Theory of a spherical quantum rotors model: low--temperature regime and finite-size scaling

Abstract

The quantum rotors model can be regarded as an effective model for the low-temperature behavior of the quantum Heisenberg antiferromagnets. Here, we consider a $d$-dimensional model in the spherical approximation confined to a general geometry of the form $L^{d-d^{\prime }}\times {\infty }^{d^{\prime }}\times L_{\tau }^z$ ( $L$-linear space size and $L_{\tau }$-temporal size) and subjected to periodic boundary conditions. Due to the remarkable opportunity it offers for rigorous study of finite-size effects at arbitrary dimensionality this model may play the same role in quantum critical phenomena as the popular Berlin-Kac spherical model in classical critical phenomena. Close to the zero-temperature quantum critical point, the ideas of finite-size scaling are utilized to the fullest extent for studying the critical behavior of the model. For different dimensions $1<d<3$ and $0\le d^{\prime }\le d$ a detailed analysis, in terms of the special functions of classical mathematics, for the susceptibility and the equation of state is given. Particular attention is paid to the two-dimensional case.

33pages, revtex+epsf, 3ps figures included submitted to PRB

References in corpus (5)

• Continuous Quantum Phase Transitions
• Quantum Phase Transitions and Conserved Charges
• Quantum description of spherical spins
• The Thermodynamics of Quantum Systems and Generalizations of Zamolodchikov's C-theorem
• Finite Size Effects and Conformal Symmetry of $O(N)$ Nonlinear $\sigma$ Model in Three Dimensions

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