We investigate the impact of random bond disorder on quantum skyrmions using a spin-half quantum Heisenberg model on the square lattice with Dzyaloshinskii-Moriya interaction, Heisenberg anisotropy, and boundary-pinned magnetic field. Utilizing the neural network quantum state technique, we explore the influence of disorder on spin textures, topological properties, and quantum entanglement. We show that the disorder reduces the stability of quantum skyrmions, ultimately causing them to collapse at high disorder strengths. In addition, our results reveal two key insights. First, the presence of disorder, rather than simply degrading skyrmion order, significantly enhances local quantum entanglement, as evidenced by the rise in second Rényi entropy. Second, our calculations show that the topological entanglement entropy calculated using the second Rényi entropy remains negligible across all the disorder strengths. This suggests long-range entanglement is absent and the skyrmion phase is not detectable using this specific probe. Overall, our work provides new insights into how disorder constructively influences quantum materials.
We investigate the impact of random bond disorder on quantum skyrmions using a spin-half quantum Heisenberg model on the square lattice with Dzyaloshinskii-Moriya interaction, Heisenberg anisotropy, and boundary-pinned magnetic field. Utilizing the neural network quantum state technique, we explore the influence of disorder on spin textures, topological properties, and quantum entanglement. We show that the disorder reduces the stability of quantum skyrmions, ultimately causing them to collapse at high disorder strengths. In addition, our results reveal two key insights. First, the presence of disorder, rather than simply degrading skyrmion order, significantly enhances local quantum entanglement, as evidenced by the rise in second Rényi entropy. Second, our calculations show that the topological entanglement entropy calculated using the second Rényi entropy remains negligible across all the disorder strengths. This suggests long-range entanglement is absent and the skyrmion phase is not detectable using this specific probe. Overall, our work provides new insights into how disorder constructively influences quantum materials.
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 interplay of disorder and Heisenberg interactions in the Kitaev model on a honeycomb lattice. The effect of disorder on the transition between Kitaev spin liquid and magnetic ordered states as well as the stability of magnetic ordering is investigated. Using Lanczos exact diagonalization we discuss the consequences of two types of disorder: (i) random-coupling disorder and (ii) singular-coupling disorder. They exhibit qualitatively similar effects in the pure Kitaev-Heisenberg model without long-range interactions. The range of spin-liquid phases is reduced and the transition to magnetic ordered phases becomes more crossoverlike. Furthermore, the long-range zigzag and stripy orderings in the clean system are replaced by their three domains with different ordering direction. Especially in the crossover range the coexistence of magnetically ordered and Kitaev spin-liquid domains is possible. With increasing the disorder strength the area of domains becomes smaller and the system goes into a spin-glass state. However, the disorder effect is different in magnetically ordered phases caused by long-range interactions. The stability of such magnetic ordering is diminished by singular-coupling disorder and, accordingly, the range of the spin-liquid regime is extended. This mechanism may be relevant to materials like $\ensuremath{\alpha}\text{\ensuremath{-}}{\mathrm{RuCl}}_{3}$ and H3LiIr2O6 where the zigzag ground state is stabilized by weak long-range interactions. We also find that the flux gap closes at a critical disorder strength and vortices appears in the flux arrangement. Interestingly, the vortices tend to form kinds of commensurate ordering.
Quantum phase transitions are driven by quantum fluctuations due to the uncertainty principle in many-body physics. In quantum phase transitions, the ground-state changes dramatically. The quantum entanglement, specific heat, magnetization and other physical quantities diverge according to certain functions, and show specific scaling behaviors. In addition, there is a topological quantum phase transition beyond the conventional Landau-Ginzburg-Wilson paradigm, which is relevant to emergent phenomena in strongly correlated electron systems, with topological nonlocal order parameters as a salient feature. Thus, topological order is a new paradigm in the study of topological quantum phase transitions. To investigate competition mechanism of the different quantum spin interactions, in this paper, the one-dimensional spin-1 bond-alternating Heisenberg model with Dzyaloshinskii-Moriya (DM) interaction is considered. The DM interaction drives the quantum fluctuations resulting in a phase transition. By using the one-dimensional infinite matrix product state algorithm in tensor network representation, the quantum entanglement entropy and order parameters are calculated from the ground-state function. The numerical result shows that with the change of bond alternating strength, there is a quantum phase transition from the topological ordered Haldane phase to the local ordered dimer phase. Based on the von Neumann entropy and order parameter, the phase diagram of this model is obtained. There is a critical line that separates the Haldane and the dimer phase. The DM interaction inhibits the dimerization of the quantum spin system and finally breaks the fully dimerization. Due to the fact that the structurally symmetry of system is broken, the local dimer order exists in the whole parameter range when the bond-alternative strength parameter changes. The first derivative of the local dimer order behaves as a peak corresponding to the critical point. Furthermore, from the numerical scaling of the first derivative of dimer order and the non-local string order near the phase transition point, the characteristic critical exponents α and β are obtained, respectively. It shows that the characteristic critical exponent α decreases, and β increases gradually with the interaction strength of DM increasing. The resulting state i.e. the anti-symmetric anisotropic DM interaction produced by spin-orbit coupling, affects the critical properties of the system in the phase transition. This reveals that the competition mechanism of the quantum spin interaction, also provides some guidance for the future study of the critical behavior in topological quantum phase transition with the DM interaction.
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1/2 per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of YbMgGaO_{4}, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO_{4} and related materials.
We analyze the effect of quenched disorder on spin-1=2 quantum magnets in which magnetic frustration promotes the formation of local singlets.Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids.We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1=2 moments.This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations.Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1=2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate.Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1=2 per statistical unit cell.These conjectures are supported by an argument for 1D spin chains.We apply insights from this study to the phenomenology of YbMgGaO 4 , a recently discovered triangular lattice spin-1=2 insulator which was proposed to be a quantum spin liquid.We instead explore a description based on the present theory.Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO 4 and related materials.
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.