arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 91 records · Page 5Linked to original sources

arXiv2024

Anomalous criticality coexists with giant cluster in the uniform forest model

We show by extensive simulations that the whole supercritical phase of the three-dimensional uniform forest model simultaneously exhibits an infinite tree and a rich variety of critical phenomena. Besides typical scalings like algebraically decaying correlation, power-law distribution of cluster sizes, and divergent correlation length, a number of anomalous behaviors emerge. The fractal dimensions for off-giant trees take different values when being measured by linear system size or gyration radius. The giant-tree size displays two-length scaling fluctuations, instead of following the central-limit theorem.

cond-mat.stat-mech↗

arXiv2024

Emergent topological ordered phase for the Ising-XY Model revealed by cluster-updating Monte-Carlo method

The two-component cold atom systems with anisotropic hopping amplitudes can be phenomenologically described by a two-dimensional Ising-XY coupled model with spatial anisotropy. At low temperatures, theoretical predictions [Phys. Rev. A 72, 053604 (2005)] and [arXiv:0706.1609] indicate the existence of a topological ordered phase characterized by Ising and XY disorder but with 2XY ordering. However, due to ergodic difficulties faced by Monte Carlo methods at low temperatures, this topological phase has not been numerically explored. We propose a linear cluster updating Monte Carlo method, which flips spins without rejection in the anisotropy limit but does not change the energy. Using this scheme and conventional Monte Carlo methods, we succeed in revealing the nature of topological phases with half-vortices and domain walls. In the constructed global phase diagram, Ising and XY type transitions are very close to each other and differ significantly from the schematic phase diagram reported earlier. We also propose and explore a wide range of quantities, including magnetism, superfluidity, specific heat, susceptibility, and even percolation susceptibility, and obtain consistent results. Furthermore, we observe first-order transitions characterized by common intersection points in magnetizations for different system sizes, as opposed to the conventional phase transition where Binder cumulants of various sizes share common intersections. The results are useful to help cold atom experiments explore the half-vortex topological phase.

cond-mat.quant-gas↗

arXiv2024

Two-dimensional XY Ferromagnet Induced by Long-range Interaction

The crossover between short-range and long-range (LR) universal behaviors remains a central theme in the physics of long-range interacting systems. The competition between LR coupling and the Berezinskii-Kosterlitz-Thouless mechanism makes the problem more subtle and less understood in the two-dimensional (2D) XY model, a cornerstone for investigating low-dimensional phenomena and their implications in quantum computation. We study the 2D XY model with algebraically decaying interaction $\sim1/r^{2+σ}$. Utilizing an advanced update strategy, we conduct large-scale Monte Carlo simulations of the model up to a linear size of $L=8192$. Our results demonstrate continuous phase transitions into a ferromagnetic phase for $σ\leq 2$, which exhibits the simultaneous emergence of a long-ranged order and a power-law decaying correlation function due to the Goldstone mode. Furthermore, we find logarithmic scaling behaviors in the low-temperature phase at $σ= 2$. The observed scaling behaviors in the low-temperature phase for $σ\le 2$ agree with our theoretical analysis. Our findings request further theoretical understandings and can be of practical application in cutting-edge experiments like Rydberg atom arrays.

cond-mat.stat-mech↗

arXiv2024

Finite-Size Scaling of the High-Dimensional Ising Model in the Loop Representation

Besides its original spin representation, the Ising model is known to have the Fortuin-Kasteleyn (FK) bond and loop representations, of which the former was recently shown to exhibit two upper critical dimensions $(d_c=4,d_p=6)$. Using a lifted worm algorithm, we determine the critical coupling as $K_c = 0.077\,708\,91(4)$ for $d=7$, which significantly improves over the previous results, and then study critical geometric properties of the loop-Ising clusters on tori for spatial dimensions $d=5$ to 7. We show that, as the spin representation, the loop Ising model has only one upper critical dimension at $d_c=4$. However, sophisticated finite-size scaling (FSS) behaviors, like two length scales, two configuration sectors and two scaling windows, still exist as the interplay effect of the Gaussian fixed point and complete-graph asymptotics. Moreover, using the Loop-Cluster algorithm, we provide an intuitive understanding of the emergence of the percolation-like upper critical dimension $d_p=6$ in the FK-Ising model. As a consequence, a unified physical picture is established for the FSS behaviors in all the three representations of the Ising model above $d_c=4$.

