arXiv subjects

Youjin Deng

Publications and source records attributed to Youjin Deng.

At least 163 records · Page 9Linked to original sources

arXiv2017

Dirac, Rashba and Weyl type spin-orbit couplings: toward experimental realization in ultracold atoms

We propose a hierarchy set of minimal optical Raman lattice schemes toward the experimental realization of spin-orbit (SO) couplings of various types for ultracold atoms, including two-dimensional (2D) Dirac type of $C_4$ symmetry, 2D Rashba and 3D Weyl types. These schemes are well accessible with current cold-atom technology, and in particular, a long-lived Bose-Einstein condensation of the 2D Dirac SO coupling has been experimentally proved. The generation of 2D Rashba and 3D Weyl types has an exquisite request that two sources of laser beams have distinct frequencies of factor-two difference. Surprisingly, we find that $^{133}$Cs atoms provide an ideal candidate for the realization. A common and essential feature is the absence of any fine-tuning and phase-locking in the realization, and the resulted SO coupled ultracold atoms have a long lifetime. These schemes essentially improve over the current experimental accessibility and controllability, and open new experimental platforms to study high-dimensional SO physics and novel topological phases with ultracold atoms.

cond-mat.mes-hall↗

arXiv2017

Magnetic Correlations in the Two-dimensional Repulsive Fermi Hubbard Model

The repulsive Fermi Hubbard model on the square lattice has a rich phase diagram near half-filling (corresponding to the particle density per lattice site $n=1$): for $n=1$ the ground state is an antiferromagnetic insulator, at $0.6 < n \lesssim 0.8$, it is a $d_{x^2-y^2}$-wave superfluid (at least for moderately strong interactions $U \lesssim 4t$ in terms of the hopping $t$), and the region $1-n \ll 1$ is most likely subject to phase separation. Much of this physics is preempted at finite temperatures and to an extent driven by strong magnetic fluctuations, their quantitative characteristics and how they change with the doping level being much less understood. Experiments on ultra-cold atoms have recently gained access to this interesting fluctuation regime, which is now under extensive investigation. In this work we employ a self-consistent skeleton diagrammatic approach to quantify the characteristic temperature scale $T_{M}(n)$ for the onset of magnetic fluctuations with a large correlation length and identify their nature. Our results suggest that the strongest fluctuations---and hence highest $T_{M}$ and easiest experimental access to this regime---are observed at $U/t \approx 4-6$.

cond-mat.str-el↗

arXiv2017

Critical percolation clusters in seven dimensions and on a complete graph

We study critical bond percolation on a seven-dimensional (7D) hypercubic lattice with periodic boundary conditions and on the complete graph (CG) of finite volume $V$. We numerically confirm that for both cases, the critical number density $n(s,V)$ of clusters of size $s$ obeys a scaling form $n(s,V) \sim s^{-τ} \tilde{n} (s/V^{d^*_{\rm f}})$ with identical volume fractal dimension $d^*_{\rm f}=2/3$ and exponent $τ= 1+1/d^*_{\rm f}=5/2$. We then classify occupied bonds into {\em bridge} bonds, which includes {\em branch} and {\em junction} bonds, and {\em non-bridge} bonds; a bridge bond is a branch bond if and only if its deletion produces at least one tree. Deleting branch bonds from percolation configurations produces {\em leaf-free} configurations, whereas, deleting all bridge bonds leads to {\em bridge-free} configurations. It is shown that the fraction of non-bridge (bi-connected) bonds vanishes $ρ_{\rm n, CG}$$\rightarrow$0 for large CGs, but converges to a finite value $ ρ_{\rm n, 7D} =0.006 \, 193 \, 1(7)$ for the 7D hypercube. Further, we observe that while the bridge-free dimension $d^*_{\rm bf}=1/3$ holds for both the CG and 7D cases, the volume fractal dimensions of the leaf-free clusters are different: $d^*_{\rm \ell f, 7D} = 0.669 (9) \approx 2/3$ and $d^*_{\rm \ell f, CG} = 0. 333 7 (17) \approx 1/3$. We also study the behavior of the number and the size distribution of leaf-free and bridge-free clusters. For the number of clusters, we numerically find the number of leaf-free and bridge-free clusters on the CG scale as $\sim \ln V$, while for 7D they scale as $\sim V$. Our work demonstrates that the geometric structure of high-dimensional percolation clusters cannot be fully accounted for by their complete-graph counterparts.

cond-mat.stat-mech↗

arXiv2017

Coupled Dipole Oscillations of a Mass-Imbalanced Bose and Fermi Superfluid Mixture

