arXiv subjects

Zi Yang Meng

Publications and source records attributed to Zi Yang Meng.

At least 181 records · Page 10Linked to original sources

arXiv2017

Caution on emergent continuous symmetry: a Monte Carlo investigation of transverse-field frustrated Ising model on triangle and honeycomb lattices

Continuous symmetries are believed to emerge at many quantum critical points in frustrated magnets. In this work, we study two candidates of this paradigm: the transverse-field frustrated Ising model (TFFIM) on the triangle and the honeycomb lattices. The former is the prototypical example of this paradigm, and the latter has recently been proposed as another realization. Our large-scale Monte Carlo simulation confirms that the quantum phase transition (QPT) in the triangle lattice TFFIM indeed hosts an emergent O(2) symmetry, but that in the honeycomb lattice TFFIM is a first-order QPT and does not have an emergent continuous symmetry. Furthermore, our analysis of the order parameter histogram reveals that such different behavior originates from the irrelevance and relevance of anisotropic terms near the QPT in the low-energy effective theory of the two models. The comparison between theoretical analysis and numerical simulation in this work paves the way for scrutinizing investigation of emergent continuous symmetry at classical and quantum phase transitions.

cond-mat.str-el↗

arXiv2017

Analytic continuation with Padé decomposition

The ill-posed analytic continuation problem for Green's functions or self-energies can be done using the Padé rational polynomial approximation. However, to extract accurate results from this approximation, high precision input data of the Matsubara Green's function are needed. The calculation of the Matsubara Green's function generally involves a Matsubara frequency summation which cannot be evaluated analytically. Numerical summation is requisite but it converges slowly with the increase of the Matsubara frequency. Here we show that this slow convergence problem can be significantly improved by utilizing the Padé decomposition approach to replace the Matsubara frequency summation by a Padé frequency summation, and high precision input data can be obtained to successfully perform the Padé analytic continuation.

cond-mat.str-el↗

arXiv2017

Gapped spin-1/2 spinon excitations in a new kagome quantum spin liquid compound Cu$_3$Zn(OH)$_6$FBr

We report a new kagome quantum spin liquid candidate Cu$_3$Zn(OH)$_6$FBr, which does not experience any phase transition down to 50 mK, more than three orders lower than the antiferromagnetic Curie-Weiss temperature ($\sim$ 200 K). A clear gap opening at low temperature is observed in the uniform spin susceptibility obtained from $^{19}$F nuclear magnetic resonance measurements. We observe the characteristic magnetic field dependence of the gap as expected for fractionalized spin-1/2 spinon excitations. Our experimental results provide firm evidence for spin fractionalization in a topologically ordered spin system, resembling charge fractionalization in the fractional quantum Hall state.

cond-mat.str-el↗

arXiv2017

Dynamical Generation of Topological Masses in Dirac Fermions

We report discovery of a topological Mott insulator in strongly-correlated Dirac semimetals. Such an interaction-driven topological state has been theoretically proposed but not yet observed with unbiased large scale numerical simulations. In our model, interactions between electrons are mediated by Ising spins in a transverse field. The results indicate that the topological mass term is dynamically generated and the resulting quantum phase transition belongs to the (2+1)D $N=8$ chiral Ising universality class. These conclusions stem from large scale sign free quantum Monte Carlo simulations.

cond-mat.str-el↗

arXiv2017

Duality between the deconfined quantum-critical point and the bosonic topological transition

Recently significant progress has been made in $(2+1)$-dimensional conformal field theories without supersymmetry. In particular, it was realized that different Lagrangians may be related by hidden dualities, i.e., seemingly different field theories may actually be identical in the infrared limit. Among all the proposed dualities, one has attracted particular interest in the field of strongly-correlated quantum-matter systems: the one relating the easy-plane noncompact CP$^1$ model (NCCP$^1$) and noncompact quantum electrodynamics (QED) with two flavors ($N = 2$) of massless two-component Dirac fermions. The easy-plane NCCP$^1$ model is the field theory of the putative deconfined quantum-critical point separating a planar (XY) antiferromagnet and a dimerized (valence-bond solid) ground state, while $N=2$ noncompact QED is the theory for the transition between a bosonic symmetry-protected topological phase and a trivial Mott insulator. In this work we present strong numerical support for the proposed duality. We realize the $N=2$ noncompact QED at a critical point of an interacting fermion model on the bilayer honeycomb lattice and study it using determinant quantum Monte Carlo (QMC) simulations. Using stochastic series expansion QMC, we study a planar version of the $S=1/2$ $J$-$Q$ spin Hamiltonian (a quantum XY-model with additional multi-spin couplings) and show that it hosts a continuous transition between the XY magnet and the valence-bond solid. The duality between the two systems, following from a mapping of their phase diagrams extending from their respective critical points, is supported by the good agreement between the critical exponents according to the proposed duality relationships.

