arXiv subjects

Shiwei Zhang

Publications and source records attributed to Shiwei Zhang.

At least 217 records · Page 12Linked to original sources

arXiv2013

Phases of attractive spin-imbalanced fermions in square lattices

We determine the relative stability of different ground-state phases of spin-imbalanced popula- tions of attractive fermions in square lattices. The phases are systematically characterized by the symmetry of the order parameter and the real- and momentum-space structures using Hartree- Fock-Bogoliubov theory. We find several type of unidirectional Larkin-Ovchinikov-type phases. We discuss the effect of commensuration between the ordering wave vector and the density imbalance, and describe the mechanism of Fermi surface reconstruction and pairing for various orders. A robust supersolid phase is shown to exist when the ordering wave vector is diagonally directed.

cond-mat.quant-gas↗

arXiv2013

Symmetry in Auxiliary-Field Quantum Monte Carlo Calculations

We show how symmetry properties can be used to greatly increase the accuracy and efficiency in auxiliary-field quantum Monte Carlo (AFQMC) calculations of electronic systems. With the Hubbard model as an example, we study symmetry preservation in two aspects of ground-state AFQMC calculations, the Hubbard-Straonovich transformation and the form of the trial wave function. It is shown that significant improvement over state-of-the-art calculations can be achieved. In unconstrained calculations, the implementation of symmetry often leads to shorter convergence time and much smaller statistical errors, thereby a substantial reduction of the sign problem. Moreover, certain excited states become possible to calculate which are otherwise beyond reach. In calculations with constraints, the use of symmetry can reduce the systematic error from the constraint. It also allows release-constraint calculations, leading to essentially exact results in many cases. Detailed comparisons are made with exact diagonalization results. Accurate ground-state energies are then presented for larger system sizes in the two-dimensional repulsive Hubbard model.

cond-mat.str-el↗

arXiv2013

Frozen-orbital and downfolding calculations with auxiliary-field quantum Monte Carlo

We describe the implementation of the frozen-orbital and downfolding approximations in the auxiliary-field quantum Monte Carlo (AFQMC) method. These approaches can provide significant computational savings compared to fully correlating all the electrons. While the many-body wave function is never explicit in AFQMC, its random walkers are Slater determinants, whose orbitals may be expressed in terms of any one-particle orbital basis. It is therefore straightforward to partition the full N-particle Hilbert space into active and inactive parts to implement the frozen-orbital method. In the frozen-core approximation, for example, the core electrons can be eliminated in the correlated part of the calculations, greatly increasing the computational efficiency, especially for heavy atoms. Scalar relativistic effects are easily included using the Douglas-Kroll-Hess theory. Using this method, we obtain a way to effectively eliminate the error due to single-projector, norm-conserving pseudopotentials in AFQMC. We also illustrate a generalization of the frozen-orbital approach that downfolds high-energy basis states to a physically relevant low-energy sector, which allows a systematic approach to produce realistic model Hamiltonians to further increase efficiency for extended systems.

physics.comp-ph↗

arXiv2013

Magnetic order in the repulsive Fermi-Hubbard model in three-dimensions and the crossover to two-dimensions

Systems of fermions described by the three-dimensional (3D) repulsive Hubbard model on a cubic lattice have recently attracted considerable attention due to their possible experimental realization via cold atoms in an optical lattice. Because analytical and numerical results are limited away from half-filling, we study the ground state of the doped system from weak to intermediate interaction strengths within the generalized Hartree-Fock approximation. The exact solution to the self-consistent-field equations in the thermodynamic limit is obtained and the ground state is shown to exhibit antiferromagnetic order and incommensurate spin-density waves (SDW). At low interaction strengths, the SDW has unidirectional character with a leading wave-vector along the $<100>$-direction, and the system is metallic. As the interaction increases, the system undergoes a simultaneous structural and metal-to-insulator transition to a unidirectional SDW state along the $<111>$-direction, with a different wavelength. We systematically determine the real- and momentum-space properties of these states. The crossover from 3D to two-dimensions (2D) is then studied by varying the inter-plane hopping amplitude, which can be experimentally realized by tuning the distance between a stack of square-lattice layers. Detailed comparisons are made between the exact numerical results and predictions from the pairing model, a variational {\em ansatz} based on the pairing of spins in the vicinity of the Fermi surface. Most of the numerical results can be understood quantitatively from the ansatz, which provides a simple picture for the nature of the SDW states.

