arXiv subjects

Gia-Wei Chern

Publications and source records attributed to Gia-Wei Chern.

At least 73 records · Page 4Linked to original sources

arXiv2024

Kinetics of orbital ordering in cooperative Jahn-Teller models: Machine-learning enabled large-scale simulations

We present a scalable machine learning (ML) force-field model for the adiabatic dynamics of cooperative Jahn-Teller (JT) systems. Large scale dynamical simulations of the JT model also shed light on the orbital ordering dynamics in colossal magnetoresistance manganites. The JT effect in these materials describes the distortion of local oxygen octahedra driven by a coupling to the orbital degrees of freedom of $e_g$ electrons. An effective electron-mediated interaction between the local JT modes leads to a structural transition and the emergence of long-range orbital order at low temperatures. Assuming the principle of locality, a deep-learning neural-network model is developed to accurately and efficiently predict the electron-induced forces that drive the dynamical evolution of JT phonons. A group-theoretical method is utilized to develop a descriptor that incorporates the combined orbital and lattice symmetry into the ML model. Large-scale Langevin dynamics simulations, enabled by the ML force-field models, are performed to investigate the coarsening dynamics of the composite JT distortion and orbital order after a thermal quench. The late-stage coarsening of orbital domains exhibits pronounced freezing behaviors which are likely related to the unusual morphology of the domain structures. Our work highlights a promising avenue for multi-scale dynamical modeling of correlated electron systems.

cond-mat.str-el↗

arXiv2024

Coarsening of chiral domains in itinerant electron magnets: A machine learning force field approach

Frustrated itinerant magnets often exhibit complex noncollinear or noncoplanar magnetic orders which support topological electronic structures. A canonical example is the anomalous quantum Hall state with a chiral spin order stabilized by electron-spin interactions on a triangular lattice. While a long-range magnetic order cannot survive thermal fluctuations in two dimensions, the chiral order which results from the breaking of a discrete Ising symmetry persists even at finite temperatures. We present a scalable machine learning (ML) framework to model the complex electron-mediated spin-spin interactions that stabilize the chiral magnetic domains in a triangular lattice. Large-scale dynamical simulations, enabled by the ML force-field models, are performed to investigate the coarsening of chiral domains after a thermal quench. While the chiral phase is described by a broken $Z_2$ Ising-type symmetry, we find that the characteristic size of chiral domains increases linearly with time, in stark contrast to the expected Allen-Cahn domain growth law for a non-conserved Ising order parameter field. The linear growth of the chiral domains is attributed to the orientational anisotropy of domain boundaries. Our work also demonstrates the promising potential of ML models for large-scale spin dynamics of itinerant magnets.

cond-mat.str-el↗

arXiv2023

Pattern formation in charge density wave states after a quantum quench

We study post-quench dynamics of charge-density-wave (CDW) order in the square-lattice $t$-$V$ model. The ground state of this system at half-filling is characterized by a checkerboard modulation of particle density. A generalized self-consistent mean-field method, based on the time-dependent variational principle, is employed to describe the dynamical evolution of the CDW states. Assuming a homogeneous CDW order throughout the quench process, the time-dependent mean-field approach is reduced to the Anderson pseudospin method. Quench simulations based on the Bloch equation for pseudospins produce three canonical behaviors of order-parameter dynamics: phase-locked persistent oscillation, Landau-damped oscillation, and dynamical vanishing of the CDW order. We further develop an efficient real-space von Neumann equation method to incorporate dynamical inhomogeneity into simulations of quantum quenches. Our large-scale simulations uncover complex pattern formations in the post-quench CDW states, especially in the strong quench regime. The emergent spatial textures are characterized by super density modulations on top of the short-period checkerboard CDW order. Our demonstration of pattern formation in quenched CDW states, described by a simple broken $Z_2$ symmetry, underscores the importance of dynamical inhomogeneity in quantum quenches of many-body systems with more complex orders.

