arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 127 records · Page 7Linked to original sources

arXiv2020

History-dependent percolation in two dimensions

We study the history-dependent percolation in two dimensions, which evolves in generations from standard bond-percolation configurations through iteratively removing occupied bonds. Extensive simulations are performed for various generations on periodic square lattices up to side length $L=4096$. From finite-size scaling, we find that the model undergoes a continuous phase transition, which, for any finite number of generations, falls into the universality of standard 2D percolation. At the limit of infinite generation, we determine the correlation-length exponent $1/ν=0.828(5)$ and the fractal dimension $d_{\rm f}=1.864\,4(7)$, which are not equal to $1/ν=3/4$ and $d_{\rm f}=91/48$ for 2D percolation. Hence, the transition in the infinite-generation limit falls outside the standard percolation universality and differs from the discontinuous transition of history-dependent percolation on random networks. Further, a crossover phenomenon is observed between the two universalities in infinite and finite generations.

cond-mat.stat-mech↗

arXiv2020

Percolation of the two-dimensional XY model in the flow representation

We simulate the two-dimensional XY model in the flow representation by a worm-type algorithm, up to linear system size $L=4096$, and study the geometric properties of the flow configurations. As the coupling strength $K$ increases, we observe that the system undergoes a percolation transition $K_{\rm perc}$ from a disordered phase consisting of small clusters into an ordered phase containing a giant percolating cluster. Namely, in the low-temperature phase, there exhibits a long-ranged order regarding the flow connectivity, in contrast to the qusi-long-range order associated with spin properties. Near $K_{\rm perc}$, the scaling behavior of geometric observables is well described by the standard finite-size scaling ansatz for a second-order phase transition. The estimated percolation threshold $K_{\rm perc}=1.105 \, 3(4)$ is close to but obviously smaller than the Berezinskii-Kosterlitz-Thouless (BKT) transition point $K_{\rm BKT} = 1.119 \, 3(10)$, which is determined from the magnetic susceptibility and the superfluid density. Various interesting questions arise from these unconventional observations, and their solutions would shed lights on a variety of classical and quantum systems of BKT phase transitions.

cond-mat.stat-mech↗

arXiv2020

Fermionic Sign Structure of High-order Feynman diagrams in a Many-fermion System

The sign cancellation between scattering amplitudes makes fermions different from bosons. We systematically investigate Feynman diagrams' fermionic sign structure in a representative many-fermion system---a uniform Fermi gas with Yukawa interaction. We analyze the role of the crossing symmetry and the global gauge symmetry in the fermionic sign cancellation. The symmetry arguments are then used to identify the sign-canceled groups of diagrams. Sign-structure analysis has two applications. Numerically, it leads to a cluster diagrammatic Monte Carlo algorithm for fast diagram evaluations. The new algorithm is about $10^5$ times faster than the conventional approaches in the sixth order. Furthermore, our analysis provides important hints in constructing the relevant effective field theory for many-fermion systems.

cond-mat.quant-gas↗

arXiv2020

Pseudo-time-reversal-symmetry-protected topological Bogoliubov excitations of Bose-Einstein condensates in optical lattices

Bogoliubov excitations of Bose-Einstein condensates in optical lattices may possess band topology in analogous to topological insulators in class AII of fermions. Using the language of the Krein-space theory, this topological property is shown to be protected by a pseudo-time-reversal symmetry that is pseudo-antiunitary and squares to $-1$, with the associated bulk topological invariant also being a $\mathbb Z_2$ index. We construct three equivalent expressions for it, relating to the Pfaffian, the pseudo-time-reversal polarization, and most practically, the Wannier center flow, all adopted from the fermionic case, defined here with respect to the pseudo inner product. In the presence of an additional pseudo-unitary and pseudo-Hermitian inversion symmetry, a simpler expression is derived. We then study two toy models feasible on cold atom platforms to numerically confirm the bulk-boundary correspondence. The Krein-space approach developed in this work is a universal formalism to study all kinds of symmetry-protected topological bosonic Bogoliubov bands.

