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Time evolution of magnetic Bloch oscillations using TEBD

Audun Skaugen

Published Jan 1, 2013• 1 citation
OpenAlex

Abstract

Linear-chain ferromagnets such as \\ce{CoCl_2\\cdot 2H_2 O} have been shown to be capable of magnetic Bloch oscillations. This means that domain walls in he material undergo Bloch oscillations, resulting in an oscilling magnetization. It was recently suggested to use lasers in resonance with energies from the Wannier-Zeeman ladder to provoke such oscillations. Simulating this process in the fully interacting system requires quantum many-body simulations. Since the system is one-dimensional, the method of time-evolving block decimation (TEBD) seems appropriate. We describe and implement this method and use it to simulate lasers acting on the linear chain. This results in robust oscillations in the magnetization with the expected Bloch frequency, with little sign of decoherence.

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Linear-chain ferromagnets such as \ce{CoCl_2\cdot 2H_2 O} have been shown to be capable of magnetic Bloch oscillations. This means that domain walls in he material undergo Bloch oscillations, resulting in an oscilling magnetization. It was recently suggested to use lasers in resonance with energies from the Wannier-Zeeman ladder to provoke such oscillations. Simulating this process in the fully interacting system requires quantum many-body simulations. Since the system is one-dimensional, the method of time-evolving block decimation (TEBD) seems appropriate. We describe and implement this method and use it to simulate lasers acting on the linear chain. This results in robust oscillations in the magnetization with the expected Bloch frequency, with little sign of decoherence.
The studies of multimagnon excitations will extend our understandings of quantum magnetism and strongly correlated matters. Here, by using the time-evolving block decimation algorithm, we investigate the Bloch oscillations of two-magnon excitations under a gradient magnetic field. Through analyzing the symmetry of our Hamiltonian, we derive a rigorous and general relation between ferromagnetic and antiferromagnetic systems. Under strong interactions, in addition to free-magnon Bloch oscillations, fractional bounded-magnon Bloch oscillations appear which can be understood by an effective single-particle model. To extract the frequencies of Bloch oscillations and determine the gradient of the magnetic field, we analyze the fidelity and the substandard deviation in both time and frequency domains. Our study not only explores the interaction-induced Bloch oscillations of multimagnon excitations, but also provides an alternative approach to determine the gradient of the magnetic field via ultracold atoms in optical lattices.
The full quantum dynamics of a spinon under external magnetic fields is investigated by using the time-evolving block decimation (TEBD) method within the microcanonical picture of transport. We show that the center of the spinon oscillates back and forth in the absence of dissipation. The quantum many-body behavior can be understood in a single-particle picture of transport and Bloch oscillations (BOs), where quantum fluctuations induce finite lifetimes. Transport, oscillations, and lifetimes can be tuned to some degree separately by external fields. Other nontrivial dynamics, such as resonance and chaos, are also discussed.
We investigate the impacts of an imaginary transverse field on the dynamics of magnetic domain walls in a quantum Ising chain. We show that an imaginary field plays a similar role as a real transverse field in forming a low-lying Wannier-Stark ladder. However, analytical and numerical calculations of the time evolutions in both systems show that the corresponding Bloch oscillations exhibit totally different patterns for the same initial states. These findings reveal the nontrivial effect of non-Hermiticity on quantum spin dynamics.
Bloch oscillations typically arise in periodic systems subjected to a constant force generated by a potential gradient. Here, we study domain-wall dynamics in coupled Ising layers under asymmetric longitudinal fields. The interlayer coupling is of Heisenberg type and acts as an effective transverse coupling in the emergent pseudospin representation. We show that the rung pseudospin structure gives rise to kinetic constraints, restricting the many-body dynamics to an emergent one-dimensional quasiparticle subspace within the original two-dimensional system. Furthermore, the imbalance between the longitudinal fields of the two layers induces an effective linear potential for the emergent domain-wall excitations, leading to their confinement between two oppositely polarized ferromagnetic domains. Remarkably, the resulting Wannier--Stark ladder of domain-wall excitations gives rise to Bloch oscillations in the absence of a conventional tilted potential, revealing a distinct mechanism for coherent quantum dynamics. Numerical simulations of time-dependent observables confirm the analytical predictions.
In recent years, the infinite time-evolving block decimation (iTEBD) method has been demonstrated to be one of the most efficient and powerful numerical schemes for time evolution in one-dimensional quantum many-body systems. However, a major shortcoming of the method, along with other state-of-the-art algorithms for many-body dynamics, has been their restriction to one spatial dimension. We present an algorithm based on a hybrid extension of iTEBD where finite blocks of a chain are first locally time evolved before an iTEBD-like method combines these processes globally. This in turn permits simulating the dynamics of many-body systems in spatial dimensions $d\ensuremath{\ge}1$ where the thermodynamic limit is achieved along one spatial dimension and where long-range interactions can also be included. Our work paves the way for simulating the dynamics of many-body phenomena that occur exclusively in higher dimensions and whose numerical treatments have hitherto been limited to exact diagonalization of small systems, which fundamentally limits a proper investigation of dynamical criticality. We expect the algorithm presented here to be of significant importance to validating and guiding investigations in state-of-the-art ion-trap and ultracold-atom experiments.
According to Faraday's law in classical physics, a varying magnetic field stimulates an electric eddy field. Intuitively, when a classical field is constant and imposed on a lattice, the Wannier-Stark ladders (WSL) can be established, resulting in Bloch oscillations. In this work, we investigate the dynamics of an interacting system on a (generalized) ring lattice threaded by a varying magnetic flux. Based on the rigorious results, we demonstrate that there exist many invariant subspaces in which the dynamics is periodic when the flux varies linearly over time. Nevertheless, for a given initial state, the evolved state differs from that driven by a linear field. However, the probability distributions of the two states are identical, referred to as the quantum analogue of Faraday's law. Our results are ubiquitous for a wide variety of interacting systems. We demonstrate these results through numerical simulations in an extended fermi-Hubbard model.