cond-mat.stat-mech↗

arXiv2023

Machine learning force-field models for metallic spin glass

Metallic spin glass systems, such as dilute magnetic alloys, are characterized by randomly distributed local moments coupled to each other through a long-range electron-mediated effective interaction. We present a scalable machine learning (ML) framework for dynamical simulations of metallic spin glasses. A Behler-Parrinello type neural-network model, based on the principle of locality, is developed to accurately and efficiently predict electron-induced local magnetic fields that drive the spin dynamics. A crucial component of the ML model is a proper symmetry-invariant representation of local magnetic environment which is direct input to the neural net. We develop such a magnetic descriptor by incorporating the spin degrees of freedom into the atom-centered symmetry function methods which are widely used in ML force-field models for quantum molecular dynamics. We apply our approach to study the relaxation dynamics of an amorphous generalization of the s-d model. Our work highlights the promising potential of ML models for large-scale dynamical modeling of itinerant magnets with quenched disorder.

cond-mat.dis-nn↗

arXiv2023

Driven Majorana Modes: A Route to Synthetic $p_x+ip_y$ Superconductivity

We propose a protocol to realize synthetic $p_x+ip_y$ superconductors in one-dimensional topological systems that host Majorana fermions. By periodically driving a localized Majorana mode across the system, our protocol realizes a topological pumping of Majorana fermions, analogous to the adiabatic Thouless pumping of electrical charges. Importantly, similar to the realization of a Chern insulator through Thouless pumping, we show that pumping of Majorana zero modes could lead to a $p_x + ip_y$ superconductor in the two dimensions of space and synthetic time. The Floquet theory is employed to map the driven one-dimensional system to a two-dimensional synthetic system by considering frequency as a new dimension. We demonstrate such Floquet $p_x + i p_y$ superconductors using the Kitaev $p$-wave superconductor chain, a prototypical 1D topological system, as well as its more realistic realization in the 1D Kondo lattice model as examples. We further show the appearance of a new $π$ Majorana mode at the Floquet zone boundary in an intermediate drive frequency region. Our work suggests a driven magnetic spiral coupled to a superconductor as a promising platform for the realization of novel topological superconductors.

cond-mat.supr-con↗

arXiv2023

Kibble-Zurek Mechanism for Nonequilibrium Generation of Magnetic Monopoles in Spin Ices

The proliferation of topological defects is a common out-of-equilibrium phenomenon when a system is driven into a phase of broken symmetry. The Kibble-Zurek mechanism (KZM) provides a theoretical framework for the critical dynamics and generation of topological defects in such scenarios. One of the early applications of KZM is the estimation of heavy magnetic monopoles left behind by the cosmological phase transitions in the early universe. The scarcity of such relic monopoles, which contradicts the prediction of KZM, is one of the main motivations for cosmological inflationary theories. On the other hand, magnetic monopoles as emergent quasi-particles have been observed in spin ices, a peculiar class of frustrated magnets that remain disordered at temperatures well below the energy scale of exchange interaction. Here we study the annihilation dynamics of magnetic monopoles when spin ice is cooled to zero temperature in a finite time. Through extensive Glauber dynamics simulations, we find that the density of residual monopole follows a power law dependence on the annealing rate. A kinetic reaction theory that precisely captures the annihilation process from Monte Carlo simulations is developed. We further show that the KZM can be generalized to describe the critical dynamics of spin ice, where the exponent of the power-law behavior is determined by the dynamic critical exponent $z$ and the cooling protocol.

cond-mat.stat-mech↗

arXiv2023

Nonequilibrium generation of charge defects in kagome spin ice under slow cooling

Kagome spin ice is one of the canonical examples of highly frustrated magnets. The effective magnetic degrees of freedom in kagome spin ice are Ising spins residing on a two-dimensional network of corner-sharing triangles. Due to strong geometrical frustration, nearest-neighbor antiferromagnetic interactions on the kagome lattice give rise to a macroscopic number of degenerate classical ground states characterized by ice rules. Elementary excitations at low temperatures are defect-triangles that violate the ice rules and carry an additional net magnetic charge relative to the background. We perform large-scale Glauber dynamics simulations to study the nonequilibrium dynamics of kagome ice under slow cooling. We show that the density of residual charge defects exhibits a power law dependence on the quench rate for the class of algebraic cooling protocols. The numerical results are well captured by the rate equation for the charge defects based on the reaction kinetics theory. As the relaxation time of the kagome ice phase remains finite, there is no dynamical freezing as in the Kibble-Zurek scenario. Instead, we show that the power-law behavior originates from a thermal excitation that decay algebraically with time at the late stage of the cooling schedule. Similarities and differences in quench dynamics of other spin ice systems are also discussed.

