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Infinite randomness and activated dynamical scaling in itinerant antiferromagnets

José A. Hoyos, Chetan Kotabage, Thomas Vojta

Published May 14, 2007• 1 citation
OpenAlex

Abstract

We study the effects of quenched disorder on the quantum phase transition of itinerant Heisenberg antiferromagnets. To this end, we apply a strong-disorder renormalization group method to the order parameter field theory of the problem. We find that the overdamped dynamics of the magnetic modes leads to a non-perturbative infinite-randomness critical point with unconventional activated dynamical scaling. We also discuss extra complications due long-range RKKY interactions as well as experimental implications for heavy fermion materials and other systems.

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We study the effects of quenched disorder on the quantum phase transition of itinerant Heisenberg antiferromagnets. To this end, we apply a strong-disorder renormalization group method to the order parameter field theory of the problem. We find that the overdamped dynamics of the magnetic modes leads to a non-perturbative infinite-randomness critical point with unconventional activated dynamical scaling. We also discuss extra complications due long-range RKKY interactions as well as experimental implications for heavy fermion materials and other systems.
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We develop a strong-disorder renormalization group to study quantum phase transitions with continuous O(N)O(N)O(N) symmetry order parameters under the influence of both quenched disorder and dissipation. For Ohmic dissipation, as realized in Hertz's theory of the itinerant antiferromagnetic transition or in the superconductor-metal transition in nanowires, we find the transition to be governed by an exotic infinite-randomness fixed point in the same universality class as the (dissipationless) random transverse-field Ising model. We determine the critical behavior and calculate key observables at the transition and in the associated quantum Griffiths phase. We also briefly discuss the cases of super-Ohmic and sub-Ohmic dissipations.
We study the effects of dissipation on a disordered quantum phase transition with O(N) order-parameter symmetry by applying a strong-disorder renormalization group to the Landau-Ginzburg-Wilson field theory of the problem. We find that Ohmic dissipation results in a nonperturbative infinite-randomness critical point with unconventional activated dynamical scaling while super-Ohmic damping leads to conventional behavior. We discuss applications to the superconductor-metal transition in nanowires and to the Hertz theory of the itinerant antiferromagnetic transition.
The effects of quenched disorder on the critical properties of itinerant quantum antiferromagnets and ferromagnets are considered. Particular attention is paid to locally ordered spatial regions that are formed in the presence of quenched disorder even when the bulk system is still in the paramagnetic phase. These rare regions or local moments are reflected in the existence of spatially inhomogeneous saddle points of the Landau-Ginzburg-Wilson functional. We derive an effective theory that takes into account small fluctuations around all of these saddle points. The resulting free energy functional contains a new term in addition to those obtained within the conventional perturbative approach, and it comprises what would be considered nonperturbative effects within the latter. A renormalization group analysis shows that in the case of antiferromagnets, the previously found critical fixed point is unstable with respect to this new term, and that no stable critical fixed point exists at one-loop order. This is contrasted with the case of itinerant ferromagnets, where we find that the previously found critical behavior is unaffected by the rare regions due to an effective long-ranged interaction between the order parameter fluctuations.
We investigate the effects of quenched disorder on first-order quantum phase transitions on the example of the NNN-color quantum Ashkin-Teller model. By means of a strong-disorder renormalization group, we demonstrate that quenched disorder rounds the first-order quantum phase transition to a continuous one for both weak and strong coupling between the colors. In the strong-coupling case, we find a distinct type of infinite-randomness critical point characterized by additional internal degrees of freedom. We investigate its critical properties in detail and find stronger thermodynamic singularities than in the random transverse field Ising chain. We also discuss the implications for higher spatial dimensions as well as unusual aspects of our renormalization-group scheme.
We study the influence of quenched disorder on quantum phase transitions in itinerant magnets with Heisenberg spin symmetry, paying particular attention to rare disorder fluctuations. In contrast to the Ising case where the Landau damping of the spin fluctuations suppresses the tunneling of the rare regions, the Heisenberg system displays strong power-law quantum Griffiths singularities in the vicinity of the quantum critical point. We discuss these phenomena based on general scaling arguments, and we illustrate them by an explicit calculation for O(N)O(N)O(N) spin symmetry in the large-NNN limit. We also discuss broad implications for the classification of quantum phase transitions in the presence of quenched disorder.