cond-mat.quant-gas↗

arXiv2020

Critical polynomials in the nonplanar and continuum percolation models

Exact or precise thresholds have been intensively studied since the introduction of the percolation model. Recently the critical polynomial $P_{\rm B}(p,L)$ was introduced for planar-lattice percolation models, where $p$ is the occupation probability and $L$ is the linear system size. The solution of $P_{\rm B} = 0$ can reproduce all known exact thresholds and leads to unprecedented estimates for thresholds of unsolved planar-lattice models. In two dimensions, assuming the universality of $P_{\rm B}$, we use it to study a nonplanar lattice model, i.e., the equivalent-neighbor lattice bond percolation, and the continuum percolation of identical penetrable disks, by Monte Carlo simulations and finite-size scaling analysis. It is found that, in comparison with other quantities, $P_{\rm B}$ suffers much less from finite-size corrections. As a result, we obtain a series of high-precision thresholds $p_c(z)$ as a function of coordination number $z$ for equivalent-neighbor percolation with $z$ up to O$(10^5)$, and clearly confirm the asymptotic behavior $zp_c-1 \sim 1/\sqrt{z}$ for $z \rightarrow \infty$. For the continuum percolation model, we surprisingly observe that the finite-size correction in $P_{\rm B}$ is unobservable within uncertainty O$(10^{-5})$ as long as $L \geq 3$. The estimated threshold number density of disks is $ρ_c = 1.436 325 05(10)$, slightly below the most recent result $ρ_c = 1.436 325 45(8)$ of Mertens and Moore obtained by other means. Our work suggests that the critical polynomial method can be a powerful tool for studying nonplanar and continuum systems in statistical mechanics.

cond-mat.stat-mech↗

arXiv2020

Finite-size Scaling of O($n$) Systems at the Upper Critical Dimensionality

Logarithmic finite-size scaling of the O($n$) universality class at the upper critical dimensionality ($d_c=4$) has a fundamental role in statistical and condensed-matter physics and important applications in various experimental systems. Here, we address this long-standing problem in the context of the $n$-vector model ($n=1, 2, 3$) on periodic four-dimensional hypercubic lattices. We establish an explicit scaling form for the free energy density, which simultaneously consists of a scaling term for the Gaussian fixed point and another term with multiplicative logarithmic corrections. In particular, we conjecture that the critical two-point correlation $g(r,L)$, with $L$ the linear size, exhibits a two-length behavior: following the behavior $r^{2-d_c}$ governed by Gaussian fixed point at shorter distance and entering a plateau at larger distance whose height decays as $L^{-d_c/2}({\rm ln}L)^{\hat{p}}$ with $\hat{p}=1/2$ a logarithmic correction exponent. Using extensive Monte Carlo simulations, we provide complementary evidence for the predictions through the finite-size scaling of observables including the two-point correlation, the magnetic fluctuations at zero and non-zero Fourier modes, and the Binder cumulant. Our work sheds light on the formulation of logarithmic finite-size scaling and has practical applications in experimental systems.

cond-mat.stat-mech↗

arXiv2020

Worm-algorithm-type Simulation of Quantum Transverse-Field Ising Model

We apply a worm algorithm to simulate the quantum transverse-field Ising model in a path-integral representation of which the expansion basis is taken as the spin component along the external-field direction. In such a representation, a configuration can be regarded as a set of non-intersecting loops constructed by "kinks" for pairwise interactions and spin-down (or -up) imaginary-time segments. The wrapping probability for spin-down loops, a dimensionless quantity characterizing the loop topology on a torus, is observed to exhibit small finite-size corrections and yields a high-precision critical point in two dimensions (2D) as $h_c \! =\! 3.044\, 330(6)$, significantly improving over the existing results and nearly excluding the best one $h_c \! =\! 3.044\, 38 (2)$. At criticality, the fractal dimensions of the loops are estimated as $d_{\ell \downarrow} (1{\rm D}) \! = \! 1.37(1) \! \approx \! 11/8 $ and $d_{\ell \downarrow} (2{\rm D}) \! = \! 1.75 (3)$, consistent with those for the classical 2D and 3D O(1) loop model, respectively. An interesting feature is that in one dimension (1D), both the spin-down and -up loops display the critical behavior in the whole disordered phase ($ 0 \! \leq \! h \! < \! h_c$), having a fractal dimension $d_{\ell} \! = \! 1.750 (7)$ that is consistent with the hull dimension $d_{\rm H} \! = \! 7/4$ for critical 2D percolation clusters. The current worm algorithm can be applied to simulate other quantum systems like hard-core boson models with pairing interactions.

