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arXiv:0904.2783 · Physical Review B

Tailoring effective exchange interactions via domain walls in coupled Heisenberg rings

Vanita Srinivasa, Jeremy Levy

Published Jul 14, 2009• 7 citations
arXivHTMLPDF

Abstract

The nature of the exchange coupling variation in an antiferromagnetic spin-$\frac{1}{2}$ system can be used to tailor its ground-state properties. In particular, dimerized Heisenberg rings containing domain walls have localized states that can serve as ``flying spin qubits'' when the domain walls are moved. We show theoretically that when two of these rings are coupled, the movement of the domain walls leads to modulation of the effective exchange interaction between the qubits. Appropriately chosen configurations of domain walls can give rise to ferromagnetic effective exchange. We describe how these spin rings may be used as basic building blocks to construct quantum spin systems whose properties are tunable by virtue of the exchange variation within the rings.

DOI
10.1103/physrevb.80.024414

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The nature of the exchange coupling variation in an antiferromagnetic spin-12\frac{1}{2}21​ system can be used to tailor its ground-state properties. In particular, dimerized Heisenberg rings containing domain walls have localized states that can serve as ``flying spin qubits'' when the domain walls are moved. We show theoretically that when two of these rings are coupled, the movement of the domain walls leads to modulation of the effective exchange interaction between the qubits. Appropriately chosen configurations of domain walls can give rise to ferromagnetic effective exchange. We describe how these spin rings may be used as basic building blocks to construct quantum spin systems whose properties are tunable by virtue of the exchange variation within the rings.
We present a method for encoding and transporting qubits within a dimerized Heisenberg spin-12\frac{1}{2}21​ chain. Logical qubits are localized at the domain walls that separate the two possible dimerized states. The domain walls can be moved to produce ``flying spin qubits.'' The topological nature of these states makes them stable against local perturbations of the exchange profile. Pairs of domain walls can be used to generate Einstein-Podolsky-Rosen pairs of entangled qubits. We discuss speed limitations within an exactly solvable three-spin model and describe a possible physical realization using quantum dot arrays.
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.
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.
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 present a certain class of two-dimensional frustrated quantum Heisenberg spin systems with multiple ring exchange interactions which are rigorously demonstrated to have quantum disordered ground states without magnetic long-range order. The systems considered in this paper are s=1∕2s=1∕2s=1∕2 antiferromagnets on a honeycomb and square lattices, and an s=1s=1s=1 antiferromagnet on a triangular lattice. We find that for a particular set of parameter values, the ground state is a short-range resonating valence bond state or a valence bond crystal state. It is shown that these systems are closely related to the quantum dimer model introduced by Rokhsar and Kivelson as an effective low-energy theory for valence bond states.
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.