We diagonalize the quantum two-dimensional spin-1/2 Heisenberg model with Dzyaloshinsky-Moriya interaction (DMI) by applying the variational quantum eigensolver, running on a quantum-computer simulator, which turns out to be a more efficient approach than a classical direct diagonalization for systems with more than 17 sites. The calculated external-magnetic-field dependence of the total energy, of the magnetization, and of the topological charge exhibits a distinctive discontinuity which hints at the existence of zero-temperature magnetic- skyrmion-like structures at the quantum level, controlled by the combination of the exchange-coupling and the DMI parameters. The potentially measurable jump in the magnetization upon changing the field indicates the investigated objects are stable enough for eventual applications in spintronics or even as information carriers.
We diagonalize the quantum two-dimensional spin-1/2 Heisenberg model with Dzyaloshinsky-Moriya interaction (DMI) by applying the variational quantum eigensolver, running on a quantum-computer simulator, which turns out to be a more efficient approach than a classical direct diagonalization for systems with more than 17 sites. The calculated external-magnetic-field dependence of the total energy, of the magnetization, and of the topological charge exhibits a distinctive discontinuity which hints at the existence of zero-temperature magnetic- skyrmion-like structures at the quantum level, controlled by the combination of the exchange-coupling and the DMI parameters. The potentially measurable jump in the magnetization upon changing the field indicates the investigated objects are stable enough for eventual applications in spintronics or even as information carriers.
Quantum computation departs from the classical paradigm of deterministic, bit-based processing by exploiting inherently quantum phenomena such as superposition and entanglement. We propose a framework for qubit realization based on skyrmionic states stabilized by the Dzyaloshinskii-Moriya interaction (DMI) in two-dimensional spin lattices. The model incorporates competing exchange interactions, perpendicular magnetic anisotropy, and Zeeman coupling, solved via exact diagonalization under periodic (PBC) and open boundary conditions (OBC). A quantum skyrmionic phase emerges for PBC within a parameter space defined by DMI, exchange, field, and anisotropy, while OBC favor classical-like, topologically protected skyrmions. Quantum logic gates (Pauli X, Y, Z, Hadamard) are implemented on both skyrmion types. Energy density and entanglement entropy analyses reveal that quantum skyrmions suffer from DMI-driven decoherence and reduced gate fidelity, whereas classical-like skyrmions maintain stability. Exact simulations of qubit dynamics, including drive effects and Lindblad decoherence, demonstrate tunable anharmonic energy levels and coherent Bloch-sphere manipulation, making these skyrmionic states promising candidates for qubit implementation. Overall, the Dzyaloshinskii-Moriya interaction plays a dual role-stabilizing skyrmionic qubits while simultaneously inducing decoherence during gate operations.
We investigate the ground state properties of quantum skyrmions in a ferromagnet using variational Monte Carlo with the neural network quantum state as variational ansatz. We study the ground states of a two-dimensional quantum Heisenberg model in the presence of the Dzyaloshinskii-Moriya interaction (DMI) and show that the ground state accommodates a quantum skyrmion for a large range of parameters, especially at large DMI. The spins in these quantum skyrmions are weakly entangled, and the entanglement increases with decreasing DMI. We also find that the central spin is completely disentangled from the rest of the lattice, establishing a non-destructive way of detecting this type of skyrmion by local magnetization measurements. While neural networks are well suited to detect weakly entangled skyrmions with large DMI, they struggle to describe skyrmions in the small DMI regime due to nearly degenerate ground states and strong entanglement. In this paper, we propose a method to identify this regime and a technique to alleviate the problem. Finally, we analyze the workings of the neural network and explore its limits by pruning. Our work shows that neural network quantum states can be efficiently used to describe the quantum magnetism of large systems exceeding the size manageable in exact diagonalization by far.
We study the dynamics of quantum skyrmions under a magnetic field gradient using neural network quantum states. First, we obtain a quantum skyrmion lattice ground state using variational Monte Carlo with a restricted Boltzmann machine as the variational ansatz for a quantum Heisenberg model with a Dzyaloshinskii-Moriya interaction. Then, using the time-dependent variational principle, we study the real-time evolution of quantum skyrmions after a Hamiltonian quench with an inhomogeneous external magnetic field. We show that field gradients are an effective way of manipulating and moving quantum skyrmions. Furthermore, we demonstrate that quantum skyrmions can decay when interacting with each other. This work shows that neural network quantum states offer a promising way of studying the real-time evolution of quantum magnetic systems that are outside the realm of exact diagonalization. Published by the American Physical Society 2024
The spin -½ Heisenberg antiferromagnet Hamiltonian with exchange integral and applied external magnetic field is studied with the help of direct exact diagonalization technique. Two site cluster lattices with open boundary conditions are considered and the criteria for the occurrence of a transition from antiferromagnetic (AFM) phase to a ferromagnetic (FM) phase are discussed.However, the results obtained shows that the temperature dependence of the uniform magnetization depends on the strength of the applied magnetic field h. If the applied magnetic field is smaller than the critical field strength, the zero temperature magnetization vanishes, otherwise it is activated.
The magnetic and thermodynamic properties of 13-atom clusters with decahedral and layered geometries have been studied with spin-1/2 using the quantum Heisenberg model. The numerical exact diagonalization technique is applied to solve the quantumspin Hamiltonian for both ferro (FM) and anti-ferromagnetic (AFM) interactions of the clusters. The ground state energies for the FM case are found to be all degenerate while for the AFM case, they are non-degenerate. In the presence of external magnetic field, we found discontinuities in the field-dependent magnetization accompanied by plateaus for the AFM interaction. The thermodynamic entities such as entropy and specific heat as a function of external magnetic field are smeared out with increasing temperature. They also show a strong dependence on the cluster geometry.
An integer winding, i.e., topological charge, is a characteristic of skyrmions, which are topologically nontrivial spin patterns in magnets. They emerge when smooth two-dimensional spin configurations are stabilized by conflicting interactions such as exchange, anisotropy, the Dzyaloshinskii-Moriya interaction, or geometric frustration. These nanoscale textures, which are typically a few to tens of nanometers in size, are strong 'particle-like' excitations because they are shielded by energy barriers connected to their topology. By exploiting their helicity, i.e., spin rotation angle or associated internal modes, as a two-level system, skyrmions can function as quantum bits or qubits. Two quantized helicity states of a nanometer-scale skyrmion encode the logical value states in a 'skyrmion qubit.' Interestingly, skyrmion qubits are topologically protected and macroscopic, i.e., they involve a large number of spins; however, external influences can still affect them. When the texture is tiny and disconnected, the helicity angle of the skyrmion becomes quantized. A qubit basis is made up of the lowest two energy eigenstates, i.e., symmetric or antisymmetric superpositions of opposite helicity, for example. Therefore, Skyrmion textures can provide valuable insights for different purposes. However, is it possible to synthetically generate skyrmion textures using quantum computing? This paper investigates the possibility and generates a few hundred different textures, producing sample comparisons from various types, which indicate a novel direction for skyrmion-based research based on quantum randomness and other criteria.