cond-mat.stat-mech↗

arXiv2020

Loop-Cluster Coupling and Algorithm for Classical Statistical Models

Potts spin systems play a fundamental role in statistical mechanics and quantum field theory, and can be studied within the spin, the Fortuin-Kasteleyn (FK) bond or the $q$-flow (loop) representation. We introduce a Loop-Cluster (LC) joint model of bond-occupation variables interacting with $q$-flow variables, and formulate a LC algorithm that is found to be in the same dynamical universality as the celebrated Swendsen-Wang algorithm. This leads to a theoretical unification for all the representations, and numerically, one can apply the most efficient algorithm in one representation and measure physical quantities in others. Moreover, by using the LC scheme, we construct a hierarchy of geometric objects that contain as special cases the $q$-flow clusters and the backbone of FK clusters, the exact values of whose fractal dimensions in two dimensions remain as an open question. Our work not only provides a unified framework and an efficient algorithm for the Potts model, but also brings new insights into rich geometric structures of the FK clusters.

cond-mat.stat-mech↗

arXiv2020

Complete graph and Gaussian fixed point asymptotics in the five-dimensional Fortuin-Kasteleyn Ising model with periodic boundaries

We present an extensive Markov-chain Monte Carlo study of the finite-size scaling behavior of the Fortuin-Kasteleyn Ising model on five-dimensional hypercubic lattices with periodic boundary conditions. We observe that physical quantities, which include the contribution of the largest cluster, exhibit complete graph asymptotics. However, for quantities, where the contribution of the largest cluster is removed, we observe that the scaling behavior is mainly controlled by the Gaussian fixed point. Our results therefore suggest that \textit{both} scaling predictions, i.e. the complete graph \textit{and} the Gaussian fixed point asymptotics, are needed to provide a complete description for the five-dimensional finite-size scaling behavior on the torus.

cond-mat.stat-mech↗

arXiv2020

$N$-cluster correlations in four- and five-dimensional percolation

We study $N$-cluster correlation functions in four- and five-dimensional (4D, 5D) bond percolation by extensive Monte Carlo simulation. We reformulate the transfer Monte Carlo algorithm for percolation [Phys. Rev. E {\bf 72}, 016126 (2005)] using the disjoint-set data structure, and simulate a cylindrical geometry $L^{d-1}\times \infty$, with the linear size up to $L=512$ for 4D and $128$ for 5D. We determine with a high precision all possible $N$-cluster exponents, for $N \! =\!2$ and $3$, and the universal amplitude for a logarithmic correlation function. From the symmetric correlator with $N \! = \!2$, we obtain the correlation-length critical exponent as $1/ν\! =\! 1.4610(12)$ for 4D and $1/ν\! =\! 1.737 (2)$ for 5D, significantly improving over the existing results. Estimates for the other exponents and the universal logarithmic amplitude have not been reported before to our knowledge. Our work demonstrates the validity of logarithmic conformal field theory and adds to the growing knowledge for high-dimensional percolation.

cond-mat.stat-mech↗

arXiv2020

Critical exponents and universal excess cluster number of percolation in four and five dimensions

We study critical bond percolation on periodic four-dimensional (4D) and five-dimensional (5D) hypercubes by Monte Carlo simulations. By classifying the occupied bonds into branches, junctions and non-bridges, we construct the whole, the leaf-free and the bridge-free clusters using the breadth-first-search algorithm. From the geometric properties of these clusters, we determine a set of four critical exponents, including the thermal exponent $y_{\rm t} \equiv 1/ν$, the fractal dimension $d_{\rm f}$, the backbone exponent $d_{\rm B}$ and the shortest-path exponent $d_{\rm min}$. We also obtain an estimate of the excess cluster number $b$ which is a universal quantity related to the finite-size scaling of the total number of clusters. The results are $y_{\rm t} = 1.461(5)$, $d_{\rm f} = 3.044 \, 6(7)$, $d_{\rm B} = 1.984\,4(11)$, $d_{\rm min} = 1.604 \, 2(5)$, $b = 0.62(1)$ for 4D; and $y_{\rm t} = 1.743(10)$, $d_{\rm f} = 3.526\,0(14)$, $d_{\rm B} = 2.022\,6(27)$, $d_{\rm min} = 1.813\, 7(16)$, $b = 0.62(2)$ for 5D. The values of the critical exponents are compatible with or improving over the existing estimates, and those of the excess cluster number $b$ have not been reported before. Together with the existing values in other spatial dimensions $d$, the $d$-dependent behavior of the critical exponents is obtained, and a local maximum of $d_{\rm B}$ is observed near $d \approx 5$. It is suggested that, as expected, critical percolation clusters become more and more dendritic as $d$ increases.

