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Journal of Magnetism and Magnetic Materials

Anomalous slow dynamics in quantum spin chains

J.G. Carvalho, Djalma Medeiros, G. G. Cabrera

Published Jan 13, 2004• 2 citations
Publisher
DOI
10.1016/j.jmmm.2003.11.359

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Additional hopping channels in a tight-binding lattice is known to introduce faster dynamics of a quantum mechanical particle. However, we show that in the case of a repulsively bound state, the dynamics becomes abnormally slow when next-nearest neighbor (NNN) hopping is allowed for the particles. We show that such slowing down occurs for some magic strength of the NNN hopping at which the bound state band exhibits a quasi-flatband feature. We reveal this anomalous dynamical behavior by analyzing the quench dynamics of two nearest neighbor (NN) spin excitations (magnons) on a ferromagnetic chain by allowing both NN and NNN couplings. By implementing digital quantum computing simulations on a NISQ device, we obtain such non-trivial signatures and complement the results with exact numerical calculations. Moreover, through perturbative arguments, we reveal that the slowing down is due to the destructive interference between different paths associated to the bound state dynamics.
Motivated by the search for a quantum analogue of the macroscopic fluctuation theory, we study quantum spin chains dissipatively coupled to quantum noise. The dynamical processes are encoded in quantum stochastic differential equations. They induce dissipative friction on the spin chain currents. We show that, as the friction becomes stronger, the noise induced dissipative effects localize the spin chain states on a slow mode manifold, and we determine the effective stochastic quantum dynamics of these slow modes. We illustrate this approach by studying the quantum stochastic Heisenberg spin chain.
The search for departures from standard hydrodynamics in many-body systems has yielded a number of promising leads, especially in low dimensions. Here, we study one of the simplest classical interacting lattice models, the nearest-neighbor Heisenberg chain, with temperature as the tuning parameter. Our numerics expose strikingly different spin dynamics between the antiferromagnet, where it is largely diffusive, and the ferromagnet, where we observe strong evidence either of spin superdiffusion or an extremely slow crossover to diffusion. This difference also governs the equilibration after a quench, and, remarkably, is apparent even at very high temperatures.