cond-mat.str-el↗

arXiv2017

Topological phase transitions with SO(4) symmetry in (2+1)d interacting Dirac fermions

Interaction-driven topological phase transitions in Dirac semimetals are investigated by means of large-scale quantum Monte Carlo (QMC) simulations. The interaction among Dirac fermions is introduced by coupling them to Ising spins that realize the quantum dynamics of the two-dimensional transverse field Ising model. The ground state phase diagram, in which the tuning parameters are the transverse field and the coupling between fermion and Ising spins, is determined. At weak and intermediate coupling, a second-order Ising quantum phase transition and a first-order topological phase transition between two topologically distinct Dirac semimetals are observed. Interestingly, at the latter, the Dirac points smear out to form nodal lines in the Brillouin zone, and collective bosonic fluctuations with SO(4) symmetry are strongly enhanced. At strong coupling, these two phase boundaries merge into a first-order transition.

cond-mat.str-el↗

arXiv2017

The amplitude mode in three-dimensional dimerized antiferromagnets

The amplitude (Higgs) mode is a ubiquitous collective excitation related to spontaneous breaking of a continuous symmetry. We combine quantum Monte Carlo (QMC) simulations with stochastic analytic continuation to investigate the dynamics of the amplitude mode in a three-dimensional dimerized quantum spin system. We characterize this mode by calculating the spin and dimer spectral functions near the quantum critical point, finding that both the energies and the intrinsic widths satisfy field-theoretical scaling predictions. While the line width of the spin response is close to that observed in neutron scattering experiments on TlCuCl$_3$, the dimer response is significantly broader. Our results demonstrate that highly non-trivial dynamical properties are accessible by modern QMC and analytic continuation methods.

cond-mat.str-el↗

arXiv2016

Self-Learning Monte Carlo Method

Monte Carlo simulation is an unbiased numerical tool for studying classical and quantum many-body systems. One of its bottlenecks is the lack of general and efficient update algorithm for large size systems close to phase transition or with strong frustrations, for which local updates perform badly. In this work, we propose a new general-purpose Monte Carlo method, dubbed self-learning Monte Carlo (SLMC), in which an efficient update algorithm is first learned from the training data generated in trial simulations and then used to speed up the actual simulation. We demonstrate the efficiency of SLMC in a spin model at the phase transition point, achieving a 10-20 times speedup.

cond-mat.str-el↗

arXiv2016

Self-Learning Determinantal Quantum Monte Carlo Method

Self-learning Monte Carlo method [arXiv:1610.03137, 1611.09364] is a powerful general-purpose numerical method recently introduced to simulate many-body systems. In this work, we implement this method in the framework of determinantal quantum Monte Carlo simulation of interacting fermion systems. Guided by a self-learned bosonic effective action, our method uses a cumulative update [arXiv:1611.09364] algorithm to sample auxiliary field configurations quickly and efficiently. We demonstrate that self-learning determinantal Monte Carlo method can reduce the auto-correlation time to as short as one near a critical point, leading to $\mathcal{O}(N)$-fold speedup. This enables to simulate interacting fermion system on a $100\times 100$ lattice for the first time, and obtain critical exponents with high accuracy.

cond-mat.str-el↗

arXiv2016

Self-Learning Monte Carlo Method in Fermion Systems

We develop the self-learning Monte Carlo (SLMC) method, a general-purpose numerical method recently introduced to simulate many-body systems, for studying interacting fermion systems. Our method uses a highly-efficient update algorithm, which we design and dub "cumulative update", to generate new candidate configurations in the Markov chain based on a self-learned bosonic effective model. From general analysis and numerical study of the double exchange model as an example, we find the SLMC with cumulative update drastically reduces the computational cost of the simulation, while remaining statistically exact. Remarkably, its computational complexity is far less than the conventional algorithm with local updates.