cond-mat.stat-mech↗

arXiv2020

Realization of ideal Weyl semimetal band in ultracold quantum gas with 3D Spin-Orbit coupling

The Weyl semimetals [1-6] are three-dimensional (3D) gapless topological phases with Weyl cones in the bulk band, and host massless quasiparticles known as Weyl fermions which were theorized by Hermann Weyl in the last twenties [7]. The lattice theory constrains that Weyl cones must come in pairs, with the minimal number of cones being two. The semimetal with only two Weyl cones is an ideal Weyl semimetal (IWSM) which is the optimal platform to explore broad Weyl physics but hard to engineer in solids. Here, we report the experimental realization of the IWSM band by synthesising for the first time a 3D spin-orbit (SO) coupling for ultracold atoms. Engineering a 3D configuration-tunable optical Raman lattice [8], we realize the Weyl type SO coupling for ultracold quantum gas, with which the IWSM band is achieved with controllability. The topological Weyl points are clearly measured via the virtual slicing imaging technique [8, 9] in equilibrium, and further resolved in the quench dynamics, revealing the key information of the realized IWSM bands. The realization of the IWSM band opens an avenue to investigate various exotic phenomena based on the optimal Weyl semimetal platforms.

cond-mat.quant-gas↗

arXiv2020

Scaling features in the spreading of COVID-19

Since the outbreak of COVID-19, many data analyses have been done. Some of them are based on the classical epidemiological approach that assumes an exponential growth, but a few studies report that a power-law scaling may provide a better fit to the currently available data. Hereby, we examine the data in China (01/20/2020--02/24/2020), and indeed find that the growth closely follows a power-law kinetics over a significantly wide time period. The exponents are $2.48(20)$, $2.21(6)$ and $4.26(12)$ for the number of confirmed infections, deaths and cured cases, respectively, indicating an underlying small-world network structure in the pandemic. While no obvious deviations from the power-law growth can be seen yet for the number of deaths and cured cases, negative deviations have clearly appeared in the number of infections, particularly that for the region outside Hubei. This suggests the beginning of the slowing-down of the virus spreading due to the huge containment effort. Meanwhile, we find that despite the dramatic difference in magnitudes, the growth kinetics of the infection number exhibits much similarity for Hubei province and the region outside Hubei. On this basis, in log-log plot, we rescale the infection number for the region outside Hubei such that it overlaps as much as possible with the total infection number in China, from which an approximate extrapolation yields the maximum of the pandemic around March 3, 2020, with the number of infections about $83,000$. Further, by analyzing the kinetics of the mortality in log-log scale, we obtains a rough estimate that near March 3, the death rate of COVID-19 would be about $4.7\%\thicksim 5.0\%$ for Hubei province and $0.7\%\thicksim1.0\%$ for the region outside Hubei. We emphasize that our predictions may be quantitatively unreliable, since the data analysis is purely empirical and various assumptions are used.

physics.soc-ph↗

arXiv2020

History-dependent percolation on multiplex networks

The structure of interconnected systems and its impact on the system dynamics is a much-studied cross-disciplinary topic. Although various critical phenomena have been found in different models, the study on the connections between different percolation transitions is still lacking. Here we propose a unified framework to study the origins of the discontinuous transitions of the percolation process on interacting networks. The model evolves in generations with the result of the present percolation depending on the previous state and thus is history-dependent. Both theoretical analysis and Monte Carlo simulations reveal that the nature of the transition remains the same at finite generations but exhibits an abrupt change for the infinite generation. We use brain functional correlation and morphological similarity data to show that our model also provides a general method to explore the network structure and can contribute to many practical applications, such as detecting the abnormal structures of human brain networks.