cond-mat.str-el↗

arXiv2012

Excited state calculations in solids by auxiliary-field quantum Monte Carlo

We present an approach for ab initio many-body calculations of excited states in solids. Using auxiliary-field quantum Monte Carlo, we introduce an orthogonalization constraint to prevent collapse of the stochastic Slater determinants in the imaginary-time propagation. Trial wave functions from density-functional calculations are used for the constraints. Detailed band structures calculated for standard semiconductors are in good agreement with GW and experimental results. For the challenging ZnO wurtzite structure, we obtain a fundamental band gap of 3.26(16) eV, consistent with experiments.

cond-mat.mtrl-sci↗

arXiv2012

Ab Initio Many-body Study of Cobalt Adatoms Adsorbed on Graphene

Many recent calculations have been performed to study a Co atom adsorbed on graphene, with significantly varying results on the nature of the bonding. We use auxiliary-field quantum Monte Carlo (AFQMC) and a size-correction embedding scheme to accurately calculate the binding energy of Co on graphene. We find that as a function of the distance h between the Co atom and the six-fold hollow site, there are three distinct ground states corresponding to three electronic configurations of the Co atom. Two of these states provide binding and exhibit a double-well feature with nearly equal binding energy of 0.4 eV at h = 1.51 and h = 1.65 angstroms, corresponding to low-spin $^2$Co (3d9 4s0) and high-spin $^4$Co (3d8 4s1), respectively.

cond-mat.mtrl-sci↗

arXiv2012

Finite-Temperature Auxiliary-Field Quantum Monte Carlo for Bose-Fermi Mixtures

We present a quantum Monte Carlo (QMC) technique for calculating the exact finite-temperature properties of Bose-Fermi mixtures. The Bose-Fermi Auxiliary-Field Quantum Monte Carlo (BF-AFQMC) algorithm combines two methods, a finite-temperature AFQMC algorithm for bosons and a variant of the standard AFQMC algorithm for fermions, into one algorithm for mixtures. We demonstrate the accuracy of our method by comparing its results for the Bose-Hubbard and Bose-Fermi-Hubbard models against those produced using exact diagonalization for small systems. Comparisons are also made with mean-field theory and the worm algorithm for larger systems. As is the case with most fermion Hamiltonians, a sign or phase problem is present in BF-AFQMC. We discuss the nature of these problems in this framework and describe how they can be controlled with well-studied approximations to expand BF-AFQMC's reach. The new algorithm can serve as an essential tool for answering many unresolved questions about many-body physics in mixed Bose-Fermi systems.

cond-mat.quant-gas↗

arXiv2011

Spin- and charge-density waves in the Hartree-Fock ground state of the two-dimensional Hubbard model

The ground states of the two-dimensional repulsive Hubbard model are studied within the unrestricted Hartree-Fock (UHF) theory. Magnetic and charge properties are determined by systematic, large-scale, exact numerical calculations, and quantified as a function of electron doping $h$. In the solution of the self-consistent UHF equations, multiple initial configurations and simulated annealing are used to facilitate convergence to the global minimum. New approaches are employed to minimize finite-size effects in order to reach the thermodynamic limit. At low to moderate interacting strengths and low doping, the UHF ground state is a linear spin-density wave (l-SDW), with antiferromagnetic order and a modulating wave. The wavelength of the modulating wave is $2/h$. Corresponding charge order exists but is substantially weaker than the spin order, hence holes are mobile. As the interaction is increased, the l-SDW states evolves into several different phases, with the holes eventually becoming localized. A simple pairing model is presented with analytic calculations for low interaction strength and small doping, to help understand the numerical results and provide a physical picture for the properties of the SDW ground state. By comparison with recent many-body calculations, it is shown that, for intermediate interactions, the UHF solution provides a good description of the magnetic correlations in the true ground state of the Hubbard model.