cond-mat.stat-mech↗

arXiv2023

Convolutional neural networks for large-scale dynamical modeling of itinerant magnets

Complex spin textures in itinerant electron magnets hold promises for next-generation memory and information technology. The long-ranged and often frustrated electron-mediated spin interactions in these materials give rise to intriguing localized spin structures such as skyrmions. Yet, simulations of magnetization dynamics for such itinerant magnets are computationally difficult due to the need for repeated solutions to the electronic structure problems. We present a convolutional neural network (CNN) model to accurately and efficiently predict the electron-induced magnetic torques acting on local spins. Importantly, as the convolutional operations with a fixed kernel (receptive field) size naturally take advantage of the locality principle for many-electron systems, CNN offers a scalable machine learning approach to spin dynamics. We apply our approach to enable large-scale dynamical simulations of skyrmion phases in itinerant spin systems. By incorporating the CNN model into Landau-Lifshitz-Gilbert dynamics, our simulations successfully reproduce the relaxation process of the skyrmion phase and stabilize a skyrmion lattice in larger systems. The CNN model also allows us to compute the effective receptive fields, thus providing a systematic and unbiased method for determining the locality of the original electron models.

cond-mat.str-el↗

arXiv2023

Crystallization dynamics of magnetic skyrmions in a frustrated itinerant magnet

We investigate the phase ordering kinetics of skyrmion lattice (SkL) in a metallic magnet. The SkL can be viewed as a superposition of magnetic stripes whose periods are determined by the quasi-nesting wave vectors of the underlying Fermi surface. An effective magnetic Hamiltonian that describes the electron-mediated spin-spin interaction is obtained for a two-dimensional s-d model with the Rashba spin-orbit coupling. Large-scale Landau-Lifshitz-Gilbert dynamics simulations based on the effective spin Hamiltonian reveal a two-stage phase ordering of the SkL phase after a thermal quench. The initial fast crystallization of skyrmions is followed by a slow relaxation dominated by the annihilation dynamics of dislocations, which are topological defects of the constituent magnetic stripe orders. The late-stage phase ordering also exhibits a dynamical scaling symmetry. We further show that the annihilation of dislocations follows a power-law time dependence with a logarithmic correction that depends on magnetic fields. Implications of our results for SkL phases in magnetic materials are also discussed.

cond-mat.str-el↗

arXiv2023

Machine learning for structure-property relationships: Scalability and limitations

We present a scalable machine learning (ML) framework for predicting intensive properties and particularly classifying phases of many-body systems. Scalability and transferability are central to the unprecedented computational efficiency of ML methods. In general, linear-scaling computation can be achieved through the divide and conquer approach, and the locality of physical properties is key to partitioning the system into sub-domains that can be solved separately. Based on the locality assumption, ML model is developed for the prediction of intensive properties of a finite-size block. Predictions of large-scale systems can then be obtained by averaging results of the ML model from randomly sampled blocks of the system. We show that the applicability of this approach depends on whether the block-size of the ML model is greater than the characteristic length scale of the system. In particular, in the case of phase identification across a critical point, the accuracy of the ML prediction is limited by the diverging correlation length. The two-dimensional Ising model is used to demonstrate the proposed framework. We obtain an intriguing scaling relation between the prediction accuracy and the ratio of ML block size over the spin-spin correlation length. Implications for practical applications are also discussed.

cond-mat.stat-mech↗

arXiv2023

Machine learning for phase ordering dynamics of charge density waves

We present a machine learning (ML) framework for large-scale dynamical simulations of charge density wave (CDW) states. The charge modulation in a CDW state is often accompanied by a concomitant structural distortion, and the adiabatic evolution of a CDW order is governed by the dynamics of the lattice distortion. Calculation of the electronic contribution to the driving forces, however, is computationally very expensive for large systems. Assuming the principle of locality for electron systems, a neural-network model is developed to accurately and efficiently predict local electronic forces with input from neighborhood configurations. Importantly, the ML model makes possible a linear complexity algorithm for dynamical simulations of CDWs. As a demonstration, we apply our approach to investigate the phase ordering dynamics of the Holstein model, a canonical system of CDW order. Our large-scale simulations uncover an intriguing growth of the CDW domains that deviates significantly from the expected Allen-Cahn law for phase ordering of Ising-type order parameter field. This anomalous domain-growth could be attributed to the complex structure of domain-walls in this system. Our work highlights the promising potential of ML-based force-field models for dynamical simulations of functional electronic materials.

