Real-time dynamics induced by quenches across the quantum critical points in gapless Fermi systems with a magnetic impurity

Kleine, Christian; Mußhoff, Julian; Anders, Frithjof B.

doi:10.1103/physrevb.90.235145

Cited by 4 publications

(10 citation statements)

References 52 publications

(179 reference statements)

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“…The quantities |α(t)| and |β(t)| hence do not show any signatures of discrete scale invariance, only a power-law fall-off determined by υ I . The physical variable in the holographic Kondo model is of course the complex vev β(t) ∼ O (16). Hence while the modulus | O(t) | decreases as a power-law, its complex phase rotates with ∼ log t. Equivalently, we see that the (bulk) gauge-invariant quantity ∆ t = µ − ∂ψ 0 falls off towards the limiting value ∆ t = 1/2 as ∼ t −1 .…”

Section: Power-law Behaviour and Discrete Scale Invariance At The Crimentioning

confidence: 75%

“…Quantum quenches in the standard SU (2) Kondo model were recently studied within condensed matter physics. These investigations include [15][16][17][18][19]. In particular, [15] deals with the study of a quantum quench caused by the absorption of a photon by a quantum dot, while [18] studies the universal behaviour of entanglement entropy after a quench of an impurity system.…”

Section: Introductionmentioning

confidence: 99%

“…In particular, [15] deals with the study of a quantum quench caused by the absorption of a photon by a quantum dot, while [18] studies the universal behaviour of entanglement entropy after a quench of an impurity system. In [16], quenches in the pseudogap single-impurity Anderson model are investigated using numerical RG techniques. The system reaches an equilibrium state at late times.…”

Section: Introductionmentioning

confidence: 99%

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Quantum quenches in a holographic Kondo model

Erdmenger

Flory

Newrzella

et al. 2017

J. High Energ. Phys.

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We study non-equilibrium dynamics and quantum quenches in a recent gauge/ gravity duality model for a strongly coupled system interacting with a magnetic impurity with SU(N ) spin. At large N , it is convenient to write the impurity spin as a bilinear in Abrikosov fermions. The model describes an RG flow triggered by the marginally relevant Kondo operator. There is a phase transition at a critical temperature, below which an operator condenses which involves both an electron and an Abrikosov fermion field. This corresponds to a holographic superconductor in AdS 2 and models the impurity screening. We quench the Kondo coupling either by a Gaussian pulse or by a hyperbolic tangent, the latter taking the system from the condensed to the uncondensed phase or vice-versa. We study the time dependence of the condensate induced by this quench. The timescale for equilibration is generically given by the leading quasinormal mode of the dual gravity model. This mode also governs the formation of the screening cloud, which is obtained as the decrease of impurity degrees of freedom with time. In the condensed phase, the leading quasinormal mode is imaginary and the relaxation of the condensate is over-damped. For quenches whose final state is close to the critical point of the large N phase transition, we study the critical slowing down and obtain the combination of critical exponents zν = 1. When the final state is exactly at the phase transition, we find that the exponential ringing of the quasinormal modes is replaced by a power-law behaviour of the form ∼ t −a sin(b log t). This indicates the emergence of a discrete scale invariance.

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Section: Power-law Behaviour and Discrete Scale Invariance At The Crimentioning

confidence: 75%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Quantum quenches in a holographic Kondo model

Erdmenger

Flory

Newrzella

et al. 2017

J. High Energ. Phys.

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“…Now we turn to the equilibrium double occupancy D eq for different bath exponent combinations (r, s). While µ 2 eff (T → 0) and Q 2 eff (T → 0) jump at and across the QCP, D eq varies continuously [7,46] as function of g as demonstrated in Fig. 4 for U/Γ 0 = 1 and Γ 0 /D = 0.01.…”

Section: E Equilibrium Double Occupancymentioning

confidence: 84%

“…Such methods, however, cannot be employed in the strong coupling limit or close to a quantum critical point (QCP) where competing orthogonal ground states need to be accounted for. In this regime, the non-equilibrium extension of Wilson's numerical renormalization group (NRG) approach [1,39], the time-dependent numerical renormalization group (TD-NRG) [40,41], has been used to access the real-time dynamics in QISs with purely fermionic or bosonic baths [40][41][42][43][44][45][46] or steady-state currents through nano devices [47][48][49]. Recently, real-time quantum Monte-Carlo approaches [50][51][52][53] and multilayer multiconfiguration time-dependent Hartree methods [54,55] have also been successfully applied to such problems as well as the density matrix renormalization group, see Ref.…”

Section: Introductionmentioning

confidence: 99%

Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

Kleine¹,

Anders²

2015

Preprint

Self Cite

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We investigate the influence of an additional bosonic bath onto the real-time dynamics of a localized orbital coupled to conduction band with an energy-dependent coupling function Γ(ε) ∝ |ε| r . Recently, a rich phase diagram has been found in this Bose-Fermi Anderson model, where the transitions between competing ground states are governed by quantum critical points. In addition to a transition between a Kondo singlet and a local moment, a localized phase has been established once the coupling to a sub-ohmic bosonic bath exceeds a critical value. Using the time-dependent numerical renormalization group approach, we show that the non-equilibrium dynamics with Ftype of bath exponents can be fully understand within an effective single-impurity Anderson model using a renormalized local Coulomb interaction Uren. For regimes with B-type of bath exponents, the nature of the bosonic bath and the coupling strength has a profound impact on the electron dynamics which can only partially be understood using an appropriate Uren. The local expectation values always reach a steady state at very long times. By a scaling analysis for Λ → 1 + , we find thermalization of the system only in the strong coupling regime. In the local moment and in the localized phase significant deviations between the steady-state value and the thermal equilibrium value are found that are related to the distance to the quantum critical point.

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Numerical renormalization group study of the Loschmidt echo in Kondo systems

Ślusarski

Wrześniewski

Weymann

2022

Sci Rep

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We study the dynamical properties of the one-channel and two-channel spin-1/2 Kondo models after quenching in Hamiltonian variables. Eigen spectrum of the initial and final Hamiltonians is calculated by using the numerical renormalization group method implemented within the matrix product states formalism. We consider multiple quench protocols in the considered Kondo systems, also in the presence of external magnetic field of different intensities. The main emphasis is put on the analysis of the behavior of the Loschmidt echo L(t), which measures the ability of the system’s revival to its initial state after a quench. We show that the decay of the Loschmidt echo strongly depends on the type of quench and the ground state of the system. For the one-channel Kondo model, we show that L(t) decays as, $$L(t)\sim (t\cdot T_K)^{-1.4}$$ L ( t ) ∼ ( t · T K ) - 1.4 , where $$T_K$$ T K is the Kondo temperature, while for the two-channel Kondo model, we demonstrate that the decay is slower and given by $$L(t)\sim (t\cdot T_K)^{-0.7}$$ L ( t ) ∼ ( t · T K ) - 0.7 . In addition, we also determine the dynamical behavior of the impurity’s magnetization, which sheds light on identification of the relevant time scales in the system’s dynamics.

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Real-time dynamics induced by quenches across the quantum critical points in gapless Fermi systems with a magnetic impurity

Cited by 4 publications

References 52 publications

Quantum quenches in a holographic Kondo model

Quantum quenches in a holographic Kondo model

Influence of a bosonic environment onto the non-equilibrium dynamics of local electronic states in a quantum impurity system close to a quantum phase transition

Numerical renormalization group study of the Loschmidt echo in Kondo systems

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