Density-matrix renormalization group for a gapless system of free fermions

Physical Review B - Condensed Matter and Materials Physics

Volumn 59, Issue 16, 1999, Pages 10493-10503

  Andersson, Martin ^a   Boman, Magnus ^a   Östlund, Stellan ^a  

^a CHALMERS UNIVERSITY OF TECHNOLOGY   (Sweden)

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EID: 4244187214     PISSN: 10980121     EISSN: 1550235X     Source Type: Journal    
DOI: 10.1103/PhysRevB.59.10493     Document Type: Article

References (23)

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16. We have chosen to include a factor of (Formula presented) in the hopping term of the Hamiltonian in order to have a translationally invariant ground state, but this is only a matter of convenience. By simply making the canonical transformation (Formula presented) we can remove this sign from H.
17. In the thermodynamic limit (Formula presented) the ground-state energy per site is given by (Formula presented)which is a complete elliptic integral of the second kind.
18. The result is derived by introducing periodic boundary conditions, letting (Formula presented) and studying the asymptotic behavior of (Formula presented) for large l.
19. From the block structure of (Formula presented) it follows that (Formula presented) has the block form (Formula presented)Assuming that (Formula presented) is an eigenvector of (Formula presented) with corresponding eigenvalue (Formula presented) it follows that (Formula presented) and (Formula presented) Defining (Formula presented) we find (Formula presented)i.e., (Formula presented) is an eigenvector of (Formula presented) corresponding to the eigenvalue (Formula presented)
20. Generally the matrix (Formula presented) is nonsymmetric, which forces us to distinguish between right and left eigenvectors.
21. We have used the ARPACK library available on Netlib.
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