arXiv subjects

Z. Y. Xie

Publications and source records attributed to Z. Y. Xie.

At least 37 records · Page 2Linked to original sources

arXiv2023

Exploring quantum phase transitions by the cross derivative of the ground state energy

In this work, the cross derivative of the Gibbs free energy, initially proposed for phase transitions in classical spin models [Phys. Rev. B 101, 165123 (2020)], is extended for quantum systems. We take the spin-1 XXZ chain with anisotropies as an example to demonstrate its effectiveness and convenience for the Gaussian-type quantum phase transitions therein. These higher-order transitions are very challenging to determine by conventional methods. From the cross derivative with respect to the two anisotropic strengths, a single valley structure is observed clearly in each system size. The finite-size extrapolation of the valley depth shows a perfect logarithmic divergence, signaling the onset of a phase transition. Meanwhile, the critical point and the critical exponent for the correlation length are obtained by a power-law fitting of the valley location in each size. The results are well consistent with the best estimations in the literature. Its application to other quantum systems with continuous phase transitions is also discussed briefly.

cond-mat.str-el↗

arXiv2022

High-temperature ferromagnetism and strong $π$-conjugation feature in two-dimensional manganese tetranitride

Two-dimensional (2D) magnetic materials have attracted tremendous research interest because of the promising application in the next-generation microelectronic devices. Here, by the first-principles calculations, we propose a two-dimensional ferromagnetic material with high Curie temperature, manganese tetranitride MnN$_4$ monolayer, which is a square-planar lattice made up of only one layer of atoms. The structure is demonstrated to be stable by the phonon spectra and the molecular dynamic simulations, and the stability is ascribed to the $π$-d conjugation between $π$ orbital of N=N bond and Mn $d$ orbital. More interestingly, the MnN$_4$ monolayer displays robust 2D ferromagnetism, which originates from the strong exchange couplings between Mn atoms due to the $π$-d conjugation. The high critical temperature of 247 K is determined by solving the Heisenberg model with the Monte Carlo method.

cond-mat.mtrl-sci↗

arXiv2022

Long-range spin-orbital order in the spin-orbital SU(2)$\times$SU(2)$\times$U(1) model

By using the tensor-network state algorithm, we study a spin-orbital model with SU(2)$\times$SU(2)$\times$U(1) symmetry on the triangular lattice. This model was proposed to describe some triangular $d^1$ materials and was argued to host a spin-orbital liquid ground state. In our work the trial wavefunction of its ground state is approximated by an infinite projected entangled simplex state and optimized by the imaginary-time evolution. Contrary to the previous conjecture, we find that the two SU(2) symmetries are broken, resulting in a stripe spin-orbital order with the same magnitude $m=0.085(10)$. This value is about half of that in the spin-1/2 triangular Heisenberg antiferromagnet. Our result demonstrates that although the long-sought spin-orbital liquid is absent in this model the spin-orbital order is significantly reduced due to the enhanced quantum fluctuation. This suggests that high-symmetry spin-orbital models are promising in searching for exotic states of matter in condensed-matter physics.

cond-mat.str-el↗

arXiv2022

Exploring explicit coarse-grained structure in artificial neural networks

We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network called TaylorNet, which aims to approximate the general mapping from input data to output result in terms of Taylor series directly, without resorting to any magic nonlinear activations. The other is a new setup for data distillation, which can perform multi-level abstraction of the input dataset and generate new data that possesses the relevant features of the original dataset and can be used as references for classification. In both cases, the coarse-grained structure plays an important role in simplifying the network and improving both the interpretability and efficiency. The validity has been demonstrated on MNIST and CIFAR-10 datasets. Further improvement and some open questions related are also discussed.

cs.LG↗

arXiv2022

Two-dimensional binary transition metal nitride $M$N$_4$ ($M$ = V, Cr, Mn, Fe, Co) with a graphene-like structure and strong magnetic properties

