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Non‐ergodicity of the 1D Heisenberg model
Author(s) -
Bak M.,
Avella A.,
Mancini F.
Publication year - 2003
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.200301688
Subject(s) - ergodicity , extrapolation , lanczos resampling , zero (linguistics) , limit (mathematics) , heisenberg model , thermodynamic limit , energy (signal processing) , zero point energy , spin (aerodynamics) , physics , mathematics , statistical physics , mathematical physics , mathematical analysis , quantum mechanics , antiferromagnetism , eigenvalues and eigenvectors , thermodynamics , linguistics , philosophy
The relevance of zero‐energy functions, coming from zero‐energy modes and present in the structure of bosonic Green's functions, is often underestimated. Usually, their values are fixed by assuming the ergodicity of the dynamics, but it can be shown that this is not always correct. As the zero‐energy functions are connected to fundamental response properties of the system under analysis (specific heat, compressibility, susceptibility, etc.), their correct determination is not an irrelevant issue. In this paper we present some results regarding the zero‐energy functions for the Heisenberg chain of spin‐1/2 with periodic boundary conditions as functions of the number of sites, temperature, and magnetic field. Calculations are pursued for finite chains, using equations of motion, exact diagonalization and Lanczos technique, and the extrapolation to the thermodynamic limit is studied.