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arXiv:cond-mat/0306713 · Physica A Statistical Mechanics and its Applications

Low-temperature quantum critical behaviour of systems with transverse Ising-like intrinsic dynamics

Alvaro CaramicoD'Auria, Luigi DeCesare, Ileana Rabuffo

Published Jun 21, 2003• 15 citations
arXivHTMLPDF
DOI
10.1016/s0378-4371(03)00403-5

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The Landau-Ginsburg free-energy functional (effective Hamiltonian) is derived for compressible Ising systems where the Ising spins are coupled with quantum phonon fields and a transverse field is present. In the zero transverse field case, the phonon dynamical modes also disappear from the effective Hamiltonian, which then compares with those studied by Sak and De Moura et al. in the non-quantum compressible Ising systems. In the presence of dynamics in the spin system (compressible transverse Ising system), the phonon modes get effectively coupled in the Hamiltonian and while at non-zero temperatures this does not affect the critical behaviour (which remains the same as in the non-quantum case), the presence of these dynamical modes effectively increases the lattice dimensionality by unity at zero-temperature transitions (T c =0) where one observes the critical behaviour corresponding to a d+1 dimensional non-quantum compressible Ising model. The critical behaviour of a cooperative Jahn-Teller phase transition when T c to 0 is also discussed.
The quantum-classical crossover critical behaviour of the Ising model in a transverse field Gamma is first studied in one dimension where exact results are obtained. The correspondence between the quantum-classical crossover behaviour of this d-dimensional quantum model and the finite-size crossover behaviour of an equivalent (d+1)-dimensional classical model exact for d=1 is extended to higher dimensions. The crossover depends strongly on the relative magnitude of the crossover exponent phi and of the critical line-shift exponent Psi . In particular, if Pi > Psi approaches the critical line along a path of constant transverse field less than the critical field Gamma c and a low temperature, only classical behaviour is seen, quantum effects do not show up. There is some controversy about the value of Psi . Experiments are suggested to give an answer.