cond-mat.str-el↗

arXiv2016

Visualizing a Bosonic Symmetry Protected Topological Phase in an Interacting Fermion Model

Symmetry protected topological (SPT) phases in free fermion and interacting bosonic systems have been classified, but the physical phenomena of interacting fermionic SPT phases have not been fully explored. Here, employing large-scale quantum Monte Carlo simulation, we investigate the edge physics of a bilayer Kane-Mele-Hubbard model with zigzag ribbon geometry. Our unbiased numerical results show that the fermion edge modes are gapped out by interaction, while the bosonic edge modes remain gapless at the $(1+1)d$ boundary, before the bulk quantum phase transition to a topologically trivial phase. Therefore, finite fermion gaps both in the bulk and on the edge, together with the robust gapless bosonic edge modes, prove that our system becomes an emergent bosonic SPT phase at low energy, which is, for the first time, directly observed in an interacting fermion lattice model.

cond-mat.str-el↗

arXiv2016

Competing pairing channels in the doped honeycomb lattice Hubbard model

Proposals for superconductivity emerging from correlated electrons in the doped Hubbard model on the honeycomb lattice range from chiral $d+id$ singlet to $p+ip$ triplet pairing, depending on the considered range of doping and interaction strength, as well as the approach used to analyze the pairing instabilities. Here, we consider these scenarios using large-scale dynamic cluster approximation (DCA) calculations to examine the evolution in the leading pairing symmetry from weak to intermediate coupling strength. These calculations focus on doping levels around the van Hove singularity (VHS) and are performed using DCA simulations with an interaction-expansion continuous-time quantum Monte Carlo cluster solver. We calculated explicitly the temperature dependence of different uniform superconducting pairing susceptibilities and found a consistent picture emerging upon gradually increasing the cluster size: while at weak coupling the $d+id$ singlet pairing dominates close to the VHS filling, an enhanced tendency towards $p$-wave triplet pairing upon further increasing the interaction strength is observed. The relevance of these systematic results for existing proposals and ongoing pursuits of odd-parity topological superconductivity are also discussed.

cond-mat.str-el↗

arXiv2016

Diagnosis of interaction-driven topological phase via exact diagonalization

We propose a general scheme for diagnosing interaction-driven topological phases in the weak interaction regime using exact diagonalization (ED). The scheme comprises the analysis of eigenvalues of the point-group operators for the many-body eigenstates and the correlation functions for physical observables to extract the symmetries of the order parameters and the topological numbers of the underlying ground states at the thermodynamic limit from a relatively small size system afforded by ED. As a concrete example, we investigate the interaction effects on the half-filled spinless fermions on the checkerboard lattice with a quadratic band crossing point. Numerical results support the existence of a spontaneous quantum anomalous Hall phase purely driven by a nearest-neighbor weak repulsive interaction, separated from a nematic Mott insulator phase at strong repulsive interaction by a first-order phase transition.

cond-mat.str-el↗

arXiv2016

Effect of nematic order on the low-energy spin fluctuations in detwinned BaFe$_{1.935}$Ni$_{0.065}$As$_2$

The origin of nematic order remains one of the major debates in iron-based superconductors. In theories based on spin nematicity, one major prediction is that the spin-spin correlation length at (0,$π$) should decrease with decreasing temperature below the structural transition temperature $T_s$. Here we report inelastic neutron scattering studies on the low-energy spin fluctuations in BaFe$_{1.935}$Ni$_{0.065}$As$_2$ under uniaxial pressure. Both intensity and spin-spin correlation start to show anisotropic behavior at high temperature, while the reduction of the spin-spin correlation length at (0,$π$) happens just below $T_s$, suggesting strong effect of nematic order on low-energy spin fluctuations. Our results favor the idea that treats the spin degree of freedom as the driving force of the electronic nematic order.

cond-mat.supr-con↗

arXiv2016

Quantum critical point of Dirac fermion mass generation without spontaneous symmetry breaking

