arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 145 records · Page 8Linked to original sources

arXiv2019

High-precision Monte Carlo study of several models in the three-dimensional U(1) universality class

We present a worm-type Monte Carlo study of several typical models in the three-dimensional (3D) U(1) universality class, which include the classical 3D XY model in the directed flow representation and its Villain version, as well as the 2D quantum Bose-Hubbard (BH) model with unitary filling in the imaginary-time world-line representation. From the topology of the configurations on a torus, we sample the superfluid stiffness $ρ_s$ and the dimensionless wrapping probability $R$. From the finite-size scaling analyses of $ρ_s$ and of $R$, we determine the critical points as $T_c ({\rm XY}) =2.201\, 844 \,1(5)$ and $T_c ({\rm Villain})=0.333\, 067\, 04(7)$ and $(t/U)_c ({\rm BH})=0.059 \, 729 \,1(8)$, where $T$ is the temperature for the classical models, and $t$ and $U$ are respectively the hopping and on-site interaction strength for the BH model. The precision of our estimates improves significantly over that of the existing results. Moreover, it is observed that at criticality, the derivative of a wrapping probability with respect to $T$ suffers from negligible leading corrections and enables a precise determination of the correlation length critical exponent as $ν=0.671 \, 83(18)$. In addition, the critical exponent $η$ is estimated as $η=0.038 \, 53(48)$ by analyzing a susceptibility-like quantity. We believe that these numerical results would provide a solid reference in the study of classical and quantum phase transitions in the 3D U(1) universality, including the recent development of the conformal bootstrap method.

cond-mat.stat-mech↗

arXiv2019

The length of self-avoiding walks on the complete graph

We study the variable-length ensemble of self-avoiding walks on the complete graph. We obtain the leading order asymptotics of the mean and variance of the walk length, as the number of vertices goes to infinity. Central limit theorems for the walk length are also established, in various regimes of fugacity. Particular attention is given to sequences of fugacities that converge to the critical point, and the effect of the rate of convergence of these fugacity sequences on the limiting walk length is studied in detail. Physically, this corresponds to studying the asymptotic walk length on a general class of pseudocritical points.

math-ph↗

arXiv2018

Geometric properties of the Fortuin-Kasteleyn representation of the Ising model

We present a Monte Carlo study of the Fortuin-Kasteleyn (FK) clusters of the Ising model on the square (2D) and simple-cubic (3D) lattices. The wrapping probability, a dimensionless quantity characterizing the topology of the FK clusters on a torus, is found to suffer from smaller finite-size corrections than the well-known Binder ratio, and yields a high-precision critical coupling as $K_c(3\rm D)=0.221\,654\,631(8)$. We then study geometric properties of the FK clusters at criticality. It is demonstrated that the distribution of the critical largest-cluster size $C_1$ follows a single-variable function as $P(C_1,L){\rm d}C_1=\tilde P(x){\rm d}x$ with $x\equiv C_1/L^{d_{\rm F}}$ ($L$ is the linear size), and that the fractal dimension $d_{\rm F}$ is identical to the magnetic exponent. An interesting bimodal feature is observed in distribution $\tilde P(x)$ in 3D, and attributed to the different approaching behaviors for $K \to K_c+0^\pm$. For a critical FK configuration, the cluster number per site $n(s,L)$ of size $s$ is confirmed to obey the standard scaling form $n(s,L)\sim s^{-τ}\tilde n(s/L^{d_{\rm F}})$, with hyper-scaling relation $τ=1+d/d_{\rm F}$ and the spatial dimension $d$. To further characterize the compactness of the FK clusters, we measure their graph distances and determine the shortest-path exponents as $d_{\rm min}(3\rm D)=1.259\,4(2)$ and $d_{\rm min}(2\rm D)=1.094\,0(3)$. Further, by excluding all the bridges from the occupied bonds, we obtain bridge-free configurations and determine the backbone exponents as $d_{\rm B}(3\rm D)=2.167\,3(15)$ and $d_{\rm B}(2\rm D)=1.732\,1(4)$. The estimates of the universal wrapping probabilities for the 3D Ising model and of the geometric critical exponents $d_{\rm min}$ and $d_{\rm B}$ either improve over the existing results or have not been reported yet.

cond-mat.stat-mech↗

arXiv2018

High Controllable and Robust 2D Spin-Orbit Coupling for Quantum Gases

We report the realization of a robust and highly controllable two-dimensional (2D) spin-orbit (SO) coupling with topological non-trivial band structure. By applying a retro-reflected 2D optical lattice, phase tunable Raman couplings are formed into the anti-symmetric Raman lattice structure, and generate the 2D SO coupling with precise inversion and $C_4$ symmetries, leading to considerably enlarged topological regions. The life time of the 2D SO coupled Bose-Einstein condensate reaches several seconds, which enables the exploring of fine tuning interaction effects. These essential advantages of the present new realization open the door to explore exotic quantum many-body effects and non-equilibrium dynamics with novel topology.

