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Physica C Superconductivity

Monte Carlo finite-size analysis of Yang-Lee zeros of the grand canonical partition function for a 2D Hubbard model

E. Abraham, Ian M. Barbour, P.H. Cullen, Elyakum G. Klepfish, Edward R. Pike, Sarben Sarkar

Published Dec 1, 1994• 0 citations
Publisher
DOI
10.1016/0921-4534(94)92433-3

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We present a technique for a numerical analysis of the phase structure of the two-dimensional Hubbard model as a function of the hole chemical potential. The grand-canonical partition function for the model is obtained via Monte Carlo simulations. The dependence of the hole occupation number on the chemical potential and the temperature is evaluated. These calculations, together with a study of the Yang-Lee zeros of the grand-canonical partition function, show evidence of a phase transition at zero temperature and particle density below half filling. The binding energy of a pair of holes is calculated in the low-temperature regime and the possibility for pairing is explored.
A finite-size scaling is applied to the Yang-Lee zeros of the grand canonical partition function for the two-dimensional Hubbard model in the complex chemical potential plane. The logarithmic scaling of the imaginary part of the zeros with the system size indicates a singular dependence of the carrier density on the chemical potential. Our analysis points to a second-order phase transition with critical exponent 1/\ensuremath{\delta}=1/2\ifmmode\pm\else\textpm\fi{}1/3, which leads to a divergence of the electronic susceptibility. We interpret these results as reflecting the singular behavior of the density of states in the quasiparticle spectrum. \textcopyright{} 1996 The American Physical Society.
Abstract To understand the distribution of the Yang–Lee zeros in quantum integrable field theories we analyse the simplest of these systems given by the 2D Yang–Lee model. The grand-canonical partition function of this quantum field theory, as a function of the fugacity z and the inverse temperature β , can be computed in terms of the thermodynamics Bethe Ansatz based on its exact S -matrix. We extract the Yang–Lee zeros in the complex plane by using a sequence of polynomials of increasing order N in z which converges to the grand-canonical partition function. We show that these zeros are distributed along curves which are approximate circles as it is also the case of the zeros for purely free theories. There is though an important difference between the interactive theory and the free theories, for the radius of the zeros in the interactive theory goes continuously to zero in the high-temperature limit β → 0 while in the free theories it remains close to 1 even for small values of β , jumping to 0 only at β = 0 .