Binary transition metal nitride with a graphene-like structure and strong magnetic properties is rare. Based on the first-principles calculations, we design two kinds of $M$N$_4$ ($M$ =transition metal) monolayers, which are transition metal nitrides with a planar structure, made up of $M$N$_4$ units aligned in the rhombic and square patterns. The two structural lattices have robust stability and good compatibility with different metal atoms, and the underlying mechanism is the combination of $sp^2$ hybridization, coordinate bond, and $π$ conjugation. With the metal atom changing from V, Cr, Mn, Fe to Co, the total charge of $M$N$_4$ system increases by one electron in turn, which results in continuous adjustability of the electronic and magnetic properties. The planar ligand field is another feature of the two $M$N$_4$ lattices, which brings about the special splitting of five suborbitals of 3$d$ metal atom and gives rise to strong magnetism. Moreover, room-temperature ferromagnetism in square-CoN$_4$ monolayer with the Curie temperatures of 321 K is determined by solving the Heisenberg model combined with Monte Carlo method.

cond-mat.mtrl-sci↗

arXiv2022

Prediction of single-atom-thick transition metal nitride CrN$_4$ with a square-planar network and high-temperature ferromagnetism

Single-atom-thick two-dimensional materials such as graphene usually have a hexagonal lattice while the square-planar lattice is uncommon in the family of two-dimensional materials. Here, we demonstrate that single-atom-thick transition metal nitride CrN$_4$ monolayer is a stable free-standing layer with a square-planar network. The stability of square-planar geometry is ascribed to the combination of N=N double bond, Cr-N coordination bond, and $π$-d conjugation, in which the double $π$-d conjugation is rarely reported in previous studies. This mechanism is entirely different from that of the reported two-dimensional materials, leading to lower formation energy and more robust stability compared to the synthesized g-C$_3$N$_4$ monolayer. On the other hand, CrN$_4$ layer has a ferromagnetic ground state, in which the ferromagnetic coupling between two Cr atoms is mediated by electrons of the half-filled large $π$ orbitals from $π$-d conjugation. The high-temperature ferromagnetism in CrN$_4$ monolayer is confirmed by solving the Heisenberg model with Monte Carlo method.

cond-mat.mtrl-sci↗

arXiv2022

Achieving high-temperature ferromagnetism by means of magnetic ions dimerization

Magnetic two-dimensional materials have potential application in next-generation electronic devices and have stimulated extensive interest in condensed matter physics and material fields. However, how to realize high-temperature ferromagnetism in two-dimensional materials remains a great challenge in physics. Herein, we propose an effective approach that the dimerization of magnetic ions in two-dimensional materials can enhance the exchange coupling and stabilize the ferromagnetism. Manganese carbonitride Mn$_2$N$_6$C$_6$ with a planar monolayer structure is taken as an example to clarify the method, in which two Mn atoms are gathered together to form a ferromagnetic dimer of Mn atoms and further these dimers are coupled together to form the overall ferromagnetism of the two-dimensional material. In Mn$_2$N$_6$C$_6$ monolayer, the near-room-temperature ferromagnetism with the Curie temperature of 272.3 K is determined by solving Heisenberg model using Monte Carlo simulations method.

cond-mat.mtrl-sci↗

arXiv2022

High-temperature ferromagnetism in two-dimensional material MnSn originated from interlayer coupling

MnSn monolayer synthesized recently is a novel two-dimensional ferromagnetic material with a hexagonal lattice, in which three Mn atom come together to form a trimer, making it remarkably different from other magnetic two-dimensional materials. Most impressively, there happens a sharp increase of Curie temperature from 54 K to 225 K when the number of layers increase from 1 to 3. However, no quantitative explanation is reported in previous studies. Herein, by means of first-principle calculations method and Monte carlo method, we demonstrate that strong interlayer ferromagnetic coupling is the essential role in enhancing its critical temperature, which act as a magnetic field to stabilize the ferromagnetism in the MnSn multilayers.

cond-mat.mtrl-sci↗

arXiv2022

Variational corner transfer matrix renormalization group method for classical statistical models

In the context of tensor network states, we for the first time reformulate the corner transfer matrix renormalization group (CTMRG) method into a variational bilevel optimization algorithm. The solution of the optimization problem corresponds to the fixed-point environment pursued in the conventional CTMRG method, from which the partition function of a classical statistical model, represented by an infinite tensor network, can be efficiently evaluated. The validity of this variational idea is demonstrated by the high-precision calculation of the residual entropy of the dimer model, and is further verified by investigating several typical phase transitions in classical spin models, where the obtained critical points and critical exponents all agree with the best known results in literature. Its extension to three-dimensional tensor networks or quantum lattice models is straightforward, as also discussed briefly.