cond-mat.quant-gas↗

arXiv2018

Random-length Random Walks and Finite-size scaling in high dimensions

We address a long-standing debate regarding the finite-size scaling of the Ising model in high dimensions, by introducing a random-length random walk model, which we then study rigorously. We prove that this model exhibits the same universal FSS behaviour previously conjectured for the self-avoiding walk and Ising model on finite boxes in high-dimensional lattices. Our results show that the mean walk length of the random walk model controls the scaling behaviour of the corresponding Green's function. We numerically demonstrate the universality of our rigorous findings by extensive Monte Carlo simulations of the Ising model and self-avoiding walk on five-dimensional hypercubic lattices with free and periodic boundaries.

cond-mat.stat-mech↗

arXiv2018

Observation of non-scalar and logarithmic correlations in 2D and 3D percolation

Percolation, a paradigmatic geometric system in various branches of physical sciences, is known to possess logarithmic factors in its correlators. Starting from its definition, as the $Q\rightarrow1$ limit of the $Q$-state Potts model with $S_Q$ symmetry, in terms of geometrical clusters, its operator content as $N$-cluster observables has been classified. We extensively simulate critical bond percolation in two and three dimensions and determine with high precision the $N$-cluster exponents and non-scalar features up to $N \! =\! 4$ (2D) and $N \! =\! 3$ (3D). The results are in excellent agreement with the predicted exact values in 2D, while such families of critical exponents have not been reported in 3D, to our knowledge. Finally, we demonstrate the validity of predictions about the logarithmic structure between the energy and two-cluster operators in 3D.

cond-mat.stat-mech↗

arXiv2018

Uncover Topology by Quantum Quench Dynamics

Topological quantum states are characterized by nonlocal invariants, and their detection is intrinsically challenging. Various strategies have been developed to study topological Hamiltonians through their equilibrium states. We present a fundamentally new, high-precision dynamical approach, revealing topology through the unitary evolution after a quench from a topological trivial initial state with a two-dimensional Chern band realized in an ultracold $^{87}$Rb atom gas. The emerging ring structure in the spin dynamics uniquely determines the Chern number for the post-quench band and enables probing the full phase diagram of the band topology with high precision. Besides, we also measure the topological band gap and the domain wall structure dynamically formed in the momentum space during the long-term evolution. Our dynamical approach provides a way towards observing a universal bulk-ring correspondence, and has broad applications in exploring topological quantum matter.

cond-mat.quant-gas↗

arXiv2018

Equivalent-neighbor percolation models in two dimensions: crossover between mean-field and short-range behavior

We investigate the influence of the range of interactions in the two-dimensional bond percolation model, by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges, as expressed by the number $z$ of equivalent neighbors. We also consider the $z \to \infty$ limit, i.e., the complete graph case, where percolation bonds are allowed between each pair of sites, and the model becomes mean-field-like. All investigated models with finite $z$ are found to belong to the short-range universality class. There is no evidence of a tricritical point separating the short-range and long-range behavior, such as is known to occur for $q=3$ and $q=4$ Potts models. We determine the renormalization exponent describing a finite-range perturbation at the mean-field limit as $y_r \approx 2/3$. Its relevance confirms the continuous crossover from mean-field percolation universality to short-range percolation universality. For finite interaction ranges, we find approximate relations between the coordination numbers and the amplitudes of the leading correction terms as found in the finite-size scaling analysis.

cond-mat.stat-mech↗

arXiv2018

The three-state Potts antiferromagnet on plane quadrangulations

We study the antiferromagnetic 3-state Potts model on general (periodic) plane quadrangulations $Γ$. Any quadrangulation can be built from a dual pair $(G,G^*)$. Based on the duality properties of $G$, we propose a new criterion to predict the phase diagram of this model. If $Γ$ is of self-dual type (i.e., if $G$ is isomorphic to its dual $G^*$), the model has a zero-temperature critical point with central charge $c=1$, and it is disordered at all positive temperatures. If $Γ$ is of non-self-dual type (i.e., if $G$ is not isomorphic to $G^*$), three ordered phases coexist at low temperature, and the model is disordered at high temperature. In addition, there is a finite-temperature critical point (separating these two phases) which belongs to the universality class of the ferromagnetic 3-state Potts model with central charge $c=4/5$. We have checked these conjectures by studying four (resp. seven) quadrangulations of self-dual (resp. non-self-dual) type, and using three complementary high-precision techniques: Monte-Carlo simulations, transfer matrices, and critical polynomials. In all cases, we find agreement with the conjecture. We have also found that the Wang-Swendsen-Kotecky Monte Carlo algorithm does not have (resp. does have) critical slowing down at the corresponding critical point on quadrangulations of self-dual (resp. non-self-dual) type.

