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arXiv:1801.09017 · Physical review. B./Physical review. B

Emergence of antiferromagnetic quantum domain walls

H. Y. Yuan, Man‐Hong Yung, X. R. Wang

Published Aug 14, 2018• 8 citations
arXivHTMLPDF

Abstract

Domain walls (DWs), as interfaces separating different magnetic domains, are widely regarded as classical objects, even though the underlying constituents, namely, electron spins and spin-spin exchange interaction, are intrinsically of quantum nature. One intriguing question is, how do DWs behave when the size of the magnetic domains is shrunk to the atomistic level? Would quantum fluctuations destroy the stability of the DWs? These questions are partly addressed for ferromagnets, but seldom studied for antiferromagnets. Here we present a microscopic quantum spin model of antiferromagnets where the ground states not only share several common properties with the classical domain walls, but also exhibit nontrivial quantum properties. Specifically, the magnetization profile highly resembles its classical counterparts, even though the spins inside the domain walls are highly entangled. Furthermore, a nonzero spin angular momentum of a quantum DW emerges and it does not depend on the system size. Finally, we show that quantum DWs can be generated through a quantum phase transition from a quantum domain and the critical point can be characterized by the global entanglement. These results provide additional physical insights on the quantum effects in spintronics, and can be experimentally verified within the current technologies in superconducting circuits and trapped ions.

