arXiv subjects

Y. Xian

Publications and source records attributed to Y. Xian.

18 recordsLinked to original sources

arXiv2022

Randomized Kaczmarz Method for Single Particle X-ray Image Phase Retrieval

In this paper, we investigate phase retrieval algorithm for the single particle X-ray imaging data. We present a variance-reduced randomized Kaczmarz (VR-RK) algorithm for phase retrieval. The VR-RK algorithm is inspired by the randomized Kaczmarz method and the Stochastic Variance Reduce Gradient Descent (SVRG) algorithm. Numerical experiments show that the VR-RK algorithm has a faster convergence rate than randomized Kaczmarz algorithm and the iterative projection phase retrieval methods, such as the hybrid input output (HIO) and the relaxed averaged alternating reflections (RAAR) methods. The VR-RK algorithm can recover the phases with higher accuracy, and is robust at the presence of noise. Experimental results on the scattering data from individual particles show that the VR-RK algorithm can recover phases and improve the single particle image identification.

q-bio.QM↗

arXiv2019

The effects of three magnons interactions in the magnon-density waves of triangular spin lattices

We investigate the magnon-density waves proposed as the longitudinal excitations in triangular lattice antiferromagnets by including the cubic and quartic corrections in the large-s expansion. The longitudinal excitation spectra for the two-dimensional (2D) triangular antiferromagnetic model and quasi-one dimensional (quasi-1D) antiferromagnetic materials have been obtained for a general quantum spin number $s$. For the 2D triangular lattice model, we find a significant reduction (about 40 %) in the energy spectra at the zone boundaries due to both the cubic and quartic corrections. For the quasi-1D antiferromagnets, since the cubic term comes from the very weak couplings on the hexagonal planes, they make very little correction to the energy spectra, whereas the major correction contribution comes from the quartic terms in the couplings along the chains with the numerical values for the energy gaps in good agreement with the experimental results as reported earlier (Ref.~41).

cond-mat.str-el↗

arXiv2019

Analytical study of the edge states in the bosonic Haldane model

We investigate the properties of magnon edge states in a ferromagnetic honeycomb spin lattice with a Dzyaloshinskii-Moriya interaction (DMI). We derive analytical expressions for the energy spectra and wavefunctions of the edge states localized on the boundaries. By introducing an external on-site potential at the outermost sites, we show that the bosonic band structure is similar to that of the fermionic graphene. We investigate the region in the momentum space where the bosonic edge states are well defined and we analyze the width of the edge state and their dependence with DMI strength. Our findings extend the predictions using topological arguments and they allow size-dependent confirmation from possible experiments

cond-mat.mes-hall↗

arXiv2019

Topological Magnon Insulator with a Kekule Bond Modulation

We examine the combined effects of a Kekule coupling texture (KC) and a Dzyaloshinskii-Moriya interaction (DMI) in a two-dimensional ferromagnetic honeycomb lattice. By analyzing the gap closing conditions and the inversions of the bulk bands, we identify the parameter range in which the system behaves as a trivial or a nontrivial topological magnon insulator. We find four topological phases in terms of the KC parameter and the DMI strength. We present the bulk-edge correspondence for the magnons in a honeycomb lattice with an armchair or a zigzag boundary. Furthermore, we find Tamm-like edge states due to the intrinsic on-site interactions along the boundary sites. Our results may have significant implications to magnon transport properties in the 2D magnets at low temperatures.

cond-mat.mes-hall↗

arXiv2018

Edge on-site potential effects in a honeycomb topological magnon insulator

The difference between the edge on-site potential and the bulk values in a magnonic topological honeycomb lattice leads to the formation of edge states in a bearded boundary, and the same difference is found to be the responsible for the absence of edge states in a zig-zag termination. In a finite lattice, the intrinsic on-site interactions along the boundary sites generate an effective defect and Tamm-like edge states appear for both zig-zag and bearded terminations. If a non-trivial gap is induced, Tamm-like and topologically protected edge states appear in the band structure. The effective defect can be strengthened by an external on-site potential and the dispersion relation, velocity and magnon-density of the edge states become tunable.