cond-mat.stat-mech↗

arXiv2018

The halon: a quasiparticle featuring critical charge fractionalization

The halon is a special critical state of an impurity in a quantum-critical environment. The hallmark of the halon physics is that a well-defined integer charge gets fractionalized into two parts: a microscopic core with half-integer charge and a critically large halo carrying a complementary charge of $\pm 1/2$. The halon phenomenon emerges when the impurity--environment interaction is fine-tuned to the vicinity of a boundary quantum critical point (BQCP), at which the energies of two quasiparticle states with adjacent integer charges approach each other. The universality class of such BQCP is captured by a model of pseudo-spin-$1/2$ impurity coupled to the quantum-critical environment, in such a way that the rotational symmetry in the pseudo-spin $xy$-plane is respected, with a small local "magnetic" field along the pseudo-spin $z$-axis playing the role of control parameter driving the system away from the BQCP. On the approach to BQCP, the half-integer projection of the pseudo-spin on its $z$-axis gets delocalized into a halo of critically divergent radius, capturing the essence of the phenomenon of charge fractionalization. With large-scale Monte Carlo simulations, we confirm the existence of halons---and quantify their universal features---in O(2) and O(3) quantum critical systems.

cond-mat.quant-gas↗

arXiv2018

Extended Coulomb liquid of paired hardcore boson model on a pyrochlore lattice

There is a growing interest in the $U(1)$ Coulomb liquid in both quantum materials in pyrochlore ice and cluster Mott insulators and cold atom systems. We explore a paired hardcore boson model on a pyrochlore lattice. This model is equivalent to the XYZ spin model that was proposed for rare-earth pyrochlores with "dipole-octupole" doublets. Since this model has no sign problem for quantum Monte Carlo (QMC) simulations in a large parameter regime, we carry out both analytical and QMC calculations. We find that the $U(1)$ Coulomb liquid is quite stable and spans a rather large portion of the phase diagram with boson pairing. Moreover, we numerically find thermodynamic evidence that the boson pairing could induce a possible $\mathbb{Z}_2$ liquid in the vicinity of the phase boundary between Coulomb liquid and $\mathbb{Z}_2$ symmetry-broken phase. Besides the materials' relevance with quantum spin ice, we point to quantum simulation with cold atoms on optical lattices.

cond-mat.str-el↗

arXiv2018

Overlap of two topological phases in the antiferromagnetic Potts model

By controlling the vortex core energy, the three-state ferromagnetic Potts model can exhibit two types of topological paradigms, including the quasi-long-range ordered phase and the vortex lattice phase [PRL 116, 097206 (2016)]. Here, by Monte Carlo simulations using an effective worm algorithm, we show that by controlling the vortex core energy, the antiferromagnetic Potts model can also exhibit the two topological phases, more interestingly, the two topological phases can overlap with each other.

cond-mat.stat-mech↗

arXiv2018

The elastic and directed percolation backbone

We argue that the elastic backbone (EB) (union of shortest paths) on a cylindrical system, recently studied by Sampaio Filho et al. [Phys. Rev. Lett. 120, 175701 (2018)], is in fact the backbone of two-dimensional directed percolation (DP). We simulate the EB on the same system as considered by these authors, and also study the DP backbone directly using an algorithm that allows backbones to be generated in a completely periodic manner. We find that both the EB in the bulk and the DP backbone have a fractal dimension of $d_{b} = d_{B,\rm DP} = 1.681\,02(15)$ at the identical critical point $p_{c,\rm{DP}} \approx 0.705\,485\,22$. We also measure the fractal dimension at the edge of the EB system and for the full DP clusters, and find $d_e = d_{\rm DP} = 1.840 \, 54 (4)$. We argue that those two fractal dimensions follow from the DP exponents as $d_{B,\rm DP} = 2-2β/ν_\parallel = 1.681 \, 07 2 (12) $ and $d_{\rm DP} = 2-β/ν_\parallel = 1.840\, 536 (6)$. Our fractal dimensions differ from the value 1.750(3) found by Sampaio Filho et al., whose value may represent a crossover effect.

cond-mat.dis-nn↗

arXiv2018

Duality and the universality class of the three-state Potts antiferromagnet on plane quadrangulations

