Phase-ordering dynamics in itinerant quantum ferromagnets

We consider an open system near a quantum critical point that is suddenly moved towards the critical point. The bath-dominated diffusive non-equilibrium dynamics after the quench is shown to follow scaling behavior, governed by a critical exponent that emerges in addition to the known equilibrium critical exponents. We determine this exponent and show that it describes universal prethermalized coarsening dynamics of the order parameter in an intermediate time regime. Implications of this quantum critical prethermalization are a powerlaw rise of order and correlations after an initial collapse of the equilibrium state and a crossover to thermalization that occurs arbitrarily late for sufficiently shallow quenches.Predicting the out-of-equilibrium dynamics of quantum many-body systems is a challenge of fundamental and practical importance. This research area has been boosted by recent experiments in cold-atom gases [1] and scaled-up quantum-circuits [2], by ultra-fast pump-probe measurements in correlated materials [3][4][5], and by performing heavy-ion collisions that explore the quark-gluon plasma [6]. In this context, the universality near a quantum critical point (QCP), well established in and near equilibrium, comes with the potential to make quantitative predictions for strongly interacting systems far from equilibrium. For example, the quantum version [7][8][9][10][11] of the Kibble-Zurek mechanism of defect formation [12,13] was developed for systems driven through a symmetry breaking QCP at a small, but finite rate. Similarly, near a QCP the long-time dynamics after a sudden change of Hamiltonian parameters, is governed by equilibrium exponents [14]. These phenomena occur in the regime of longest time scales.Recently, however, many physical systems away from equilibrium were identified which display novel dynamical behavior on intermediate time scales, a behavior often referred to as prethermalization [15][16][17][18][19][20][21][22][23][24][25]. The question arises whether one can expect universality during prethermalization if one drives a system towards a QCP. Even if this is done at a finite rate 1/τ , a system will fall out of equilibrium at some point, a behavior owed to the critical slowing down near the QCP. Then a scaling theory with characteristic time scale τ can be developed [10], where regions of the size of the freeze-out length ∝ τ 1/z emerge that behave like in equilibrium. z is the dynamic critical exponent. In case of a quantum quench, the time scale τ and the freeze-out length become comparable to microscopic time and length scales, respectively and the system instantly falls out of equilibrium. The detailed recovery of this out-of-equilibrium dynamics, along with the time dependence of length scales, order-parameter correlations, and the potential for outof-equilibrium universality are major theoretical and experimental challenges.In this Letter, we show that the time evolution of observables in an open system that is suddenly moved to a QCP displays universal behavior (see Fig. 1(a-b)...

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“…Performing the limit z → 2 in the coefficient in Eq. (16) in front of I 0 , we obtain the result for the exponent given in the main paper:…”

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confidence: 67%

“…Recently, however, many physical systems away from equilibrium were identified which display novel dynamical behavior on intermediate time scales, a behavior often referred to as prethermalization [15][16][17][18][19][20][21][22][23][24][25]. The question arises whether one can expect universality during prethermalization if one drives a system towards a QCP.…”

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confidence: 99%

Universal Postquench Prethermalization at a Quantum Critical Point

2014

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“…Quenches, i.e., rapid changes of external parameter values, at T = 0 in both clean and disordered metallic FMs are interesting. Belitz et al (2007) have shown that the coupling of the OP to the fermionic soft modes leads to qualitatively new effects for the late-stage coarsening. Gagel et al (2014) have shown that there is universal pre-asymptotic behavior in general quantum quench problems due to long-range boundary effects.…”

Section: B Open Problemsmentioning

confidence: 99%

Metallic quantum ferromagnets

et al. 2016

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We give an overview of quantum phase transitions (QPTs) in metallic ferromagnets, discussing both experimental and theoretical aspects. These QPTs can be classified with respect to the presence and strength of quenched disorder: Clean systems generically show a discontinuous, or first-order, QPT from a ferromagnetic to a paramagnetic state as a function of some control parameter, as predicted by theory. Disordered systems are much more complicated, depending on the disorder strength and the distance from the QPT. In many disordered materials the QPT is continuous, or second order, and Griffiths-phase effects coexist with QPT singularities near the transition. In other systems the transition from the ferromagnetic state at low temperatures is to a different type of long-range order, such as an antiferromagnetic or a spin-density-wave state. In still other materials a transition to a state with glass-like spin dynamics is suspected. The review provides a comprehensive discussion of the current understanding of these various transitions, and of the relation between experiment and theory.

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“…The reasonable assumption whereby fluctuations within domains should be determined by quantum and thermal fluctuations while the dynamics of interfaces should be close to the ones of their classical counterparts has been demonstrated in some solvable mean-field models [85,86]. A scenario for the time-dependence of a growing length with several crossovers, in the coarsening dynamics of 3d itinerant ferromagnets was put forward in [87].…”

Section: Beyond Physicsmentioning

confidence: 99%

Coarsening phenomena

Cugliandolo

2015

Comptes Rendus. Physique

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Phase-ordering dynamics in itinerant quantum ferromagnets

Cited by 4 publications

References 19 publications

Universal Postquench Prethermalization at a Quantum Critical Point

Universal Postquench Prethermalization at a Quantum Critical Point

Metallic quantum ferromagnets

Coarsening phenomena

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