cond-mat.mes-hall↗

arXiv2013

Longitudinal Excitations in Bipartite and Hexagonal Antiferromagnetic Spin Lattices

Based on our recently proposed magnon-density-waves using the microscopic many-body approach, we investigate the longitudinal excitations in quantum antiferromagnets by including the second order corrections in the large-$s$ expansion. The longitudinal excitation spectra for a general spin quantum number using the antiferromagnetic Heisenberg Hamiltonian are obtained for various spin lattice models. For bipartite lattice models, we find that the numerical results for the energy gaps for the longitudinal modes at $q\to0$ and the magnetic ordering wavevector $\bf Q$ are reduced by about $40-50\%$ after including the second order corrections. Thus, our estimate of the energy gaps for the quasi-one-dimensional (quasi-1D) antiferromagnetic compound KCuF$_3$ is in better agreement with the experimental result. For the quasi-1D antiferromagnets on hexagonal lattices, the full excitation spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We find two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. We compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and also find good agreement after the higher-order contributions are included in our calculations.

cond-mat.str-el↗

arXiv2013

Excited states of the quasi-one-dimensional hexagonal quantum antiferromagnets

We investigate the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compare our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreement after the higher-order contributions are included in our calculations.

cond-mat.str-el↗

arXiv2012

Longitudinal excitations in triangular lattice antiferromagnets

We study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone $Γ(\mathbf q=0)$ and at the magnetic ordering wavevectors $\pm[\mathbf Q= (4π/3,0)]$, the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We also discuss a possible second longitudinal mode in the triangular lattice model due to the noncollinear nature of its magnetic order.

cond-mat.str-el↗

arXiv2012

Coupled-cluster calculations for the ground- and excited-states of the spin-half XXZ model

The coupled-cluster method is applied to the spin-1/2 antiferromagnetic XXZ model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.

cond-mat.str-el↗

arXiv2007

A variational Jastrow coupled-cluster theory of quantum many-body systems

We study many-body correlations in the ground states of a general quantum system of bosons or fermions by including an additional Jastrow function in our ecently proposed variational coupled-cluster method. Our approach combines the dvantages of state-dependent correlations in the coupled-cluster theory and of strong, short-ranged correlations of the Jastrow function. We apply a generalized linked-cluster expansion for the Jastrow wavefunction and provide detailed analysis for practical evaluation of Hamiltonian expectation value as an energy functional of the Jastrow function and the bare density-distribution functions introduced and calculated in our earlier publications; a simple, first-order energy functional is derived and detailed formulas for higher-order contributions are provided. Our energy functional does not suffer the divergence as in most coupled-cluster calculations when applying to Hamiltonians with hardcore potentials. We also discuss relations between our energy functional and the energy functionals from other theories.

cond-mat.str-el↗

arXiv2007

Excited states of quantum many-body interacting systems: A variational coupled-cluster description

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum many-body interacting systems. We discuss, in general terms, both quasiparticle excitations and quasiparticle-density-wave excitations (collective modes). In application to quantum antiferromagnets, we reproduce the well-known spin-wave excitations, i.e. quasiparticle magnons of spin $\pm 1$. In addition, we obtain new, spin-zero magnon-density-wave excitations which has been missing in Anserson's spin-wave theory. Implications of these new collective modes are discussed.

cond-mat.other↗

arXiv2006

A variational coupled-cluster study of magnon-density-wave excitations in quantum antiferromagnets

We extend recently proposed variational coupled-cluster method to describe excitation states of quantum antiferromagnetic bipartite lattices. We reproduce the spin-wave excitations (i.e., magnons with spin $\pm 1$). In addition, we obtain a new, spin-zero excitation (magnon-density waves) which has been missing in all existing spin-wave theories. Within our approximation, this magnon-density-wave excitation has a nonzero energy gap in a cubic lattice and is gapless in a square lattice, similar to those charge-density-wave excitations (plasmons) in quantum electron gases.

