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arXiv:1008.1106 · Journal of Physics Condensed Matter

Influence of super-ohmic dissipation on a disordered quantum critical point

Thomas Vojta, José A. Hoyos, Priyanka Mohan, Rajesh Narayanan

Published Feb 17, 2011• 12 citations
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Abstract

We investigate the combined influence of quenched randomness and dissipation on a quantum critical point with O(N) order-parameter symmetry. Utilizing a strong-disorder renormalization group, we determine the critical behavior in one space dimension exactly. For super-ohmic dissipation, we find a Kosterlitz-Thouless type transition with conventional (power-law) dynamical scaling. The dynamical critical exponent depends on the spectral density of the dissipative baths. We also discuss the Griffiths singularities, and we determine observables.

DOI
10.1088/0953-8984/23/9/094206

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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 interplay between disorder, quantum fluctuations, and dissipation is studied in the random transverse Ising chain coupled to a dissipative Ohmic bath with a real space renormalization group. A typically very large length scale L* is identified above which the physics of frozen clusters dominates. Below L* a strong-disorder fixed point determines scaling at a pseudocritical point. In a Griffiths-McCoy region frozen clusters produce already a finite magnetization resulting in a classical low temperature behavior of the susceptibility and specific heat. These override the confluent singularities that are characterized by a continuously varying exponent z and are visible above a temperature T*approximately L*-z.
We study the effects of Ohmic, super-Ohmic, and sub-Ohmic dissipation on the zero-temperature quantum phase transition in the random transverse-field Ising chain by means of an (asymptotically exact) analytical strong-disorder renormalization-group approach. We find that Ohmic damping destabilizes the infinite-randomness critical point and the associated quantum Griffiths singularities of the dissipationless system. The quantum dynamics of large magnetic clusters freezes completely, which destroys the sharp phase transition by smearing. The effects of sub-Ohmic dissipation are similar and also lead to a smeared transition. In contrast, super-Ohmic damping is an irrelevant perturbation; the critical behavior is thus identical to that of the dissipationless system. We discuss the resulting phase diagrams, the behavior of various observables, and the implications to higher dimensions and experiments.
We study the effect of dissipation on the infinite randomness fixed point and the Griffiths-McCoy singularities of random transverse Ising systems in chains, ladders and in two-dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of Ohmic dissipation the susceptibility displays a crossover from Griffiths-McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature T∗T^*T∗. The specific heat displays Griffiths-McCoy singularities over the whole temperature range. For super-Ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths-McCoy phase can be determined analytically.
We study the effect of dissipation on the infinite randomness fixed point and the Griffiths–McCoy singularities of random transverse Ising systems in chains, ladders and in two dimensions. A strong disorder renormalization group scheme is presented that allows the computation of the finite temperature behavior of the magnetic susceptibility and the spin specific heat. In the case of ohmic dissipation the susceptibility displays a crossover from Griffiths–McCoy behavior (with a continuously varying dynamical exponent) to classical Curie behavior at some temperature T * . The specific heat displays Griffiths–McCoy singularities over the whole temperature range. For super-ohmic dissipation we find an infinite randomness fixed point within the same universality class as the transverse Ising system without dissipation. In this case the phase diagram and the parameter dependence of the dynamical exponent in the Griffiths–McCoy phase can be determined analytically.