cond-mat.str-el↗

arXiv2011

Assessing weak hydrogen binding on Ca+ centers: An accurate many-body study with large basis sets

Weak H2 physisorption energies present a significant challenge to even the best correlated theoretical many-body methods. We use the phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to accurately predict the binding energy of Ca+ - 4H2. Attention has recently focused on this model chemistry to test the reliability of electronic structure methods for H2 binding on dispersed alkaline earth metal centers. A modified Cholesky decomposition is implemented to realize the Hubbard-Stratonovich transformation efficiently with large Gaussian basis sets. We employ the largest correlation-consistent Gaussian type basis sets available, up to cc-pCV5Z for Ca, to accurately extrapolate to the complete basis limit. The calculated potential energy curve exhibits binding with a double-well structure.

physics.comp-ph↗

arXiv2011

Validity of the scattering length approximation in strongly interacting Fermi systems

We investigate the energy spectrum of systems of two, three and four spin-1/2 fermions with short range attractive interactions both exactly, and within the scattering length approximation. The formation of molecular bound states and the ferromagnetic transition of the excited scattering state are examined systematically as a function of the 2-body scattering length. Identification of the upper branch (scattering states) is discussed and a general approach valid for systems with many particles is given. We show that an adiabatic ferromagnetic transition occurs, but at a critical transition point kF a much higher than predicted from previous calculations, almost all of which use the scattering length approximation. In the 4-particle system the discrepancy is a factor of 2. The exact critical interaction strength calculated in the 4-particle system is consistent with that reported by experiment. To make comparisons with the adiabatic transition, we study the quench dynamics of the pairing instability using the eigenstate wavefunctions.

cond-mat.quant-gas↗

arXiv2011

Finite-size correction in many-body electronic structure calculations of magnetic systems

We extend the post-processing finite-size (FS) correction method, developed by Kwee, Zhang, and Krakauer [Phys. Rev. Lett. 100, 126404 (2008)], to spin polarized systems. The method estimates the FS effects in many-body electronic structure calculations of extended systems by a modified density functional theory (DFT) calculation, without having to repeat expensive many-body simulations. We construct a unified FS DFT exchange-correlation functional for spin unpolarized and fully spin polarized systems, under the local density approximation. The results are then interpolated to arbitrary spin polarizations. Generalization to other functional forms in DFT are discussed. The application of this FS correction method to several typical magnetic systems with varying supercell sizes demonstrates that it consistently removes most of the FS errors, leading to rapid convergence of the many-body results to the infinite size limit.

cond-mat.str-el↗

arXiv2011

Auxiliary Field quantum Monte Carlo for Strongly Paired Fermions

We demonstrate that the inclusion of a BCS importance function dramatically increases the efficiency of the auxiliary field method for strong pairing. We calculate the ground-state energy of an unpolarized fermi gas at unitarity with up to 66 particles and lattices of up to $27^3$ sites. The method has no fermion sign problem, and an accurate result is obtained for the universal parameter $ξ$. Several different forms of the kinetic energy adjusted to the unitary limit but with different effective ranges extrapolate to the same continuum limit within error bars. The finite effective range results for different interactions are consistent with a linear term proportional to the Fermi momentum times the effective range. The new method described herein will have many applications in superfluid cold atom systems and in both electronic and nuclear structures when pairing is important.

cond-mat.quant-gas↗

arXiv2010

Charge-density-wave and topological transitions in interacting Haldane model

Haldane model is a noninteracting model for spinless fermions showing nontrivial topological properties. Effect of the electron-electron interaction on the topological phase poses an intriguing question. By means of the Hartree-Fock mean field, the exact diagonalization and the constrained-path Monte Carlo methods we mapped out the phase diagram of the interacting Haldane model. It is found that interaction breaks down the topological phase and drives the system into the charge-density-wave state. Sequence of the two transitions depends on the strength of next-nearest-neighbor hopping. Many-body Chern number and the charge excitation gap are used to characterize the topological transition.

cond-mat.str-el↗

arXiv2010

Itinerant ferromagnetism in a Fermi gas with contact interaction: Magnetic properties in a dilute Hubbard model

