Glassy quantum dynamics of disordered Ising spins

Schultzen, Philipp; Franz, Titus; Geier, Sebastian; Salzinger, Andre; Tebben, Annika; Hainaut, Clément; Zürn, Gerhard; Weidemüller, Matthias; Gärttner, Martin

doi:10.48550/arxiv.2104.00349

Cited by 3 publications

(9 citation statements)

References 31 publications

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“…In contrast to dissipative systems, closed quantum systems are subjected to unitary dynamics where relaxation can solely be explained by interactions. In recent work, we have derived analytically the occurrence of stretched exponential law for the disordered quantum Ising model in the thermodynamic limit, where the interactions between different spins feature a scale-invariant distribution [18]. These observations indicate also in disordered quantum systems that scale-invariance implies glassy dynamics.…”

Section: Introductionmentioning

confidence: 86%

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

Schultzen,

Franz,

Hainaut

et al. 2021

Preprint

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We numerically study out-of-equilibrium dynamics in a family of Heisenberg models with 1/r 6 power-law interactions and positional disorder. Using the semi-classical discrete truncated Wigner approximation (dTWA) method, we investigate the time evolution of the magnetization and ensemble-averaged single-spin purity for a strongly disordered system after initializing the system in an out-of-equilibrium state. We find that both quantities display robust glassy behavior for almost any value of the anisotropy parameter of the Heisenberg Hamiltonian. Furthermore, a systematic analysis allows us to quantitatively show that, for all the scenarios considered, the stretch power lies close to the one analytically obtained in the Ising limit. This indicates that glassy relaxation behavior occurs widely in disordered quantum spin systems, independent of the particular symmetries and integrability of the Hamiltonian.

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Section: Introductionmentioning

confidence: 86%

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

Schultzen,

Franz,

Hainaut

et al. 2021

Preprint

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“…For a disordered spin-1/2 system, recent studies confirmed a stretched-exponential decay of magnetization in both Ising [8] and Heisenberg [9,10] models, where the pairwise spin-spin interaction exhibits a pow-law dependence on the inter-spin distance r, J(r) ∝ 1/r α with α ≥ d in the d-dimension. The scale invariance is guaranteed since pairwise contribution to the relaxation dynamics is determined by J(r)t, which is invariant under the following rescaling of space and time: r → λr and * Electronic address: bzhu@physi.uni-heidelberg.de t → λ α t.…”

Section: Introductionmentioning

confidence: 88%

“…Following the same derivation procedure in Ref. [8], by replacing the ensemble average with an average over all possible configurations of placing N − 1 spins around a reference one at r 1 = 0, Eq. ( 3) can be transformed to…”

Section: B Homogeneous Samples: the Thermodynamic Limitmentioning

confidence: 99%

“…For the power-law interaction (∝ 1/r α ) a shortdistance cutoff has to be introduced to avoid the divergence of interaction strength for further simplifying Eq. ( 4) [8], which is not necessary for the soft-core potential considered here. By introducing a new variable y = J 0 t/[1 + (r/Rc) α ] and integrating by parts, Eq.…”

Section: B Homogeneous Samples: the Thermodynamic Limitmentioning

confidence: 99%

“…For example, many relaxations in glass materials (normal or spin-type) follow a simple stretched-exponential law (∝ exp[−(γt) β ], β < 1) [1,6]. Klafter and Shlesinger found that a scale-invariant distribution of relaxation times was the common underlying structure for three different physical models showing a stretched-exponential decay [7], which was generalized to closed quantum systems by Schultzen and coworkers recently [8].…”

Section: Introductionmentioning

confidence: 99%

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Dynamics of position disordered Ising spins with a soft-core potential

Tan,

Lin,

Zhou

et al. 2021

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We theoretically study magnetization relaxation of Ising spins distributed randomly in a ddimension homogeneous and Gaussian profile under a soft-core two-body interaction potential ∝ 1/[1 + (r/Rc) α ] (α ≥ d), where r is the inter-spin distance and Rc is the soft-core radius. The dynamics starts with all spins polarized in the transverse direction. In the homogeneous case, an analytic expression is derived at the thermodynamic limit, which starts as ∝ exp(−kt 2 ) with a constant k and follows a stretched-exponential law at long time with an exponent β = d/α. In between an oscillating behaviour is observed with a damping amplitude. For Gaussian samples, the degree of disorder in the system can be controlled by the ratio lρ/Rc with lρ the mean inter-spin distance and the magnetization dynamics is investigated numerically. In the limit of lρ/Rc 1, a coherent many-body dynamics is recovered for the total magnetization despite of the position disorder of spins. In the opposite limit of lρ/Rc 1, a similar dynamics as that in the homogeneous case emerges at later time after a initial fast decay of the magnetization. We obtain a stretched exponent of β ≈ 0.18 for the asymptotic evolution with d = 3, α = 6, which is different from that in the homogeneous case (β = 0.5).

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Effects of critical correlations on quantum percolation in two dimensions

De Tomasi,

Hart,

Glittum

et al. 2022

Preprint

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We analyze the out-of-equilibrium dynamics of a quantum particle coupled to local magnetic degrees of freedom that undergo a classical phase transition. Specifically, we consider a two-dimensional tight-binding model that interacts with a background of classical spins in thermal equilibrium, which are subject to Ising interactions and act as emergent, correlated disorder for the quantum particle. Particular attention is devoted to temperatures close to the ferromagnet-to-paramagnet transition.To capture the salient features of the classical transition, namely the effects of long-range correlations, we focus on the strong coupling limit, in which the model can be mapped onto a quantum percolation problem on spin clusters generated by the Ising model. By inspecting several dynamical probes such as energy level statistics, inverse participation ratios, and wave-packet dynamics, we provide evidence that the classical phase transition might induce a delocalization-localization transition in the quantum system at certain energies. We also identify further important features due to the presence of Ising correlations, such as the suppression of compact localized eigenstates.

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Glassy quantum dynamics of disordered Ising spins

Cited by 3 publications

References 31 publications

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

Semiclassical simulations predict glassy dynamics for disordered Heisenberg models

Dynamics of position disordered Ising spins with a soft-core potential

Effects of critical correlations on quantum percolation in two dimensions

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