cond-mat.str-el↗

arXiv2022

Intertwined Orders and Electronic Structure in Superconducting Vortex Halos

We present a comprehensive study of vortex structures in $d$-wave superconductors from large-scale renormalized mean-field theory of the square-lattice $t$-$t'$-$J$ model, which has been shown to provide a quantitative modeling for high-$T_c$ cuprate superconductors. With an efficient implementation of the kernel polynomial method for solving electronic structures, self-consistent calculations involving up to $10^5$ variational parameters are performed to investigate the vortex solutions on lattices of up to $10^4$ sites. By taking into account the strong correlation of the model, our calculations shed new lights on two puzzling results that have emerged from recent scanning tunneling microscopy (STM) experiments. The first concerns the issue of the zero-biased-conductance peak (ZBCP) at the vortex core for a uniform $d$-wave superconducting state. Despite its theoretical prediction, the ZBCP was not observed in most doping range of cuprates except in heavily over-doped samples at low magnetic field. The second issue is the nature of the checkerboard charge density waves (CDWs) with a period of about 8 unit cells in the vortex halo at optimal doping. Although it has been suggested that such bipartite structure arises from low-energy quasiparticle interference, another intriguing scenario posits that the checkerboard CDWs originate from an underlying bidirectional pair-density wave (PDW) ordering with the same period. We present a coherent interpretation of these experimental results based on systematic studies of the doping and magnetic field effects on vortex solutions with and without a checkerboard structure. The mechanism of the emergent intertwined orders within the vortex halo is also discussed.

cond-mat.supr-con↗

arXiv2022

Atomistic simulation of Mott transition in fluid metals: Combining molecular dynamics with dynamical mean-field theory

We present a new quantum molecular dynamics (MD) method where the electronic structure and atomic forces are solved by a real-space dynamical mean-field theory (DMFT). Contrary to most quantum MD methods that are based on effective single-particle wave functions, the DMFT approach is able to describe correlation-induced Mott metal-insulator transitions and the associated incoherent electronic excitations in an atomic liquid. We apply the DMFT-MD method to study Mott transitions in an atomic liquid model which can be viewed as the liquid-state generalization of the Hubbard model. The half-filled Hubbard liquids also provide a minimum model for alkali fluid metals. Our simulations uncover two distinct types of Mott transition depending on the atomic bonding and short-range structures in the electronically delocalized phase. In the first scenario where atoms tend to form dimers, increasing the Hubbard repulsion gives rise to a transition from a molecular insulator to an atomic insulator with a small window of enhanced metallicity in the vicinity of the localization transition. On the other hand, for Hubbard liquids with atoms forming large conducting clusters, the localization of electrons leads to the fragmentation of clusters and is intimately related to the liquid-gas transition of atoms. Implications of our results for metal-insulator transitions in fluid alkali metals are discussed.

cond-mat.str-el↗

arXiv2022

Anisotropic MagnetoMemristance

In the last decade, nanoscale resistive devices with memory have been the subject of intense study because of their possible use in brain-inspired computing. However, operational endurance is one of the limiting factors in the adoption of such technology. For this reason, we discuss the emergence of current-induced memristance in magnetic materials, known for their durability. We show analytically and numerically that a single ferromagnetic layer can possess GHz memristance, due to a combination of two factors: a current-induced transfer of angular momentum (Zhang-Li torque) and the anisotropic magnetoresistance (AMR). We term the resulting effect the anisotropic magneto-memristance (AMM). We connect the AMM to the topology of the magnetization state, within a simple model of a 1-dimensional annulus-shaped magnetic layer, confirming the analytical results with micromagnetic simulations for permalloy. Our results open a new path towards the realization of single-layer magnetic memristive devices operating at GHz frequencies.