cond-mat.stat-mech↗

arXiv2024

Nature of the mixed-parity pairing of attractive fermions with spin-orbit coupling in optical lattice

The admixture of spin-singlet and spin-triplet pairing states in superconductors can be typically induced by breaking spatial inversion symmetry. Employing the {\it numerically exact} auxiliary-field Quantum Monte Carlo method, we study such mixed-parity pairing phenomena of attractive fermions with Rashba spin-orbit coupling (SOC) in two-dimensional optical lattice at finite temperature. We systematically demystify the evolution of the essential pairing structure in both singlet and triplet channels versus the temperature, fermion filling, SOC and interaction strengths, via computing the condensate fraction and pair wave function. Our numerical results reveal that the singlet channel dominates in the fermion pairing and the triplet pairing has relatively small contribution to the superfluidity for physically relevant parameters. In contrast to the singlet channel mainly consisted of the on-site Cooper pairs, the triplet pairing has plentiful patterns in real space with the largest contributions from several nearest neighbors. As the SOC strengh increases, the pairing correlation is firstly enhanced and then suppressed for triplet pairing while it's simply weakened in singlet channel. We have also obtained the Berezinskii-Kosterlitz-Thouless transition temperatures through the finite-size analysis of condensate fraction. Our results can serve as quantitative guide for future optical lattice experiments as well as accurate benchmarks for theories and other numerical methods.

cond-mat.str-el↗

arXiv2024

Observation of counterflow superfluidity in a two-component Mott insulator

The counterflow superfluidity (CSF) was predicted two decades ago. Counterintuitively, while both components in the CSF have fluidity, their correlated counterflow currents cancel out leading the overall system to an incompressible Mott insulator. However, realizing and identifying the CSF remain challenging due to the request on extreme experimental capabilities in a single setup. Here, we observe the CSF in a binary Bose mixture in optical lattices. We prepare a low-entropy spin-Mott state by conveying and merging two spin-1/2 bosonic atoms at every site and drive it adiabatically to the CSF at $\sim$ 1 nK. Antipair correlations of the CSF are probed though a site- and spin-resolved quantum gas microscope in both real and momentum spaces. These techniques and observations provide accessibility to the symmetry-protected topological quantum matters.

cond-mat.quant-gas↗

arXiv2024

Observation of the antiferromagnetic phase transition in the fermionic Hubbard model

The fermionic Hubbard model (FHM)[1], despite its simple form, captures essential features of strongly correlated electron physics. Ultracold fermions in optical lattices[2, 3] provide a clean and well-controlled platform for simulating FHM. Doping its antiferromagnetic ground state at half filling, various exotic phases are expected to arise in the FHM simulator, including stripe order[4], pseudogap[5], and d-wave superconductors[6], offering valuable insights into high-temperature superconductivity[7{9]. Although notable progress, such as the observation of antiferromagnetic correlations over short[10] and extended distances[11], has been obtained, the antiferromagnetic phase has yet to be realized due to the significant challenges of achieving low temperatures in a large and uniform quantum simulator. Here, we report the observation of the antiferromagnetic phase transition in a three-dimensional fermionic Hubbard system comprising lithium-6 atoms in a uniform optical lattice with approximately 800,000 sites. When the interaction strength, temperature, and doping concentration are finely tuned to approach their respective critical values, sharp increases in the spin structure factor (SSF) are observed. These observations can be well described by a power-law divergence, with a critical exponent of 1.396 from the Heisenberg universality class[12]. At half filling and with optimal interaction strength, the measured SSF reaches 123(8), signifying the establishment of an antiferromagnetic phase. Our results set the stage for exploring the low-temperature phase diagram of FHM.