DOI
10.1103/physrevb.98.060407

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Domain walls (DWs), as interfaces separating different magnetic domains, are widely regarded as classical objects, even though the underlying constituents, namely, electron spins and spin-spin exchange interaction, are intrinsically of quantum nature. One intriguing question is, how do DWs behave when the size of the magnetic domains is shrunk to the atomistic level? Would quantum fluctuations destroy the stability of the DWs? These questions are partly addressed for ferromagnets, but seldom studied for antiferromagnets. Here we present a microscopic quantum spin model of antiferromagnets where the ground states not only share several common properties with the classical domain walls, but also exhibit nontrivial quantum properties. Specifically, the magnetization profile highly resembles its classical counterparts, even though the spins inside the domain walls are highly entangled. Furthermore, a nonzero spin angular momentum of a quantum DW emerges and it does not depend on the system size. Finally, we show that quantum DWs can be generated through a quantum phase transition from a quantum domain and the critical point can be characterized by the global entanglement. These results provide additional physical insights on the quantum effects in spintronics, and can be experimentally verified within the current technologies in superconducting circuits and trapped ions.
Nanoscale topological spin textures in magnetic systems are emerging as promising candidates for scalable quantum architectures. Despite their potential as qubits, previous studies have been limited to semiclassical approaches, leaving a critical gap: the lack of a fully quantum demonstration. Here, we address this challenge by employing the density matrix renormalization group (DMRG) method to establish domain wall (DW) qubits in coupled quantum spin-1/2 chains. We calculate the ground-state energies and excitation gaps of the system and find that DWs with opposite chiralities form a well-defined low-energy sector, distinctly isolated from higher excited states in the presence of anisotropies. This renders the chirality states suitable for encoding quantum information, serving as robust qubits. Interestingly, when a magnetic field is applied, we observe tunneling between quantum DW states with opposite chiralities. Through quantum simulations, we construct an effective qubit Hamiltonian that exhibits strongly anisotropic ggg factors, offering a way to implement single-qubit gates. Furthermore, we obtain an effective interacting Hamiltonian for two mobile DWs in coupled quantum spin chains from DMRG simulations, enabling the implementation of two-qubit gates. Single-qubit and two-qubit gates are also demonstrated in real-time simulations using the time-dependent variational principle. Our work represents a critical step from semiclassical constructions to a fully quantum demonstration of the potential of DW textures for scalable quantum computing, establishing a solid foundation for future quantum architectures based on topological magnetic textures.
Domain walls (DWs) on magnetic racetracks are at the core of the field of spintronics, providing a basic element for classical information processing. Here, we show that mobile DWs also provide a blueprint for large-scale quantum computers. Remarkably, these DW qubits showcase exceptional versatility, serving not only as stationary qubits, but also performing the role of solid-state flying qubits that can be shuttled in an ultrafast way. We estimate that the DW qubits are long-lived because they can be operated at sweet spots to reduce potential noise sources. Single-qubit gates are implemented by moving the DW, and two-qubit entangling gates exploit naturally emerging interactions between different DWs. These gates, sufficient for universal quantum computing, are fully compatible with current state-of-the-art experiments on racetrack memories. Further, we discuss possible strategies for qubit readout and initialization, paving the way toward future quantum computers based on mobile topological textures on magnetic racetracks.
We discuss entanglement in the spin-1∕2 anisotropic ferromagnetic Heisenberg chain in the presence of a boundary magnetic field generating domain walls. By increasing the magnetic field, the model undergoes a first-order quantum phase transition from a ferromagnetic to a kink-type phase, which is associated to a jump in the content of entanglement available in the system. Above the critical point, pairwise entanglement is shown to be nonvanishing and independent of the boundary magnetic field for large chains. Based on this result, we provide an analytical expression for the entanglement between arbitrary spins. Moreover, the effects of the quantum domains on the gapless region and for antiferromagnetic anisotropy are numerically analyzed. Finally multiparticle entanglement properties are considered, from which we establish a characterization of the critical anisotropy separating the gapless regime from the kink-type phase.
In this thesis, we investigate strongly correlated phenomena in quantum spin systems. In the first part of this work, we study geometrically frustrated antiferromagnets (AFMs). Generalizing the SU(2) Heisenberg Hamiltonian to Sp(N) symmetry, we obtain, in the large-N limit, the mean-field phase diagrams for the planar pyrochlore and cubic AFMs. We then use gauge theories to consider fluctuation effects about their respective mean-field configurations. We find, in addition to conventional Neel states, a plethora of novel magnetically disordered phases: two kinds of spin liquids, Z2 in 2+1D and U(1)in 3+1D, and several valence bond solids such as two and three-dimensional plaquette and columnar singlet states. We use the same approach to study the diamond lattice AFM which possesses extended classical ground state degeneracy. We demonstrate that quantum and entropic fluctuations lift this degeneracy in different ways. In the second part of the thesis, we study ultracold spinor atoms confined in optical lattices. We first demonstrate the feasibility of experimental realization of rotor models using ultracold spin-one Bose atoms in a spin-dependent and disordered optical lattice. We show that the ground state of such disordered rotor models with quadrupolar interactions can exhibit biaxial nematic ordering in the disorder-averaged sense, and suggest an imaging experiment to detect the biaxial nematicity in such systems. Finally, using variational wavefunction methods, we study the Mott phases and superfluid-insulator transition of spin-three bosons in an optical lattice with an anisotropic two dimensional optical trap. We chart out the phase diagrams for Mott states with n = 1 and n = 2 atoms per lattice site. We show that the long-range dipolar interaction stabilizes a state characterized by antiferromagnetic chains made of ferromagnetically aligned spins. We also obtain the mean-field phase boundary for the superfluid-insulator transition, and show that inside the superfluid phase and near the superfluid-insulator phase boundary, the system undergoes a first order antiferromagnetic-ferromagnetic spin ordering transition.
We study spin-polarized states and their stability in the antiferromagnetic phase of spinor (F=1)(F=1)(F=1) quasi-one-dimensional Bose-Einstein condensates. Using analytical approximations and numerical methods, we find various types of polarized states, including patterns of the Thomas-Fermi type, structures featuring a pulse in one component inducing a hole in the other components, states with holes in all three components, and domain walls (DWs). The stability analysis based on the Bogoliubov--de Gennes equations reveals intervals of weak oscillatory instability in families of these states, except for the DWs, which are always stable. The development of the instabilities is examined by means of direct simulations.
Quantum computers allow to solve efficiently certain problems that are intractable for classical computers. For the realization of a quantum computer, a qubit design as the basic building block is a nontrivial starting point. Within a nanoscale ferromagnetic domain wall stabilized by achiral energy, two degenerate chirality forms exist which can be regarded as the two qubit states. Our numerical demonstration shows that the manipulation of spin configurations of the ferromagnetic domain walls is governed by magnetic and electric fields for single-qubit quantum gates, while the Ising exchange coupling facilitates the two-qubit gates. The incorporation of these quantum gates permits universal quantum computation. Furthermore, we discuss the estimation of the coherence time, as well as the initialization and readout of the qubits. Our findings show a practical implementation of quantum computing architectures based on the domain-wall qubits in ferromagnetic materials.