cond-mat.str-el↗

arXiv2022

Laboratory observation of plasmoid-dominated magnetic reconnection in hybrid collisional-collisionless regime

Magnetic reconnection, breaking and reorganization of magnetic field topology, is a fundamental process for rapid release of magnetic energy into plasma particles that occurs pervasively throughout the universe. In most natural circumstances, the plasma properties on either side of the reconnection layer are asymmetric, in particular for the collision rates that are associated with a combination of density and temperature and critically determine the reconnection mechanism. To date, all laboratory experiments on magnetic reconnections have been limited to purely collisional or collisionless regimes. Here, we report a well-designed experimental investigation on asymmetric magnetic reconnections in a novel hybrid collisional-collisionless regime by interactions between laser-ablated Cu and CH plasmas. We show that the growth rate of the tearing instability in such a hybrid regime is still extremely large, resulting in rapid formation of multiple plasmoids, lower than that in the purely collisionless regime but much higher than the collisional case. In addition, we, for the first time, directly observe the topology evolutions of the whole process of plasmoid-dominated magnetic reconnections by using highly-resolved proton radiography.

physics.plasm-ph↗

arXiv2022

Magnetization of the spin-1/2 Heisenberg antiferromagnet on the triangular lattice

After decades of debate, now there is a rough consensus that at zero temperature the spin-$1/2$ Heisenberg antiferromagnet on the triangular lattice is three-sublattice $120^\circ$ magnetically ordered, in contrast to a quantum spin liquid as originally proposed. However, there remains considerable discrepancy in the magnetization reported among various methods. To resolve this issue, in this work we revisit this model by the tensor-network state algorithm. The ground-state energy per bond $E_b$ and magnetization per spin $M_0$ in the thermodynamic limit are obtained with high precision. The former is estimated to be $E_b = -0.18334(10)$. This value agrees well with that from the series expansion. The three-sublattice magnetic order is firmly confirmed and the magnetization is determined as $M_0 = 0.161(5)$. It is about $32\%$ of its classical value and slightly below the lower bound from the series expansion. In comparison with the best estimated value by Monte Carlo and density-matrix renormalization group, our result is about $20\%$ smaller. This magnetic order is consistent with further analysis of the three-body correlation. Our work thus provides new benchmark results for this prototypical model.

cond-mat.str-el↗

arXiv2021

First-order transition between the plaquette valence bond solid and antiferromagnetic phases of the Shastry-Sutherland model

We study the ground state phase diagram of the Shastry-Sutherland model by using the variational optimization of the infinite tensor network states, and find a weakly first-order transition between the plaquette and the antiferromagnetic states. The full plaquette state strongly competes with the empty plaquette ground state, with an energy difference less than $10^{-4}J$. We show a staggered ring exchange interaction that preserves the Shastry-Sutherland lattice symmetry can stabilize the full plaquette ground state. In light of this, we propose the triple point where the full plaquette, empty plaquette, and antiferromagnetic phases meet as a deconfined quantum critical point.

cond-mat.str-el↗

arXiv2021

Enabling Lightweight Fine-tuning for Pre-trained Language Model Compression based on Matrix Product Operators

This paper presents a novel pre-trained language models (PLM) compression approach based on the matrix product operator (short as MPO) from quantum many-body physics. It can decompose an original matrix into central tensors (containing the core information) and auxiliary tensors (with only a small proportion of parameters). With the decomposed MPO structure, we propose a novel fine-tuning strategy by only updating the parameters from the auxiliary tensors, and design an optimization algorithm for MPO-based approximation over stacked network architectures. Our approach can be applied to the original or the compressed PLMs in a general way, which derives a lighter network and significantly reduces the parameters to be fine-tuned. Extensive experiments have demonstrated the effectiveness of the proposed approach in model compression, especially the reduction in finetuning parameters (91% reduction on average).

