An official website of the United States government
Dimerized valence bond solids appear naturally in spin-1/2 systems on bipartite lattices, with the geometric frustrations playing a key role both in their stability and the eventual `melting' due to quantum fluctuations. Here, we ask the question of the stability of such dimerized solids in spin-1 systems, taking the anisotropic square lattice with bilinear and biquadratic spin-spin interactions as a paradigmatic model. The lattice can be viewed as a set of coupled spin-1 chains, which in the limit of vanishing inter-chain coupling are known to possess a stable dimer phase. We study this model using the density matrix renormalization group (DMRG) and infinite projected entangled-pair states (iPEPS) techniques, supplemented by the analytical mean-field and linear flavor wave theory calculations. While the latter predicts the dimer phase to remain stable up to a reasonably large interchain-to-intrachain coupling ratio r≲0.6, the DMRG and iPEPS find that the dimer solid melts for much weaker interchain coupling not exceeding r≲0.15. We find the transition into a magnetically ordered state to be first order, manifested by a hysteresis and order parameter jump, precluding the deconfined quantum critical scenario. The apparent lack of stability of dimerized phases in 2D spin-1 systems is indicative of strong quantum fluctuations that melt the dimer solid.
more »
« less
Atomistic mechanisms of phase nucleation and propagation in a model two-dimensional system
We present a computational study on the solid–solid phase transition of a model two-dimensional system between hexagonal and square phases under pressure. The atomistic mechanism of phase nucleation and propagation are determined using solid-state Dimer and nudged elastic band (NEB) methods. The Dimer is applied to identify the saddle configurations and NEB is applied to generate the transition minimum energy path (MEP) using the outputs of Dimer. Both the atomic and cell degrees of freedom are used in saddle search, allowing us to capture the critical nuclei with relatively small supercells. It is found that the phase nucleation in the model material is triggered by the localized shear deformation that comes from the relative shift between two adjacent atomic layers. In addition to the conventional layer-by-layer phase propagation, an interesting defect-assisted low barrier propagation path is identified in the hexagonal to square phase transition. The study demonstrates the significance of using the Dimer method in exploring unknown transition paths without a priori assumption. The results of this study also shed light on phase transition mechanisms of other solid-state and colloidal systems.
more »
« less
- PAR ID:
- 10465478
- Date Published:
- Journal Name:
- Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- Volume:
- 478
- Issue:
- 2268
- ISSN:
- 1364-5021
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
More Like this
-
-
Using in situ atomic-resolution scanning transmission electron microscopy, atomic movements and rearrangements associated with diffusive solid to solid phase transformations in the Pt−Sn system are captured to reveal details of the underlying atomistic mechanisms that drive these transformations. In the PtSn4 to PtSn2 phase transformation, a periodic superlattice substructure and a unique intermediate structure precede the nucleation and growth of the PtSn2 phase. At the atomic level, all stages of the transformation are templated by the anisotropic crystal structure of the parent PtSn4 phase. In the case of the PtSn2 to Pt2Sn3 transformation, the anisotropy in the structure of product Pt2Sn3 dictates the path of transformation. Analysis of atomic configurations at the transformation front elucidates the diffusion pathways and lattice distortions required for these phase transformations. Comparison of multiple Pt−Sn phase transformations reveals the structural parameters governing solid to solid phase transformations in this technologically interesting intermetallic system.more » « less
-
null (Ed.)In systems with many local degrees of freedom, high-symmetry points in the phase diagram can provide an important starting point for the investigation of their properties throughout the phase diagram. In systems with both spin and orbital (or valley) degrees of freedom such a starting point gives rise to SU(4)-symmetric models.Here we consider SU(4)-symmetric "spin'' models, corresponding to Mott phases at half-filling, i.e. the six-dimensional representation of SU(4). This may be relevant to twisted multilayer graphene.In particular, we study the SU(4) antiferromagnetic "Heisenberg'' model on the triangular lattice, both in the classical limit and in the quantum regime. Carrying out a numerical study using the density matrix renormalization group (DMRG), we argue that the ground state is non-magnetic.We then derive a dimer expansion of the SU(4) spin model. An exact diagonalization (ED) study of the effective dimer model suggests that the ground state breaks translation invariance, forming a valence bond solid (VBS) with a 12-site unit cell.Finally, we consider the effect of SU(4)-symmetry breaking interactions due to Hund's coupling, and argue for a possible phase transition between a VBS and a magnetically ordered state.more » « less
-
We study structure formation in two-dimensional turbulence driven by an external force, interpolating between linear instability forcing and random stirring, subject to nonlinear damping. Using extensive direct numerical simulations, we uncover a rich parameter space featuring four distinct branches of stationary solutions: large-scale vortices, hybrid states with embedded shielded vortices (SVs) of either sign, and two states composed of many similar SVs. Of the latter, the first is a dense vortex gas where all SVs have the same sign and diffuse across the domain. The second is a hexagonal vortex crystal forming from this gas when the linear instability is sufficiently weak. These solutions coexist stably over a wide parameter range. The late-time evolution of the system from small-amplitude initial conditions is nearly self-similar, involving three phases: initial inverse cascade, random nucleation of SVs from turbulence and, once a critical number of vortices is reached, a phase of explosive nucleation of SVs, leading to a statistically stationary state. The vortex gas is continued in the forcing parameter, revealing a sharp transition towards the crystal state as the forcing strength decreases. This transition is analysed in terms of the diffusivity of individual vortices using ideas from statistical physics. The crystal can also decay via an inverse cascade resulting from the breakdown of shielding or insufficient nonlinear damping acting on SVs. Our study highlights the importance of the forcing details in two-dimensional turbulence and reveals the presence of non-trivial SV states in this system, specifically the emergence and melting of a vortex crystal.more » « less
-
Access to well-defined, model-like, non-noble metal intermetallic compound nanomaterials (<10 nm) with phase pure bulk, bulk-like 1st-atomic-layer surface composition, and unique electronic and surface chemical properties is critical for the fields of catalysis, electronics, and sensor development. Non-noble metal intermetallic compounds are compositionally ordered solid compounds composed of transition metals and semimetals or post-transition metals. Their synthesis as model-like high-surface-area supported nanoparticles is challenging due to the elevated reactivity of the constituent elements and their interaction with the support material. In this study, we have developed a systematic understanding of the fundamental phenomena that control the synthesis of these materials such that phase pure bulk nanoparticles (<10 nm) may be produced with bulk-like surface terminations. The effects of the precursor and support choice, chemical potential of H 2 , reduction temperature, and annealing procedures were investigated to understand the fundamental kinetics of particle formation and interactions that dictate phase purity and stability and 1st-atomic-layer surface composition. The understanding developed may serve as a foundation for further developing advanced synthesis procedures for well-defined nanoparticles with increasing compositional complexity.more » « less
- Free Publicly Accessible Full Text
-
Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1098/rspa.2022.0388