cond-mat.quant-gas↗

arXiv2023

Sweeny dynamics for the random-cluster model with small $Q$

The Sweeny algorithm for the $Q$-state random-cluster model in two dimensions is shown to exhibit a rich mixture of critical dynamical scaling behaviors. As $Q$ decreases, the so-called critical speeding-up for non-local quantities becomes more and more pronounced. However, for some quantity of specific local pattern -- e.g., the number of half faces on the square lattice, we observe that, as $Q \to 0$, the integrated autocorrelation time $τ$ diverges as $Q^{-ζ}$, with $ζ\simeq 1/2$, leading to the non-ergodicity of the Sweeny method for $Q \to 0$. Such $Q$-dependent critical slowing-down, attributed to the peculiar form of the critical bond weight $v=\sqrt{Q}$, can be eliminated by a combination of the Sweeny and the Kawasaki algorithm. Moreover, by classifying the occupied bonds into bridge bonds and backbone bonds, and the empty bonds into internal-perimeter bonds and external-perimeter bonds, one can formulate an improved version of the Sweeny-Kawasaki method such that the autocorrelation time for any quantity is of order $O(1)$.

cond-mat.stat-mech↗

arXiv2023

Extraordinary-log Universality of Critical Phenomena in Plane Defects

The recent discovery of the extraordinary-log (E-Log) criticality is a celebrated achievement in modern critical theory and calls for generalization. Using large-scale Monte Carlo simulations, we study the critical phenomena of plane defects in three- and four-dimensional O($n$) critical systems. In three dimensions, we provide the first numerical proof for the E-Log criticality of plane defects. In particular, for $n=2$, the critical exponent $\hat{q}$ of two-point correlation and the renormalization-group parameter $α$ of helicity modulus conform to the scaling relation $\hat{q}=(n-1)/(2 πα)$, whereas the results for $n \geq 3$ violate this scaling relation. In four dimensions, it is strikingly found that the E-Log criticality also emerges in the plane defect. These findings have numerous potential realizations and would boost the ongoing advancement of conformal field theory.

cond-mat.stat-mech↗

arXiv2023

Two-point functions of random-length random walk on high-dimensional boxes

We study the two-point functions of a general class of random-length random walks on finite boxes in $\ZZ^d$ with $d\ge3$, and provide precise asymptotics for their behaviour. We show that the finite-box two-point function is asymptotic to the infinite-lattice two-point function when the typical walk length is $o(L^2)$, but develops a plateau when the typical walk length is $Ω(L^2)$. We also numerically study walk length moments and limiting distributions of the self-avoiding walk and Ising model on five-dimensional tori, and find that they agree asymptotically with the known results for self-avoiding walk on the complete graph, both at the critical point and also for a broad class of scaling windows/pseudocritical points. Furthermore, we show that the two-point function of the finite-box random-length random walk, with walk length chosen via the complete graph self-avoiding walk, agrees numerically with the two-point functions of the self-avoiding walk and Ising model on five-dimensional tori. We conjecture that these observations in five dimensions should also hold in all higher dimensions.

math-ph↗

arXiv2023

Precursory Cooper Flow in Ultralow-Temperature Superconductors

Superconductivity at low temperature -- observed in lithium and bismuth, as well as in various low-density superconductors -- calls for developing reliable theoretical and experimental tools for predicting ultralow critical temperatures, $T_c$, of Cooper instability in a system demonstrating nothing but normal Fermi liquid behavior in a broad range of temperatures below the Fermi energy, $T_{\rm F}$. Equally important are controlled predictions of stability in a given Cooper channel. We identify such a protocol within the paradigm of precursory Cooper flow -- a universal ansatz describing logarithmically slow temperature evolution of the linear response of the normal state to the pair-creating perturbation. Applying this framework to the two-dimensional uniform electron gas, we reveal a series of exotic superconducting states, pushing controlled theoretical predictions of $T_c$ to the unprecedentedly low scale of $10^{-100} T_{\rm F}$.

