Condensed Matter Physics, 2014, vol. 17, No. 2, p. 23002:1-6
DOI:10.5488/CMP.17.23002           arXiv:1407.2050

Title: On the particle-hole symmetry of the fermionic spinless Hubbard model in D=1
  M.T. Thomaz (Instituto de Física, Universidade Federal Fluminense, Av. Gal. Milton Tavares de Souza s/no, CEP 24210-346, Niterói-RJ, Brazil) ,
  E.V. Corrêa Silva (Departamento de Matemática, Física e Computação, Faculdade de Tecnologia, Universidade do Estado do Rio de Janeiro, Rodovia Presidente Dutra km 298 s/no, Pólo Industrial, CEP 27537-000, Resende-RJ, Brazil) ,
  O. Rojas (Departamento de Ciências Exatas, Universidade Federal de Lavras, Caixa Postal 3037, CEP 37200-000, Lavras-MG, Brazil)

We revisit the particle-hole symmetry of the one-dimensional (D=1) fermionic spinless Hubbard model, associating that symmetry to the invariance of the Helmholtz free energy of the one-dimensional spin-1/2 XXZ Heisenberg model, under reversal of the longitudinal magnetic field and at any finite temperature. Upon comparing two regimes of that chain model so that the number of particles in one regime equals the number of holes in the other, one finds that, in general, their thermodynamics is similar, but not identical: both models share the specific heat and entropy functions, but not the internal energy per site, the first-neighbor correlation functions, and the number of particles per site. Due to that symmetry, the difference between the first-neighbor correlation functions is proportional to the z-component of magnetization of the XXZ Heisenberg model. The results presented in this paper are valid for any value of the interaction strength parameter V, which describes the attractive/null/repulsive interaction of neighboring fermions.

Key words: quantum statistical mechanics, strongly correlated electron system, spin chain models
PACS: 05.30.Fk, 71.27.+a, 75.10.Pq

Full text [pdf] << List of papers