Recent experimental realizations of superfluid mixtures of Bose and Fermi quantum gases provide a unique platform for exploring diverse superfluid phenomena. We study dipole oscillations of a double superfluid in a cigar-shaped optical dipole trap, consisting of $^{41}$K and $^{6}$Li atoms with a large mass imbalance, where the oscillations of the bosonic and fermionic components are coupled via the Bose-Fermi interaction. In our high-precision measurements, the frequencies of both components are observed to be shifted from the single-species ones, and exhibit unusual features. The frequency shifts of the $^{41}$K component are upward (downward) in the radial (axial) direction, whereas the $^{6}$Li component has down-shifted frequencies in both directions. Most strikingly, as the interaction strength is varied, the frequency shifts display a resonant-like behavior in both directions, for both species, and around a similar location at the BCS side of fermionic superfluid. These rich phenomena challenge theoretical understanding of superfluids.

cond-mat.quant-gas↗

arXiv2017

Geometric explanation of anomalous finite-size scaling in high dimensions

We give an intuitive geometric explanation for the apparent breakdown of standard finite-size scaling in systems with periodic boundaries above the upper critical dimension. The Ising model and self-avoiding walk are simulated on five-dimensional hypercubic lattices with free and periodic boundary conditions, by using geometric representations and recently introduced Markov-chain Monte Carlo algorithms. We show that previously observed anomalous behaviour for correlation functions, measured on the standard Euclidean scale, can be removed by defining correlation functions on a scale which correctly accounts for windings.

cond-mat.stat-mech↗

arXiv2017

Monte Carlo simulation of quantum Potts model

Using Monte Carlo simulations in the frame of stochastic series expansion (SSE), we study the three-state quantum Potts model. The cluster algorithm we used is a direct generalization of that for the quantum Ising model. The simulations include the one dimensional and two dimensional ferromagnetic three-state quantum Potts model and the two dimensional antiferromagnetic three-state quantum Potts model. Our results show that the phase transition of the one dimensional ferromagnetic quantum Potts model belongs to the same universality class of the two dimensional classical Potts model, the two dimensional ferromagnetic quantum Potts model undergoes a first order transition, which is also in analogy to its classical correspondence. The phase transition of the antiferromagnetic quantum Potts model is continuous, whose universality class belongs to the three-dimensional classical XY model, owing to an `emergent' O(2) symmetry at the critical point, although its ordered phase breaks the Z_6 symmetry.

cond-mat.stat-mech↗

arXiv2017

Irreversible Markov chain Monte Carlo algorithm for self-avoiding walk

We formulate an irreversible Markov chain Monte Carlo algorithm for the self-avoiding walk (SAW), which violates the detailed balance condition and satisfies the balance condition. Its performance improves significantly compared to that of the Berretti-Sokal algorithm, which is a variant of the Metropolis-Hastings method. The gained efficiency increases with the spatial dimension (D), from approximately $10$ times in 2D to approximately $40$ times in 5D. We simulate the SAW on a 5D hypercubic lattice with periodic boundary conditions, for a system with a linear size up to $L=128$, and confirm that as for the 5D Ising model, the finite-size scaling of the SAW is governed by renormalized exponents $ν^*=2/d$ and $γ/ν^*=d/2$. The critical point is determined, which is approximately $8$ times more precise than the best available estimate.

cond-mat.stat-mech↗

arXiv2016

Equivalent-neighbor Potts models in two dimensions

We investigate the two-dimensional $q=3$ and 4 Potts models with a variable interaction range by means of Monte Carlo simulations. We locate the phase transitions for several interaction ranges as expressed by the number $z$ of equivalent neighbors. For not too large $z$, the transitions fit well in the universality classes of the short-range Potts models. However, at longer ranges the transitions become discontinuous. For $q=3$ we locate a tricritical point separating the continuous and discontinuous transitions near $z=80$, and a critical fixed point between $z=8$ and 12. For $q=4$ the transition becomes discontinuous for $z > 16$. The scaling behavior of the $q=4$ model with $z=16$ approximates that of the $q=4$ merged critical-tricritical fixed point predicted by the renormalization scenario.

cond-mat.stat-mech↗

arXiv2016

Emergent O(n) Symmetry in a series of three-dimensional Potts Models

We study the q-state Potts model on the simple cubic lattice with ferromagnetic interactions in one lattice direction, and antiferromagnetic interactions in the two other directions. As the temperature T decreases, the system undergoes a second-order phase transition that fits in the universality class of the 3D O(n) model with n=q-1. This conclusion is based on the estimated critical exponents, and histograms of the order parameter. At even smaller T we find, for q=4 and 5, a first-order transition to a phase with a different type of long-range order. This long-range order dissolves at T=0, and the system effectively reduces to a disordered two-dimensional Potts antiferromagnet. These results are obtained by means of Monte Carlo simulations and finite-size scaling.

