Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

Shi, Hao; Zhang, Shiwei

doi:10.1103/physrevb.95.045144

Cited by 24 publications

(22 citation statements)

References 28 publications

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“…The computational manipulations necessary for using such a wave function with the Kohn-Sham plus p-n Hartree Hamiltonian are readily available (see e.g., Ref. 62 ).…”

Section: Discussionmentioning

confidence: 99%

Charge density waves in a quantum plasma

2019

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We analyze the instability of an unpolarized uniform quantum plasma consisting of two oppositely charged fermionic components with varying mass ratios, against charge and spin density waves (CDW's and SDW's). Using density functional theory, we treat each component with the local spin density approximation and a rescaled exchange-correlation functional. Interactions between different components are treated with a mean-field approximation. In both two-and three-dimensions, we find leading unstable CDW modes in the second-order expansion of the energy functional, which would induce the transition to quantum liquid crystals. The transition point and the length of the wave-vector are computed numerically. Discontinuous ranges of the wave-vector are found for different mass ratios between the two components, indicating exotic quantum phase transitions. Phase diagrams are obtained and a scaling relation is proposed to generalize the results to twocomponent fermionic plasmas with any mass scale. We discuss the implications of our results and directions for further improvement in treating quantum plasmas.

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“…The computational manipulations necessary for using such a wave function with the Kohn-Sham plus p-n Hartree Hamiltonian are readily available (see e.g., Ref. 62 ).…”

Section: Discussionmentioning

confidence: 99%

Charge density waves in a quantum plasma

2019

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“…We next outline some algebraic results for suitable matrix elements of operators between a BCS wave function as in (3) and a Slater determinant as in (1). Some of the results have been derived before [18,29] but we include them here to facilitate ensuing discussions. The central object is the overlap matrix:…”

Section: Slater Determinants and Projected Bcs Wave Functionsmentioning

confidence: 99%

“…(If we use BCS trial wave function on both ends of the path, we could alternatively view the formalism as propagating in HFB space, which has been discussed in Ref. [29].) Similarly, the same technique we have discussed can be used in a mean-field context, which can be considered a specialized case of the AFQMC, with only a single path instead of the path integral.…”

Section: B Possible Extensionsmentioning

confidence: 99%

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

2019

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We introduce an efficient and numerically stable technique to make use of a BCS trial wave function in the computation of correlation functions of strongly correlated quantum fermion systems. The technique is applicable to any projection approach involving paths of independent-fermion propagators, for example in mean-field or auxiliary-field quantum Monte Carlo (AFQMC) calculations. Within AFQMC, in the absence of the sign problem, the methodology allows the use of a BCS reference state which can greatly reduce the required imaginary time of projection, and improves Monte Carlo sampling efficiency and statistical accuracy for systems where pairing correlations are important. When the sign problem is present, the approach provides a powerful generalization of the constrained-path AFQMC technique which usually uses Slater determinant trial wave functions. As a demonstration of the capability of the methodology, we present benchmark results for the attractive Hubbard model, both spin-balanced (no sign problem) and with a finite spin polarization (with sign problem). arXiv:1905.05012v1 [cond-mat.str-el]

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“…We note that Hamiltonians which include pairing terms can be treated with an additional generalization, where the walker is extend to Hartree-Fock-Bogoliubov space [49].…”

Section: Generalizations To Socmentioning

confidence: 99%

Accurate computations of Rashba spin-orbit coupling in interacting systems: From the Fermi gas to real materials

Rosenberg

Shi

Zhang

2019

Journal of Physics and Chemistry of Solids

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We describe the treatment of Rashba spin-orbit coupling (SOC) in interacting many-fermion systems within the auxiliary-field quantum Monte Carlo framework, and present a set of illustrative results. These include numerically exact calculations on the ground-state properties of the spin-balanced, attractive twodimensional Fermi gas, as well as a study of a tight-binding Hamiltonian with repulsive interaction. These systems are formally connected via the Hubbard Hamiltonian with SOC, but cover different physics ranging from superfluidity and triplet pairing to SOC in real materials in the presence of strong interactions in localized orbitals. We carry out detailed benchmark studies of the method in the latter case when an approximation is needed to control the sign problem for repulsive Coulomb interactions. The methods presented here provide an approach for predictive computations in materials to study the interplay of SOC and strong correlation.

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Many-body computations by stochastic sampling in Hartree-Fock-Bogoliubov space

Cited by 24 publications

References 28 publications

Charge density waves in a quantum plasma

Charge density waves in a quantum plasma

Calculating ground-state properties of correlated fermionic systems with BCS trial wave functions in Slater determinant path-integral approaches

Accurate computations of Rashba spin-orbit coupling in interacting systems: From the Fermi gas to real materials

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