cond-mat.mes-hall↗

arXiv2022

Enhancement of Atomic Diffusion due to Electron Delocalization in Fluid Metals

We present a general theory of atomic self-diffusion in the vicinity of a Mott metal-insulator transition in fluid metals. Upon decreasing the electron correlation from the Mott insulating phase, the delocalization of electrons gives rise to an increasing attractive interatomic interaction, which is expected to introduce an additional friction, hence reducing the atomic diffusivity. Yet, our quantum molecular dynamics simulations find an intriguing enhancement of the diffusion coefficient induced by the emerging attractive force. We show that this counterintuitive phenomenon results from the reduction of the repulsive core and the suppression of the attractive tail by thermal fluctuations. The proposed scenario is corroborated by the Chapman-Enskog theory and classical molecular dynamics simulations on a standard liquid model based on the Morse potential. Our work not only provides a general mechanism of the attraction-facilitated diffusion enhancement in simple liquids, but also sheds new lights on the nontrivial effects of electron correlation on atomic dynamics.

cond-mat.str-el↗

arXiv2022

Evidence for pressure induced unconventional quantum criticality in the coupled spin ladder antiferromagnet C$_9$H$_{18}$N$_2$CuBr$_4$

Quantum phase transitions in quantum matter occur at zero temperature between distinct ground states by tuning a nonthermal control parameter. Often, they can be accurately described within the Landau theory of phase transitions, similarly to conventional thermal phase transitions. However, this picture can break down under certain circumstances. Here, we present a comprehensive study of the effect of hydrostatic pressure on the magnetic structure and spin dynamics of the spin-1/2 ladder compound C$_9$H$_{18}$N$_2$CuBr$_4$. Single-crystal heat capacity and neutron diffraction measurements reveal that the N$\rm \acute{e}$el-ordered phase breaks down beyond a critical pressure of $P_{\rm c}$$\sim$1.0 GPa through a continuous quantum phase transition. Estimates of the critical exponents suggest that this transition may fall outside the traditional Landau paradigm. The inelastic neutron scattering spectra at 1.3 GPa are characterized by two well-separated gapped modes, including one continuum-like and another resolution-limited excitation in distinct scattering channels, which further indicates an exotic quantum-disordered phase above $P_{\rm c}$.

cond-mat.str-el↗

arXiv2022

Machine learning predictions for local electronic properties of disordered correlated electron systems

We present a scalable machine learning (ML) model to predict local electronic properties such as on-site electron number and double occupation for disordered correlated electron systems. Our approach is based on the locality principle, or the nearsightedness nature, of many-electron systems, which means local electronic properties depend mainly on the immediate environment. A ML model is developed to encode this complex dependence of local quantities on the neighborhood. We demonstrate our approach using the square-lattice Anderson-Hubbard model, which is a paradigmatic system for studying the interplay between Mott transition and Anderson localization. We develop a lattice descriptor based on group-theoretical method to represent the on-site random potentials within a finite region. The resultant feature variables are used as input to a multi-layer fully connected neural network, which is trained from datasets of variational Monte Carlo (VMC) simulations on small systems. We show that the ML predictions agree reasonably well with the VMC data. Our work underscores the promising potential of ML methods for multi-scale modeling of correlated electron systems.

cond-mat.str-el↗

arXiv2022

Descriptors for Machine Learning Model of Generalized Force Field in Condensed Matter Systems

We outline the general framework of machine learning (ML) methods for multi-scale dynamical modeling of condensed matter systems, and in particular of strongly correlated electron models. Complex spatial temporal behaviors in these systems often arise from the interplay between quasi-particles and the emergent dynamical classical degrees of freedom, such as local lattice distortions, spins, and order-parameters. Central to the proposed framework is the ML energy model that, by successfully emulating the time-consuming electronic structure calculation, can accurately predict a local energy based on the classical field in the intermediate neighborhood. In order to properly include the symmetry of the electron Hamiltonian, a crucial component of the ML energy model is the descriptor that transforms the neighborhood configuration into invariant feature variables, which are input to the learning model. A general theory of the descriptor for the classical fields is formulated, and two types of models are distinguished depending on the presence or absence of an internal symmetry for the classical field. Several specific approaches to the descriptor of the classical fields are presented. Our focus is on the group-theoretical method that offers a systematic and rigorous approach to compute invariants based on the bispectrum coefficients. We propose an efficient implementation of the bispectrum method based on the concept of reference irreducible representations. Finally, the implementations of the various descriptors are demonstrated on well-known electronic lattice models.

cond-mat.str-el↗