cond-mat.supr-con↗

arXiv2023

Clock Factorized Quantum Monte Carlo Method for Long-range Interacting Systems

Simulating long-range interacting systems is a challenging task due to its computational complexity that the computational effort for each local update is of order $\cal{O}$$(N)$, where $N$ is the size of system. Recently, a technique, called hereby the clock factorized quantum Monte Carlo method, was developed on the basis of the so-called factorized Metropolis filter [Phys. Rev. E 99 010105 (2019)]. In this work, we first explain step by step how the clock factorized quantum Monte Carlo method is implemented to reduce the computational overhead from $\cal{O}$$(N)$ to $\cal{O}$(1). In particular, the core ingredients, including the concepts of bound probabilities and bound rejection events, the tree-like data structure, and the fast algorithms for sampling an extensive set of discrete and small probabilities, are elaborated. Next, we show how the clock factorized quantum Monte Carlo method can be flexibly implemented in various update strategies, like the Metropolis and worm-type algorithms, and can be generalized to simulate quantum systems. Finally, we demonstrate the high efficiency of the clock factorized quantum Monte Carlo algorithms in the examples of the quantum Ising model and the Bose-Hubbard model with long-range interactions and/or long-range hopping amplitudes. We expect that the clock factorized quantum Monte Carlo algorithms would find broad applications in statistical and condensed-matter physics.

physics.comp-ph↗

arXiv2023

Interplay of the complete-graph and Gaussian fixed-point asymptotics in finite-size scaling of percolation above the upper critical dimension

Percolation has two mean-field theories, the Gaussian fixed point (GFP) and the Landau mean-field theory or the complete graph (CG) asymptotics. By large-scale Monte Carlo simulations, we systematically study the interplay of the GFP and CG effects to the finite-size scaling of percolation above the upper critical dimension $d_c = 6$ with periodic, free, and cylindrical boundary conditions. Our results suggest that, with periodic boundaries, the \emph{unwrapped} correlation length scales as $L^{d/6}$ at the critical point, diverging faster than $L$ above $d_c$. As a consequence, the scaling behaviours of macroscopic quantities with respect to the linear system size $L$ follow the CG asymptotics. The distance-dependent properties, such as the short-distance behaviour of the two-point correlation function and the Fourier transformed quantities with non-zero modes, are still controlled by the GFP. With free boundaries, since the correlation length is cutoff by $L$, the finite-size scaling at the critical point is controlled by the GFP. However, some quantities are observed to exhibit the CG aysmptotics at the low-temperature pseudo-critical point, such as the sizes of the two largest clusters. With cylindrical boundaries, due to the interplay of the GFP and CG effects, the correlation length along the axial direction of the cylinder scales as $ξ_L \sim L^{(d-1)/5}$ within the critical window of size $O(L^{-2(d-1)/5})$, distinct from both periodic and free boundaries. A field-theoretical calculation for deriving the scaling of $ξ_L$ is also presented. Moreover, the one-point surface correlation function along the axial direction of the cylinder is observed to scale as $τ^{(1-d)/2}$ for short distance but then enter a plateau of order $L^{-3(d-1)/5}$ before it decays significantly fast.

cond-mat.stat-mech↗

arXiv2023

Graphical Representations and Worm Algorithms for the O($N$) Spin Model

We present a family of graphical representations for the O($N$) spin model, where $N \ge 1$ represents the spin dimension, and $N=1,2,3$ corresponds to the Ising, XY and Heisenberg models, respectively. With an integer parameter $0 \le \ell \le N/2$, each configuration is the coupling of $\ell$ copies of subgraphs consisting of directed flows and $N -2\ell$ copies of subgraphs constructed by undirected loops, which we call the XY and Ising subgraphs, respectively. On each lattice site, the XY subgraphs satisfy the Kirchhoff flow-conservation law and the Ising subgraphs obey the Eulerian bond condition. Then, we formulate worm-type algorithms and simulate the O($N$) model on the simple-cubic lattice for $N$ from 2 to 6 at all possible $\ell$. It is observed that the worm algorithm has much higher efficiency than the Metropolis method, and, for a given $N$, the efficiency is an increasing function of $\ell$. Beside Monte Carlo simulations, we expect that these graphical representations would provide a convenient basis for the study of the O($N$) spin model by other state-of-the-art methods like the tensor network renormalization.

