration mixing scheme to describe ground and excited states, with well defined quantum numbers, of the two-dimensional Hubbard model with nearest-neighbor hopping and periodic boundary conditions. Results for the half-filled $2\ifmmode\times\else\texttimes\fi{}4$, $4\ifmmode\times\else\texttimes\fi{}4$, and $6\ifmmode\times\else\texttimes\fi{}6$ lattices as well as doped $4\ifmmode\times\else\texttimes\fi{}4$ systems, compare well with available results, both exact and from other state-of-the-art approximations. We report spectral functions and density of states obtained from a well-controlled ansatz for the $({N}_{e}\ifmmode\pm\else\textpm\fi{}1)$-electron system. Symmetry projected methods have been widely used for the many-body nuclear physics problem but have received little attention in the solid state community. Given their relatively low (mean-field) computational cost and the high quality of results here reported, we believe that they deserve further scrutiny.

arXiv:1204.2006Physical Review BJun 26, 201248 citations

A Variational Moments Approach to the One Dimensional Hubbard Model

Zhi Hua Cheng, Yick Hong Chan, Jun Hui Liang +4 more

Bulletin of the American Physical SocietyMar 5, 20150 citations

Improved energy extrapolation with infinite projected entangled-pair states applied to the two-dimensional Hubbard model

Philippe Corboz

An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for two-dimensional wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$ . We show that for the doped Hubbard model in the strongly correlated regime $(U/t=8,n=0.875)$ the iPEPS yields lower variational energies than state-of-the-art variational methods in the large two-dimensional limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite- $D$ limit we introduce and test an extrapolation technique based on a truncation error computed in the iPEPS imaginary time evolution algorithm. The extrapolated energies are compared with accurate quantum Monte Carlo results at half-filling and with various other methods in the doped, strongly correlated regime.An infinite projected entangled-pair state (iPEPS) is a variational tensor network ansatz for two-dimensional wave functions in the thermodynamic limit where the accuracy can be systematically controlled by the bond dimension $D$. We show that for the doped Hubbard model in the strongly correlated regime $(U/t=8,n=0.875)$ the iPEPS yields lower variational energies than state-of-the-art variational methods in the large two-dimensional limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite-$D$ limit we introduce and test an extrapolation technique based on a truncation error computed in the iPEPS imaginary time evolution algorithm. The extrapolated energies are compared with accurate quantum Monte Carlo results at half-filling and with various other methods in the doped, strongly correlated regime.

arXiv:1508.04003Physical review. B./Physical review. BJan 14, 2016110 citations

N=12

and

N=14

lattices not only for the energies and occupation numbers of the ground but also of the lowest excited states rather well. Furthermore, a system of ten electrons in an

N=12

lattice is investigated and, finally, an

N=30

lattice is studied. In addition to energies and occupation numbers we present the spectral functions computed with the help of the symmetry-projected wave functions as well.

D

. We show that for the doped Hubbard model in the strongly correlated regime

(U/t=8,n=0.875)

the iPEPS yields lower variational energies than state-of-the-art variational methods in the large two-dimensional limit, which demonstrates the competitiveness of the method. In order to obtain an accurate estimate of the energy in the exact infinite-

D

limit we introduce and test an extrapolation technique based on a truncation error computed in the iPEPS imaginary time evolution algorithm. The extrapolated energies are compared with accurate quantum Monte Carlo results at half-filling and with various other methods in the doped, strongly correlated regime.