Twisted boundary conditions and effective mass in Heisenberg-Ising and Hubbard rings
Abstract
We identify the boundary energy of a many-body system of fermions on a lattice under twisted boundary conditions as the inverse of the effective charge-carrying mass, or the stiffness, renormalizing nontrivially under interactions due to the absence of Galilean invariance. We point out that this quantity is a sensitive and direct probe of the metal-insulator transitions possible in these systems, i.e., the Mott-Hubbard transition or Density-wave formation. We calculate exactly the stiffness, or the effective mass, in the 1D Heisenberg-Ising ring and the 1D Hubbard model by using the ansatz of Bethe. For the Hubbard ring we also calculate a spin stiffness by extending the nested ansatz of Bethe-Yang to this case.
- Publication:
-
Physical Review Letters
- Pub Date:
- July 1990
- DOI:
- 10.1103/PhysRevLett.65.243
- Bibcode:
- 1990PhRvL..65..243S
- Keywords:
-
- 71.30.+h;
- 75.10.Jm;
- Metal-insulator transitions and other electronic transitions;
- Quantized spin models