cond-mat.stat-mech↗

arXiv2023

Geometric scaling behaviors of the Fortuin-Kasteleyn Ising model in high dimensions

Recently, we argued [Chin. Phys. Lett. $39$, 080502 (2022)] that the Ising model simultaneously exhibits two upper critical dimensions $(d_c=4, d_p=6)$ in the Fortuin-Kasteleyn (FK) random-cluster representation. In this paper, we perform a systematic study of the FK Ising model on hypercubic lattices with spatial dimensions $d$ from 5 to 7, and on the complete graph. We provide a detailed data analysis of the critical behaviors of a variety of quantities at and near the critical points. Our results clearly show that many quantities exhibit distinct critical phenomena for $4 < d < 6$ and $d\geq 6$, and thus strongly support the argument that $6$ is also an upper critical dimension. Moreover, for each studied dimension, we observe the existence of two configuration sectors, two lengthscales, as well as two scaling windows, and thus, two sets of critical exponents are needed to describe these behaviors. Our finding enriches the understanding of the critical phenomena in the Ising model.

cond-mat.stat-mech↗

arXiv2023

Machine learning of percolation models using graph convolutional neural networks

Percolation is an important topic in climate, physics, materials science, epidemiology, finance, and so on. Prediction of percolation thresholds with machine learning methods remains challenging. In this paper, we build a powerful graph convolutional neural network to study the percolation in both supervised and unsupervised ways. From a supervised learning perspective, the graph convolutional neural network simultaneously and correctly trains data of different lattice types, such as the square and triangular lattices. For the unsupervised perspective, combining the graph convolutional neural network and the confusion method, the percolation threshold can be obtained by the "W" shaped performance. The finding of this work opens up the possibility of building a more general framework that can probe the percolation-related phenomenon.

cond-mat.stat-mech↗

arXiv2023

Explosive Percolation Obeys Standard Finite-Size Scaling in an Event-based Ensemble

Explosive percolation in the Achlioptas process, which has attracted much research attention, is known to exhibit a rich variety of critical phenomena that are anomalous from the perspective of continuous phase transitions. Hereby, we show that, in an event-based ensemble, the critical behaviors in explosive percolation are rather clean and obey the standard finite-size scaling theory, except for the large fluctuation of pseudo-critical points. In the fluctuation window, multiple fractal structures emerge and the values can be derived from a crossover scaling theory. Further, their mixing effects account well for the previously observed anomalous phenomena. Making use of the clean scaling in the event-based ensemble, we determine with a high precision the critical points and exponents for a number of bond-insertion rules, and clarify ambiguities about their universalities. Our findings hold true for any spatial dimensions.

cond-mat.stat-mech↗

arXiv2023

Geometric properties of the complete-graph Ising model in the loop representation

The exact solution of the Ising model on the complete graph (CG) provides an important, though mean-field, insight for the theory of continuous phase transitions. Besides the original spin, the Ising model can be formulated in the Fortuin-Kasteleyn random-cluster and the loop representation, in which many geometric quantities have no correspondence in the spin representations. Using a lifted-worm irreversible algorithm, we study the CG-Ising model in the loop representation, and, based on theoretical and numerical analyses, obtain a number of exact results including volume fractal dimensions and scaling forms. Moreover, by combining with the Loop-Cluster algorithm, we demonstrate how the loop representation can provide an intuitive understanding to the recently observed rich geometric phenomena in the random-cluster representation, including the emergence of two configuration sectors, two length scales and two scaling windows.

cond-mat.stat-mech↗