cs.LG↗

arXiv2021

Theory of competing Chern-Simons orders and emergent phase transitions

Based on the Chern-Simons fermionization of spin-1/2 operators, we propose a systematic framework to investigate the competition between emergent phases in frustrated two-dimensional XY quantum magnets. Application of the method to the antiferromagnetic honeycomb spin-1/2 $J_1$-$J_2$ XY model reveals an unconventional phase transition between two Chern-Simons orders: the Chern-Simons superconductor and the exciton insulator of Chern-Simons fermions. We show that in the spin language, this transition translates to the transition from the planar Néel state to the non-uniform chiral spin-liquid that was proposed earlier in the literature. Namely, the Chern-Simons superconductor describes the planar Néel state, while the Chern-Simons exciton insulator corresponds to the non-uniform chiral spin-liquid. These results are further confirmed by our high-precision tensor network calculation, which provides the first numerical evidence for the transition from Néel order to a non-uniform chiral spin-liquid. We argue that the developed method can be applied to other frustrated quantum magnets of XXZ type and can detect unconventional phase transitions.

cond-mat.str-el↗

arXiv2020

Automatic Differentiation for Second Renormalization of Tensor Networks

Tensor renormalization group (TRG) constitutes an important methodology for accurate simulations of strongly correlated lattice models. Facilitated by the automatic differentiation technique widely used in deep learning, we propose a uniform framework of differentiable TRG ($\partial$TRG) that can be applied to improve various TRG methods, in an automatic fashion. Essentially, $\partial$TRG systematically extends the concept of second renormalization [PRL 103, 160601 (2009)] where the tensor environment is computed recursively in the backward iteration, in the sense that given the forward process of TRG, $\partial$TRG automatically finds the gradient through backpropagation, with which one can deeply "train" the tensor networks. We benchmark $\partial$TRG in solving the square-lattice Ising model, and demonstrate its power by simulating one- and two-dimensional quantum systems at finite temperature. The deep optimization as well as GPU acceleration renders $\partial$TRG manybody simulations with high efficiency and accuracy.

cond-mat.str-el↗

arXiv2020

Critical properties of the two-dimensional $q$-state clock model

We perform the state-of-the-art tensor network simulations directly in the thermodynamic limit to clarify the critical properties of the $q$-state clock model on the square lattice. We determine accurately the two phase transition temperatures through the singularity of the classical analog of the entanglement entropy, and provide extensive numerical evidences to show that both transitions are of the Berezinskii-Kosterlitz-Thouless (BKT) type for $q\ge 5$ and that the low-energy physics of this model is well described by the $\mathbb{Z}_q$-deformed sine-Gordon theory. We also determine the characteristic conformal parameters, especially the compactification radius, that govern the critical properties of the intermediate BKT phase.

cond-mat.stat-mech↗

arXiv2020

Compressing deep neural networks by matrix product operators

A deep neural network is a parametrization of a multilayer mapping of signals in terms of many alternatively arranged linear and nonlinear transformations. The linear transformations, which are generally used in the fully connected as well as convolutional layers, contain most of the variational parameters that are trained and stored. Compressing a deep neural network to reduce its number of variational parameters but not its prediction power is an important but challenging problem toward the establishment of an optimized scheme in training efficiently these parameters and in lowering the risk of overfitting. Here we show that this problem can be effectively solved by representing linear transformations with matrix product operators (MPOs), which is a tensor network originally proposed in physics to characterize the short-range entanglement in one-dimensional quantum states. We have tested this approach in five typical neural networks, including FC2, LeNet-5, VGG, ResNet, and DenseNet on two widely used data sets, namely, MNIST and CIFAR-10, and found that this MPO representation indeed sets up a faithful and efficient mapping between input and output signals, which can keep or even improve the prediction accuracy with a dramatically reduced number of parameters. Our method greatly simplifies the representations in deep learning, and opens a possible route toward establishing a framework of modern neural networks which might be simpler and cheaper, but more efficient.

cs.LG↗

arXiv2019

Cross derivative: a universal and efficient method for phase transitions in classical spin models

With an auxiliary weak external magnetic field, we reexamine the fundamental thermodynamic function, Gibbs free energy F(T, h), to study the phase transitions in the classical spin lattice models. A cross derivative, i.e. the second-order partial derivative of F(T, h) with respect to both temperature and field, is calculated to precisely locate the critical temperature, which also reveals the nature of a transition. The strategy is efficient and universal, as exemplified by the 5-state clock model, 2-dimensional (2D) and 3D Ising models, and the XY model, no matter a transition is trivial or exotic with complex excitations. More importantly, other conjugate pairs could also be integrated into a similar cross derivative if necessary, which would greatly enrich our vision and means to investigate phase transitions both theoretically and experimentally.

cond-mat.str-el↗