cond-mat.stat-mech↗

arXiv2016

Trapping Centers at the Superfluid-Mott-insulator Criticality: Transition between Charge-quantized States

Under the conditions of superfluid-Mott-insulator criticality in two dimensions, the trapping centers--i.e., local potential wells and bumps--are generically characterized by an integer charge corresponding to the number of trapped particles (if positive) or holes (if negative). Varying the strength of the center leads to a transition between two competing ground states with charges differing by $\pm 1$. The hallmark of the transition scenario is a splitting of the number density distortion, $δn(r)$, into a half-integer core and a large halo carrying the complementary charge of $\pm 1/2$. The sign of the halo changes across the transition and the radius of the halo, $r_0$, diverges on the approach to the critical strength of the center, $V = V_c$, by the law $r_0 \propto |V-V_c|^{-\tildeν}$, with $\tildeν \approx 2.33(5)$.

cond-mat.quant-gas↗

arXiv2016

Observation of two-species vortex lattices in a mixture of mass-imbalance Bose and Fermi superfluids

The superfluid mixture of interacting Bose and Fermi species is a remarkable many-body quantum system. Dilute degenerate atomic gases, especially for two species of distinct masses, are excellent candidates for exploring fundamental features of superfluid mixture. However, producing a mass-imbalance Bose-Fermi superfluid mixture, providing an unambiguous visual proof of two-species superfluidity and probing inter-species interaction effects remain challenging. Here, we report the realization of a two-species superfluid of lithium-6 and potassium-41. By rotating the dilute gases, we observe the simultaneous existence of vortex lattices in both species, and thus present a definitive visual evidence for the simultaneous superfluidity of the two species. Pronounced effects of the inter-species interaction are demonstrated through a series of precision measurements on the formation and decay of two-species vortices. Our system provides a new platform for studying novel macroscopic quantum phenomena in vortex matter of interacting species.

cond-mat.quant-gas↗

arXiv2016

No-enclave percolation corresponds to holes in the cluster backbone

The no-enclave percolation (NEP) model introduced recently by Sheinman et al. can be mapped to a problem of holes within a standard percolation backbone, and numerical measurements of these holes gives the size-distribution exponent $τ= 1.82(1)$ of the NEP model. An argument is given that $τ=1 + d_B/2 \approx 1.822$ where $d_B$ is the backbone dimension. On the other hand, a model of simple holes within a percolation cluster implies $τ= 1 + d_f/2 = 187/96 \approx 1.948$, where $d_f$ is the fractal dimension of the cluster, and this value is consistent with Sheinman et al.'s experimental results of gel collapse which gives $τ= 1.91(6)$. Both models yield a discontinuous maximum hole size at $p_c$, signifying explosive percolation behavior. At $p_c$, the largest hole fills exactly half the system, due to symmetry. Extensive numerical simulations confirm our results.

cond-mat.dis-nn↗

arXiv2016

Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice

We study the low-temperature physics of the $SU(2)$-symmetric spin-$1/2$ Heisenberg antiferromagnet on a pyrochlore lattice and find fingerprint evidence for the thermal spin-ice state in this frustrated quantum magnet. Our conclusions are based on the results of bold diagrammatic Monte Carlo simulations, with good convergence of the skeleton series down to the temperature $T/J=1/6$. The identification of the spin-ice state is done through a remarkably accurate microscopic correspondence for the static structure factor between the quantum Heisenberg, classical Heisenberg, and Ising models at all accessible temperatures, and the characteristic bowtie pattern with pinch points observed at $T/J=1/6$. The dynamic structure factor at real frequencies (obtained by the analytic continuation of numerical data) is consistent with diffusive spinon dynamics at the pinch points.

cond-mat.str-el↗

arXiv2015

Solutions of the Two Dimensional Hubbard Model: Benchmarks and Results from a Wide Range of Numerical Algorithms