We provide a new criterion based on graph duality to predict whether the 3-state Potts antiferromagnet on a plane quadrangulation has a zero- or finite-temperature critical point, and its universality class. The former case occurs for quadrangulations of self-dual type, and the zero-temperature critical point has central charge $c=1$. The latter case occurs for quadrangulations of non-self-dual type, and the critical point belongs to the universality class of the 3-state Potts ferromagnet. We have tested this criterion against high-precision computations on four lattices of each type, with very good agreement. We have also found that the Wang-Swendsen-Kotecký algorithm has no critical slowing-down in the former case, and critical slowing-down in the latter.

cond-mat.stat-mech↗

arXiv2018

Dynamics of Topological Excitations in a Model Quantum Spin Ice

We study the quantum spin dynamics of a frustrated XXZ model on a pyrochlore lattice by using large-scale quantum Monte Carlo simulation and stochastic analytic continuation. In the low-temperature quantum spin ice regime, we observe signatures of coherent photon and spinon excitations in the dynamic spin structure factor. As the temperature rises to the classical spin ice regime, the photon disappears from the dynamic spin structure factor, whereas the dynamics of the spinon remain coherent in a broad temperature window. Our results provide experimentally relevant, quantitative information for the ongoing pursuit of quantum spin ice materials.

cond-mat.str-el↗

arXiv2017

Frustrated superfluids in a non-Abelian flux

We study possible superfluid states of the Rashba spin-orbit coupled (SOC) spinor bosons with the spin anisotropic interaction $ λ$ hopping in a square lattice. The frustrations from the non-abelian flux due to the SOC leads to novel spin-bond correlated superfluids. By using a recently developed systematic "order from quantum disorder" analysis, we not only determine the true quantum ground state, but also evaluate the mass gap in the spin sector at $ λ< 1 $, especially compute the the excitation spectrum of the Goldstone mode in the spin sector at $ λ=1 $ which would be quadratic without the analysis. The analysis also leads to different critical exponents on the two sides of the 2nd order transition driven by a roton touchdown at $ λ=1 $. The intimate analogy at $ λ=1 $ with the charge neutral Goldstone mode in the pseudo-spin sector in the Bilayer quantum Hall systems at the total filling factor $ ν_T=1 $ are stressed. The experimental implications and detections of these novel phenomena in cold atoms loaded on a optical lattice are presented.

cond-mat.quant-gas↗

arXiv2017

Symmetry protected bosonic topological phase transitions: Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice

We study possible many body phenomena in the Quantum Anomalous Hall system of weakly interacting spinor bosons in a square lattice. There are various novel spin-bond correlated superfluids (SF) and quantum or topological phase transitions among these SF phases. One transition is a first order one driven by roton droppings ( but with non-zero gaps $ Δ_R $ ) tuned by the Zeeman field $ h $. Another is a second order bosonic Lifshitz transition with the dynamic exponents $ z_x=z_y=2 $ and an accompanying $ [C_4 \times C_4]_D $ symmetry breaking. It is driven by the softening of the superfluid Goldstone mode tuned by the ratio of spin-orbit coupled (SOC) strength over the hopping strength. The two phase boundaries meet at a topological tri-critical (TT) point which separates the $ h=0 $ line into two SF phases with $ N=2 $ and $ N=4 $ condensation momenta respectively. At the $ h=0 $ line where the system has an anti-unitary $ Z_2 $ Reflection symmetry, there are infinite number of classically degenerate family of states on both sides. We perform a systematic order from quantum disorder analysis to find the quantum ground states, also calculate the roton gaps $ Δ_R $ generated by the order from disorder mechanism on both sides of the TT point. The $ N=2 $ and $ N=4 $ SF phases have the same spin-orbital XY-AFM spin structure, respect the anti-unitary symmetry and break the $ [C_4 \times C_4]_D $ symmetry, so they be distinguished only by the different topology of the BEC condensation momenta instead of by any differences in the symmetry breaking patterns. All these novel quantum or topological phenomena can be probed in the recent experimentally realized weakly interacting Quantum Anomalous Hall (QAH) model of $ ^87 Rb $ by Wu, {\sl et.al}, Science 354, 83-88 (2016).

cond-mat.quant-gas↗

arXiv2017

Lifted Worm Algorithm for the Ising Model

We design an irreversible worm algorithm for the zero-field ferromagnetic Ising model by using the lifting technique. We study the dynamic critical behavior of an energy estimator on both the complete graph and toroidal grids, and compare our findings with reversible algorithms such as the Prokof'ev-Svistunov worm algorithm. Our results show that the lifted worm algorithm improves the dynamic exponent of the energy estimator on the complete graph, and leads to a significant constant improvement on toroidal grids.

cond-mat.stat-mech↗