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arXiv:cond-mat/9604175 · Physical review. B, Condensed matter

Multiconfigurational symmetrized-projector quantum Monte Carlo method for low-lying excited states of the Hubbard model

Bhargavi Srinivasan, S. Ramasesha, H. R. Krishnamurthy

Published Jul 15, 1996• 5 citations
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Abstract

We develop a multiconfigurational symmetrized-projector quantum Monte Carlo (MSPQMC) method to calculate excited-state properties of Hubbard models. We compare the MSPQMC results for finite Hubbard chains with exact results (where available) or with density-matrix renormalization-group results for longer chains. The energies and correlation functions of the excited states are in good agreement with those obtained from the alternate techniques.

DOI
10.1103/physrevb.54.r2276

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We develop a multiconfigurational symmetrized-projector quantum Monte Carlo (MSPQMC) method to calculate excited-state properties of Hubbard models. We compare the MSPQMC results for finite Hubbard chains with exact results (where available) or with density-matrix renormalization-group results for longer chains. The energies and correlation functions of the excited states are in good agreement with those obtained from the alternate techniques.
We present in detail the recently developed multiconfigurational symmetrized projector quantum Monte Carlo method for excited states of the Hubbard model. We describe the implementation of the Monte Carlo method for a multiconfigurational trial wave function. We give a detailed discussion of issues related to the symmetry of the projection procedure that validates our Monte Carlo procedure for excited states. In this context we discuss various averaging procedures for the Green function and present an analysis of the errors incurred in these procedures. We study the ground-state energy and correlation functions of the one-dimensional Hubbard model at half-filling to confirm these analyses. We then study the energies and correlation functions of excited states of Hubbard chains. Hubbard rings away from half-filling are also studied and the pair binding energies for holes of 4n4n4n and 4n+24n+24n+2 systems are compared with the Bethe ansatz results of Fye, Martins, and Scalettar [Phys. Rev. B 42, 6809 (1990)]. Our study of the two-dimensional Hubbard model includes the $4\ifmmode\times\else\texttimes\fi{}2$ ladder and the $3\ifmmode\times\else\texttimes\fi{}4$ lattice with periodic boundary conditions. The $3\ifmmode\times\else\texttimes\fi{}4$ lattice is nonbipartite and amenable to exact diagonalization studies and is, therefore, a good candidate for checks on the method. We are able to reproduce accurately the energies of ground and excited states, both at and away from half-filling. We study the properties of the $4\ifmmode\times\else\texttimes\fi{}2$ Hubbard ladder with bond alternation as the correlation strength and filling are varied. The method reproduces the correlation functions accurately. We also examine the severity of sign problem for one- and two-dimensional systems.
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We extend the density-matrix renormalization-group (DMRG) method to exploit parity, C2{\mathit{C}}_{2}C2​ (rotation by \ensuremath{\pi}), and electron-hole symmetries of model Hamiltonians. We demonstrate the power of this method by obtaining the lowest-energy states in all eight symmetry subspaces of Hubbard chains with up to 50 sites. The ground-state energy, optical gap, and spin gap of regular U=4t and U=6t Hubbard chains agree very well with exact results. This development extends the scope of the DMRG method and allows future applications to study of optical properties of low-dimensional conjugated polymeric systems. \textcopyright{} 1996 The American Physical Society.
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