We study a lattice model of interacting Dirac fermions in $(2+1)$ dimension space-time with an SU(4) symmetry. While increasing interaction strength, this model undergoes a {\it continuous} quantum phase transition from the weakly interacting Dirac semimetal to a fully gapped and nondegenerate phase without condensing any Dirac fermion bilinear mass operator. This unusual mechanism for mass generation is consistent with recent studies of interacting topological insulators/superconductors, and also consistent with recent progresses in lattice QCD community.

cond-mat.str-el↗

arXiv2016

Bona fide interaction-driven topological phase transition in correlated SPT states

It is expected that the interplay between non-trivial band topology and strong electron correlation will lead to very rich physics. Thus a controlled study of the competition between topology and correlation is of great interest. Here, employing large-scale quantum Monte Carlo (QMC) simulations, we provide a concrete example of the Kane-Mele-Hubbard (KMH) model on an AA stacking bilayer honeycomb lattice with inter-layer antiferromagnetic interaction. Our simulation identified several different phases: a quantum spin-Hall insulator (QSH), a $xy$-plane antiferromagnetic Mott insulator ($xy$-AFM) and an inter-layer dimer-singlet insulator (dimer-singlet). Most importantly, a bona fide topological phase transition between the QSH and the dimer-singlet insulators, purely driven by the inter-layer antiferromagnetic interaction is found. At the transition, the spin and charge gap of the system close while the single-particle excitations remain gapped, which means that this transition has no mean field analogue and it can be viewed as a transition between bosonic SPT states. At one special point, this transition is described by a $(2+1)d$ $O(4)$ nonlinear sigma model (NLSM) with {\it exact} $SO(4)$ symmetry, and a topological term at {\it exactly} $Θ= π$. Relevance of this work towards more general interacting SPT states is discussed.

cond-mat.str-el↗

arXiv2015

Mott insulating states and quantum phase transitions of correlated SU(2N) Dirac fermions

The interplay between charge and spin degrees of freedom in strongly correlated fermionic systems, in particular of Dirac fermions, is a long-standing problem in condensed matter physics. We investigate the competing orders in the half-filled SU(2N) Hubbard model on a honeycomb lattice, which can be accurately realized in optical lattices with large-spin ultra-cold alkaline-earth fermions. Employing large-scale projector determinant quantum Monte Carlo simulations, we have explored quantum phase transitions from the gapless Dirac semi-metals to the gapped Mott-insulating phases in the SU(4) and SU(6) cases. Both of these Mott-insulating states are found to be columnar valence bond solid (cVBS) and to be absent of the antiferromagnetic Neel ordering and the loop current ordering. Inside the cVBS phases, the dimer ordering is enhanced by increasing fermion components and behaves non-monotonically as the interaction strength increases. Although the transitions generally should be of first order due to a cubic invariance possessed by the cVBS order, the coupling to gapless Dirac fermions can soften the transitions to second order through a non-analytic term in the free energy. Our simulations provide important guidance for the experimental exploration of novel states of matter with ultra-cold alkaline earth fermions.

cond-mat.quant-gas↗

arXiv2015

Topological invariants for interacting topological insulators: I. Efficient numerical evaluation scheme and implementations

The aim of this series of two papers is to discuss topological invariants for interacting topological insulators (TIs). In the first paper (I), we provide a paradigm of efficient numerical evaluation scheme for topological invariants, in which we demystify the procedures and techniques employed in calculating Z2 invariant and spin Chern number via zero-frequency single-particle Green's function in quantum Monte Carlo (QMC) simulations. Here we introduce a periodization process to overcome the ubiquitous finite-size effect, so that the calculated spin Chern number shows ideally quantized values. We also show that making use of symmetry properties of the underlying systems can greatly reduce the computational effort. To demonstrate the effectiveness of our numerical evaluation scheme, especially the periodization process, of topological invariants, we apply it on two independent two-dimensional models of interacting topological insulators. In the subsequent paper (II), we apply the scheme developed here to wider classes of models of interacting topological insulators, for which certain limitation of constructing topological invariant via single-particle Green's functions will be presented.

cond-mat.str-el↗