Dynamical Hartree-Fock-Bogoliubov Theory of Vortices in Bose-Einstein Condensates at Finite Temperature

Self-consistent Description of Bose-Bose Droplets: Modified Gapless Hartree-Fock-Bogoliubov Method

We define a formalism of a self-consistent description of the ground state of a weakly interacting Bose system, accounting for higher order terms in expansion of energy in the diluteness parameter. The approach is designed to be applied to a Bose-Bose mixture in a regime of weak collapse where quantum fluctuations lead to stabilization of the system and formation of quantum liquid droplets. The approach is based on the Generalized Gross -- Pitaevskii equation accounting for quantum depletion and anomalous density terms. The equation is self-consistently coupled to modified Bogoliubov equations…

Hartree-Fock-Bogoliubov波函数流形中的蒙特卡洛方法

Monte Carlo Methods in the Manifold of Hartree-Fock-Bogoliubov Wave Functions

本文研究在Hartree-Fock-Bogoliubov波函数流形中实现随机游走，以扩展约束路径辅助场量子蒙特卡洛方法至FFLO和三重态配对等复杂超导体系。

Technical aspects of the evaluation of the overlap of Hartree- Fock- Bogoliubov wave functions

Several technical aspects concerning the evaluation of the overlap between two mean field wave functions of the Hartree Fock Bogoliubov type, are discussed. The limit when several orbitals become fully occupied is derived as well as the formula to reduce the dimensionality of the problem when exactly empty orbitals are present. The formalism is also extended to deal with the case where the bases of each of the wave functions are different. Several practical results concerning the evaluation of pfaffians as well as the canonical decomposition of norm overlaps are also discussed in the appendice…

Generalized Hartree-Fock-Bogoliubov Description of the Frohlich Polaron

We adapt the generalized Hartree-Fock-Bogoliubov (HFB) method to an interacting many-phonon system free of impurities. The many-phonon system is obtained from applying the Lee-Low-Pine (LLP) transformation to the Frohlich model which describes a mobile impurity coupled to noninteracting phonons. We specialize our general HFB description of the Frohlich polaron to Bose polarons in quasi-1D cold atom mixtures. The LLP transformed many-phonon system distinguishes itself with an artificial phonon-phonon interaction which is very different from the usual two-body interaction. We use the quasi-one-d…

Hartree-Fock-Bogoliubov theory of trapped one-dimensional imbalanced Fermi systems

Ground state Hartree-Fock-Bogoliubov (HFB) theory is applied to imbalanced spin-1/2 one-dimensional Fermi systems that are spatially confined by either a harmonic or a hard-wall trapping potential. It has been hoped that such systems, which can be realized using ultracold atomic gases, would exhibit the long-sought-after Fulde-Ferrell-Larkin-Ovchinnikov (FFLO) superfluid phase. The HFB formalism generalizes the standard Bogoliubov quasi-particle transformation, by allowing for Cooper pairing to exist between all possible single-particle states, and accounts for the effects of the inhomogeneous…

Contour-time approach to the Bose-Hubbard model in the strong coupling regime: Studying two-point spatio-temporal correlations at the Hartree-Fock-Bogoliubov level

We develop a formalism that allows the study of correlations in space and time in both the superfluid and Mott insulating phases of the Bose-Hubbard Model. Specifically, we obtain a two particle irreducible effective action within the contour-time formalism that allows for both equilibrium and out of equilibrium phenomena. We derive equations of motion for both the superfluid order parameter and two-point correlation functions. To assess the accuracy of this formalism, we study the equilibrium solution of the equations of motion and compare our results to existing strong coupling methods as we…

Phaseless quantum Monte-Carlo approach to strongly correlated superconductors with stochastic Hartree-Fock-Bogoliubov wavefunctions

The so-called phaseless quantum Monte-Carlo method currently offers one of the best performing theoretical framework to investigate interacting Fermi systems. It allows to extract an approximate ground-state wavefunction by averaging independent-particle states undergoing a Brownian motion in imaginary-time. Here, we extend the approach to a random walk in the space of Hartree-Fock-Bogoliubov (HFB) vacua that are better suited for superconducting or superfluid systems. Well-controlled statistical errors are ensured by constraining stochastic paths with the help of a trial wavefunction, also gu…

BCS-BEC crossover in nuclear matter with the relativistic Hartree-Bogoliubov theory

Based on the relativistic Hartree-Bogoliubov theory, the influence of the pairing interaction strength on the di-neutron correlations and the crossover from superfluidity of neutron Cooper pairs in the $^{1}S_{0}$ channel to Bose-Einstein condensation of di-neutron pairs is systematically investigated in the nuclear matter. The bare nucleon-nucleon interaction Bonn-B is taken in the particle-particle channel with an effective factor to simulate the medium effects and take into account the possible ambiguity of pairing force, and the effective interaction PK1 is used in the particle-hole channe…

相互作用费米子的加权Hartree-Fock-Bogoliubov方法：在超冷费米超流体中的应用

Weighted Hartree-Fock-Bogoliubov method for interacting fermions: An application to ultracold Fermi superfluids

针对幺正超流体中因粒子-空穴散射导致的基态能量和化学势发散问题，提出加权Hartree-Fock-Bogoliubov理论，解决相互作用分解通道难题，得到含多通道修正的相图并发现弱相互作用下新超流相。