Numerical results for ground state and excited state properties (energies, double occupancies, and Matsubara-axis self energies) of the single-orbital Hubbard model on a two-dimensional square lattice are presented, in order to provide an assessment of our ability to compute accurate results in the thermodynamic limit. Many methods are employed, including auxiliary field quantum Monte Carlo, bare and bold-line diagrammatic Monte Carlo, method of dual fermions, density matrix embedding theory, density matrix renormalization group, dynamical cluster approximation, diffusion Monte Carlo within a fixed node approximation, unrestricted coupled cluster theory, and multi-reference projected Hartree-Fock. Comparison of results obtained by different methods allows for the identification of uncertainties and systematic errors. The importance of extrapolation to converged thermodynamic limit values is emphasized. Cases where agreement between different methods is obtained establish benchmark results that may be useful in the validation of new approaches and the improvement of existing methods.

cond-mat.str-el↗

arXiv2015

Ground state phase diagram of the repulsive fermionic $t-t^{\prime}$ Hubbard model on the square lattice from weak-coupling

We obtain a complete and exact in the weak-coupling limit ($U \rightarrow 0$) ground state phase diagram of the repulsive fermionic Hubbard model on the square lattice for filling factors $0 < n < 2$ and next-nearest-neighbour hopping amplitudes $0 \le t^{\prime} \le 0.5$. Phases are distinguished by the symmetry and the number of nodes of the superfluid order parameter. The phase diagram is richer than may be expected and typically features states with a high --- higher than that of the fundamental mode of the corresponding irreducible representation --- number of nodes. The effective coupling strength in the Cooper channel $λ$, which determines the critical temperature $T_c$ of the superfluid transition, is calculated in the whole parameter space and regions with high values of $λ$ are identified. It is shown that besides the expected increase of $λ$ near the Van Hove singularity line, joining the ferromagnetic and antiferromagnetic points, another region with high values of $λ$ can be found at quarter filling and $t^{\prime}=0.5$ due to the presence of a line of nesting at $t^{\prime} \ge 0.5$. The results can serve as benchmarks for controlled non-perturbative methods and guide the ongoing search for high-$T_c$ superconductivity in the Hubbard model.

cond-mat.str-el↗

arXiv2015

The Massive Goldstone (Higgs) mode in two-dimensional ultracold atomic lattice systems

We discuss how to reveal the massive Goldstone mode, often referred to as the Higgs amplitude mode, near the Superfluid-to-Insulator quantum critical point (QCP) in a system of two-dimensional ultracold bosonic atoms in optical lattices. The spectral function of the amplitude response is obtained by analytic continuation of the kinetic energy correlation function calculated by Monte Carlo methods. Our results enable a direct comparison with the recent experiment [M. Endres, T. Fukuhara, D. Pekker, M. Cheneau, P. Schauß, C. Gross, E. Demler, S. Kuhr, and I. Bloch, Nature 487, 454-458 (2012)], and demonstrate a good agreement for temperature shifts induced by lattice modulation. Based on our numerical analysis, we formulate the necessary conditions in terms of homogeneity, detuning from the QCP and temperature in order to reveal the massive Goldstone resonance peak in spectral functions experimentally. We also propose to apply a local modulation at the trap center to overcome the inhomogeneous broadening caused by the parabolic trap confinement.

cond-mat.quant-gas↗

arXiv2015

Realization of Two-Dimensional Spin-orbit Coupling for Bose-Einstein Condensates

Cold atoms with laser-induced spin-orbit (SO) interactions provide intriguing new platforms to explore novel quantum physics beyond natural conditions of solids. Recent experiments demonstrated the one-dimensional (1D) SO coupling for boson and fermion gases. However, realization of 2D SO interaction, a much more important task, remains very challenging. Here we propose and experimentally realize, for the first time, 2D SO coupling and topological band with $^{87}$Rb degenerate gas through a minimal optical Raman lattice scheme, without relying on phase locking or fine tuning of optical potentials. A controllable crossover between 2D and 1D SO couplings is studied, and the SO effects and nontrivial band topology are observed by measuring the atomic cloud distribution and spin texture in the momentum space. Our realization of 2D SO coupling with advantages of small heating and topological stability opens a broad avenue in cold atoms to study exotic quantum phases, including the highly-sought-after topological superfluid phases.

cond-mat.quant-gas↗

arXiv2015

Clique percolation in random graphs

As a generation of the classical percolation, clique percolation focuses on the connection of cliques in a graph, where the connection of two $k$-cliques means that they share at least $l 1$ makes a step-function-like discontinuous phase transition in the thermodynamic limit and a continuous phase transition for $l=1$. More interesting, our analysis shows that at the critical point, the order parameter $ϕ_c$ for $l>1$ is neither $0$ nor $1$, but a constant depending on $k$ and $l$. All these theoretical findings are in agreement with the simulation results, which give theoretical support and clarification for previous simulation studies of clique percolation.

cond-mat.stat-mech↗