Ground state of a spin-phonon system. II. Adiabatic limit |
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Authors: | Eugene P. Gross |
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Affiliation: | (1) The Martin Fisher School of Physics, Brandeis University, 02254 Waltham, Massachusetts |
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Abstract: | The phase transition for a spin in a magnetic fieldB coupled to acoustic phonons by a coupling constant is studied. The caseB 1 with an upper cutoff of unity for the phonons is studied systematically by using an adiabatic canonical transformation. In leading order the transition line is at =2 /B=1. In the normal phase ( <1) the ground-state energy is –B/2 plus a function of that is given explicitly as the solution of a pair theory. In the broken symmetry phase ( >1) the energy is the classical energy plus the same function of =1/ 2. It is found that the first derivatives of the energy with respect to and with respect toB have finite jumps across the transition line. Quantum fluctuations in both phases are treated. Higher-order terms are a series of powers of 1/B times functions of . The case of a small transverse fieldB is also studied. The sharp transition disappears and is replaced by rapid variation in a region of order (B1/B)2/3 about =1. |
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Keywords: | Spin phonon adiabatic transition spin phonon ground state |
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