cond-mat.str-el↗

arXiv2005

Diagrammatic approach in the variational coupled-cluster method

Recently, as demonstrated by an antiferromagnetic spin-lattice application, we have successfully extended the coupled-cluster method (CCM) to a variational formalism in which two sets of distribution functions are introduced to evaluate Hamiltonian expectation. We calculated these distribution functions by employing an algebraic scheme. Here we present an alternative calculation based on a diagrammatic technique. Similar to the method of correlated-basis functionals (CBF), a generating functional is introduced and calculated by a linked-cluster expansion in terms of diagrams which are categorized and constructed according to a few simple rules and using correlation coefficients and Pauli exclusion principle (or Pauli line) as basic elements. Infinite resummations of diagrams can then be done in a straightforward manner. One such resummation, which includes all so-called ring diagrams and ignores Pauli exclusion principle, reproduces spin-wave theory (SWT). Approximations beyond SWT are also given. Interestingly, one such approximation including all so-called super-ring diagrams by a resummation of infinite Pauli lines in additional to resummations of ring diagrams produces a convergent, precise number for the order-parameter of the one-dimensional isotropic model, contrast to the well-known divergence of SWT. We also discuss the direct relation between our variational CCM and CBF and discuss a possible unification of the two theories.

cond-mat.str-el↗

arXiv2002

An extension of the coupled-cluster method: A variational formalism

A general quantum many-body theory in configuration space is developed by extending the traditional coupled cluter method (CCM) to a variational formalism. Two independent sets of distribution functions are introduced to evaluate the Hamiltonian expectation. An algebraic technique for calculating these distribution functions via two self-consistent sets of equations is given. By comparing with the traditional CCM and with Arponen's extension, it is shown that the former is equivalent to a linear approximation to one set of distribution functions and the later is equivalent to a random-phase approximation to it. In additional to these two approximations, other higher-order approximation schemes within the new formalism are also discussed. As a demonstration, we apply this technique to a quantum antiferromagnetic spin model.

cond-mat.str-el↗

arXiv1995

Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Some rigorous results are presented for a first-order quantum phase transition between the dimerized state and Haldane-type state (i.e., a state similar to the ground state of the one-dimensional spin-1 Heisenberg chain) in the spin-1/2 coupled chains with nearest-neighbour and next-nearest-neighbour Heisenberg interactions. Also presented are the exact excited states in both phases. A partial phase diagram of the general spin-1/2 coupled chains is discussed.

cond-mat↗

arXiv1994

A nonperturbative microscopic theory of Hamiltonian lattice gauge systems

A review is given of our recent application of a systematic microscopic formulation of quantum many-body theory, namely the coupled-cluster method (CCM), to Hamiltonian $U(1)$ lattice gauge models in the pure gauge sector. It is emphasized that our CCM results represent a natural extension or resummation of the results from the strong-coupling perturbation theory.

cond-mat↗

arXiv1994

Systematic Inclusion of High-Order Multi-Spin Correlations for the Spin-$1\over2$ $XXZ$ Models

We apply the microscopic coupled-cluster method (CCM) to the spin-$1\over2$ $XXZ$ models on both the one-dimensional chain and the two-dimensional square lattice. Based on a systematic approximation scheme of the CCM developed by us previously, we carry out high-order {\it ab initio} calculations using computer-algebraic techniques. The ground-state properties of the models are obtained with high accuracy as functions of the anisotropy parameter. Furthermore, our CCM analysis enables us to study their quantum critical behavior in a systematic and unbiased manner.

cond-mat↗

arXiv1993

Exact Results of Dimerization Order Parameter in $SU(n)$ Antiferromagnetic Chains

After a proper definition of the dimerization order parameter for a spin-$S$ system, I show that this order parameter in the $SU(n)$ ($n=2S+1$) antiferromagnetic chains (or equivalently the $SU(2)$ spin-$S$ chains with Hamiltonians which project out singlet states) is, in the thermodynamic limit, directly proportional to the staggered-magnetization in the corresponding spin-$1\over2$ $XXZ$ chains which had already been mapped onto the $SU(n)$ chains.

cond-mat↗