Ground state properties of the repulsive Hubbard model on a cubic lattice are investigated by means of the auxiliary-field quantum Monte Carlo method. We focus on low-density systems with varying on-site interaction $U/t$, as a model relevant to recent experiments on itinerant ferromagnetism in a dilute Fermi gas with contact interaction. Twist-average boundary conditions are used to eliminate open-shell effects and large lattice sizes are studied to reduce finite-size effects. The sign problem is controlled by a generalized constrained path approximation. We find no ferromagnetic phase transition in this model. The ground-state correlations are consistent with those of a paramagnetic Fermi liquid.

cond-mat.quant-gas↗

arXiv2009

Spin and charge order in doped Hubbard model: long-wavelength collective modes

Determining the ground state properties of the two-dimensional Hubbard model has remained an outstanding problem. Applying recent advances in constrained path auxiliary-field quantum Monte Carlo techniques and simulating large rectangular periodic lattices, we calculate the long-range spin and charge correlations in the ground state as a function of doping. At intermediate interaction strengths, an incommensurate spin density wave (SDW) state is found, with antiferromagnetic order and essentially homogeneous charge correlation. The wavelength of the collective mode decreases with doping, as does its magnitude. The SDW order vanishes beyond a critical doping. As the interaction is increased, the holes go from a wave-like to a particle-like state, and charge ordering develops which eventually evolves into stripe-like states.

cond-mat.str-el↗

arXiv2009

Pressure-induced diamond to beta-tin transition in bulk silicon: a near-exact quantum Monte Carlo study

The pressure-induced structural phase transition from diamond to beta-tin in silicon is an excellent test for theoretical total energy methods. The transition pressure provides a sensitive measure of small relative energy changes between the two phases (one a semiconductor and the other a semimetal). Experimentally, the transition pressure is well characterized. Density-functional results have been unsatisfactory. Even the generally much more accurate diffusion Monte Carlo method has shown a noticeable fixed-node error. We use the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method to calculate the relative energy differences in the two phases. In this method, all but the error due to the phaseless constraint can be controlled systematically and driven to zero. In both structural phases we were able to benchmark the error of the phaseless constraint by carrying out exact unconstrained AFQMC calculations for small supercells. Comparison between the two shows that the systematic error in the absolute total energies due to the phaseless constraint is well within 0.5 mHa/atom. Consistent with these internal benchmarks, the transition pressure obtained by the phaseless AFQMC from large supercells is in very good agreement with experiment.

cond-mat.mtrl-sci↗

arXiv2008

Excited state calculations using phaseless auxiliary-field quantum Monte Carlo: potential energy curves of low lying C2 singlet states

We show that the recently developed phaseless auxiliary-field quantum Monte Carlo (AFQMC) method can be used to study excited states, providing an alternative to standard quantum chemistry methods. The phaseless AFQMC approach, whose computational cost scales as M^3-M^4 with system size M, has been shown to be among the most accurate many-body methods in ground state calculations. For excited states, prevention of collapse into the ground state and control of the Fermion sign/phase problem are accomplished by the approximate phaseless constraint with a trial wave function. Using the challenging C2 molecule as a test case, we calculate the potential energy curves of the ground and two low-lying singlet excited states. The trial wave function is obtained by truncating complete active space wave functions, with no further optimization. The phaseless AFQMC results using a small basis set are in good agreement with exact full configuration interaction calculations, while those using large basis sets are in good agreement with experimental spectroscopic constants.

physics.comp-ph↗

arXiv2008

Spatially inhomogeneous phase in the two-dimensional repulsive Hubbard model

Using recent advances in auxiliary-field quantum Monte Carlo techniques and the phaseless approximation to control the sign/phase problem, we determine the equation of state in the ground state of the two-dimensional repulsive single-band Hubbard model at intermediate interactions. Shell effects are eliminated and finite-size effects are greatly reduced by boundary condition integration. Spin-spin correlation functions and structure factors are also calculated. In lattice sizes up to $16\times 16$, the results show signal for phase-separation. Upon doping, the system separates into one phase of density $n=1$ (hole-free) and the other at density $n_c$ ($\sim 0.9$). The long-range antiferromagnetic order is coupled to this process, and is lost below $n_c$.

cond-mat.str-el↗