Relaxation dynamics of a quantum spin coupled to a topological edge state

Abstract

A classical impurity spin coupled to the spinful Su-Schrieffer-Heeger (SSH) chain is known to exhibit complex switching dynamics with incomplete spin relaxation. Here, we study the corrections that result from a full quantum treatment of the impurity spin. We find that in the topologically trivial case, the quantum spin behaves similarly to the classical one due to the absence of the Kondo effect for the trivial insulator. In the topological case, the quantum spin is significantly less likely to relax: It can be stuck at a pre-relaxation plateau with a sizable deviation from the expected relaxed value, and there is a large parameter regime where it does not relax at all but features an anomalously large Larmor frequency. Furthermore, we find an additional quantum effect where the pre-relaxation plateau can be hyperpolarized, i.e., the spin is stuck at a polarization value larger than the ground-state expectation value. This is possible due to the (incomplete) Kondo screening of the quantum spin, which is absent in the classical case. Our results are obtained via the ground state density matrix renormalization group (DMRG) algorithm and the time-dependent variational principle (TDVP), where the charge-SU(2) symmetry of the problem was exploited. Furthermore, we introduce and benchmark a method to predict the dynamics from the given numerical data based on the sparse identification of nonlinear dynamics (SINDy). This allows us to prolong the simulation timescale by a factor of 2.5, up to a maximal time of $10^3$ inverse hoppings.

References in corpus (20)

• Discovering governing equations from data: Sparse identification of nonlinear dynamical systems
• Unifying time evolution and optimization with matrix product states
• SINDy-PI: A Robust Algorithm for Parallel Implicit Sparse Identification of Nonlinear Dynamics
• The Non-Abelian Density Matrix Renormalization Group Algorithm
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• How long does it take for the Kondo effect to develop?
• Sparse Identification of Nonlinear Dynamics for Rapid Model Recovery
• Atomistic spin dynamic method with both damping and moment of inertia effects included from first principles
• Quantum distillation: dynamical generation of low-entropy states of strongly correlated fermions in an optical lattice
• An efficient method for quantum impurity problems out of equilibrium
• Renormalization Group Approach to Non-equilibrium Green Functions in Correlated Impurity Systems
• Spatial and temporal propagation of Kondo correlations
• Spin dynamics and relaxation in the classical-spin Kondo-impurity model beyond the Landau-Lifschitz-Gilbert equation
• Anomalous spin precession under a geometrical torque
• Detection of spin reversal and nutations through current measurements
• Inertia effects in the real-time dynamics of a quantum spin coupled to a Fermi sea
• Long-time relaxation dynamics of a spin coupled to a Chern insulator
• Spin dynamics of $3d$ and $4d$ impurities embedded in prototypical topological insulators
• Single atom anisotropic magnetoresistance on a topological insulator surface
• Prerelaxation in quantum, classical, and quantum-classical two-impurity models