Study of One-Dimensional Quantum Spin Systems by the Transfer-Matrix Method | Zendy

Hiroshi Betsuyaku | Zendy

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Study of One-Dimensional Quantum Spin Systems by the Transfer-Matrix Method

Author(s) -

Hiroshi Betsuyaku

Publication year - 1985

Publication title -

progress of theoretical physics

Language(s) - English

Resource type - Journals

eISSN - 1347-4081

pISSN - 0033-068X

DOI - 10.1143/ptp.73.319

Subject(s) - physics , extrapolation , partition function (quantum field theory) , spin (aerodynamics) , mathematical physics , matrix (chemical analysis) , limiting , quantum mechanics , convergence (economics) , quantum , ising model , transfer matrix , statistical physics , mathematical analysis , mathematics , thermodynamics , materials science , computer science , computer vision , mechanical engineering , engineering , economics , economic growth , composite material

, ' The Suzuki-Trotter formula has been used to get the mth approximant to the classical representation of the partition function of the one-dimensional N-spin 5=+ quantum spin systems. The equivalent two-dimensional (NX2m) Ising model with four-spin interactions has been studied in detail by using the numerically exact transfer-matrix method for T;;;;O.05 and m~8. The convergence properties have been examined in two different representations; checkerboard decomposition (CBD) and real-space decomposition (RSD). The spin correlation functions in RSD converge much faster than those in CBD. The limiting m --+ 00 behavior has been estimated from the extrapolation formula of the form: E( m) = E( 00 ) +a/m 2 • The limiting values of the energy derived from the nearest-neighbor correlation agree with: the correct values excellently.

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