cond-mat.stat-mech↗

arXiv2020

Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model

The ground state of the Hubbard model with nearest-neighbor hopping on the square lattice at half filling is known to be that of an antiferromagnetic (AFM) band insulator for any on-site repulsion. At finite temperature, the absence of long-range order makes the question of how the interaction-driven insulator is realized nontrivial. We address this problem with controlled accuracy in the thermodynamic limit using self-energy diagrammatic determinant Monte Carlo and dynamical cluster approximation methods and show that development of long-range AFM correlations drives an extended crossover from Fermi liquid to insulating behavior in the parameter regime that precludes a metal-to-insulator transition. The intermediate crossover state is best described as a non-Fermi liquid with a partially gapped Fermi surface.

cond-mat.str-el↗

arXiv2020

Oscillatory-like Expansion of a Fermionic Superfluid

We study the expansion behaviours of a Fermionic superfluid in a cigar-shaped optical dipole trap for the whole BEC-BCS crossover and various temperatures. At low temperature ($0.06(1) T_F$), the atom cloud undergoes an anisotropic hydrodynamic expansion over 30~ms, which behaves like oscillation in the horizontal plane. By analyzing the expansion dynamics according to the superfluid hydrodynamic equation, the effective polytropic index $\barγ$ of Equation-of-State of Fermionic superfluid is extracted. The $\barγ$ values show a non-monotonic behavior over the BEC-BCS crossover, and have a good agreement with the theoretical results in the unitarity and BEC side. The normalized quasi-frequencies of the oscillatory expansion are measured, which drop significantly from the BEC side to the BCS side and reach a minimum value of 1.73 around $1/k_Fa=-0.25$. Our work improves the understanding of the dynamic properties of strongly interacting Fermi gas.

cond-mat.quant-gas↗

arXiv2019

Evidences for interaction-induced Haldane fractional exclusion statistics in one and higher dimensions

Haldane fractional exclusion statistics (FES) has a long history of intense studies, but its realization in physical systems is rare. Here we study repulsively interacting Bose gases at and near a quantum critical point, and find evidences that such strongly correlated gases obey simple non-mutual FES over a wide range of interaction strengths in both one and two dimensions. Based on exact solutions in one dimension, quantum Monte Carlo simulations and experiments in both dimensions, we show that the thermodynamic properties of these interacting gases, including entropy per particle, density and pressure, are essentially equivalent to those of non-interacting particles with FES. Accordingly, we establish a simple interaction-to-FES mapping that reveals the statistical nature of particle-hole symmetry breaking induced by interaction in such quantum many-body systems. Whereas strongly interacting Bose gases reach full fermionization in one dimension, they exhibit incomplete fermionization in two dimensions. Our results open a route to understanding correlated interacting systems via non-interacting particles with FES in arbitrary dimensions.

cond-mat.quant-gas↗

arXiv2019

Clock Monte Carlo methods

We propose the clock Monte Carlo technique for sampling each successive chain step in constant time. It is built on a recently proposed factorized transition filter and its core features include its O(1) computational complexity and its generality. We elaborate how it leads to the clock factorized Metropolis (clock FMet) method, and discuss its application in other update schemes. By grouping interaction terms into boxes of tunable sizes, we further formulate a variant of the clock FMet algorithm, with the limiting case of a single box reducing to the standard Metropolis method. A theoretical analysis shows that an overall acceleration of ${\rm O}(N^κ)$ ($0 \! \leq \! κ\! \leq \! 1$) can be achieved compared to the Metropolis method, where $N$ is the system size and the $κ$ value depends on the nature of the energy extensivity. As a systematic test, we simulate long-range O$(n)$ spin models in a wide parameter regime: for $n \! = \! 1,2,3$, with disordered algebraically decaying or oscillatory Ruderman-Kittel-Kasuya-Yoshida-type interactions and with and without external fields, and in spatial dimensions from $d \! = \! 1, 2, 3$ to mean-field. The O(1) computational complexity is demonstrated, and the expected acceleration is confirmed. Its flexibility and its independence from the interaction range guarantee that the clock method would find decisive applications in systems with many interaction terms.

cond-mat.stat-mech↗