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Weak disorder effects on criticality in quantum systems

Gaetano Busiello, L. De Cesare, Ileana Rabuffo

Published Jan 1, 1986• 1 citation
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•Jan 1, 2007•0 citations
A field-theoretic description of the critical behavior of the weakly disordered systems is given. Directly, for three- and two-dimensional systems a renormalization analysis of the effective Hamiltonian of a model with replica symmetry breaking (RSB) potentials is carried out in the two-loop approximation. For the case with 1-step RSB the fixed points (FP's) corresponding to stability of the various types of critical behavior are identified with the use of the Pade-Borel summation technique. Analysis of FP's has shown a stability of the critical behavior of the weakly disordered systems with respect to RSB effects and realization of a former scenario of disorder influence on critical behavior.
Critical properties of quantum spin chains with varying degrees of disorder are studied at zero temperature by analytical and extensive density matrix renormalization methods. Generally the phase diagram is found to contain three phases. The weak disorder regime, where the critical behavior is controlled by the fixed points of the pure system, and the strong disorder regime, which is attracted by an infinite randomness fixed point, are separated by an intermediate disorder regime, where dynamical scaling is anisotropic and the static and dynamical exponents are disorder dependent.
We reconcile the possible presence of a quantum critical point in metal insulator transition phenomena in two-dimensional electron systems with observed electronic properties in the low resistivity region which are those of a weakly disordered Fermi liquid. The central issue of whether the ground state of an interacting 2D electron system in the presence of weak potential scattering from disorder is a metal or an insulator remains unresolved. Additional new effects which may become important at extremely low electron densities are briefly mentioned.