Path integral and winding number in singular magnetic field

On the Thermodynamics of Fermions at any Temperature based on Parametrized Partition Function

“…Here, we use Eqs. (10) and (11) to calculate the energy of different temperatures for ξ = 0 and ξ = 1 so that one may follow our calculation and method more easily. By reliable interpolation and fitting, we can get two energy functions f 0 (T ) for ξ = 0 and f 1 (T ) for ξ = 1.…”

“…Those methods have been applied to gain valuable insights into the atomic structure; unfortunately though, they treat the quantum correlation and exchange effects in an approximate manner, and being able to take such effects into account is crucial for realistic many body quantum systems. Later on, a numerically exact method based on the path integral formulation of quantum mechanics was developed, known as path integral Monte Carlo/molecular dynamics [1][2][3] , and it has been successfully applied to extract thermodynamic properties of Bose systems from ab initio simulations [4][5][6][7][8][9][10][11][12] . In principle, path integral Monte Carlo/molecular dynamics takes all quantum effects into account but when we try to apply this methodology to fermions, we encounter an insurmountable difficulty known as fermion sign problem [13][14][15][16][17][18][19][20][21][22][23][24][25][26][27] , where the probabilities used for sampling become negative.…”

Path integral molecular dynamics for thermodynamics and Green’s function of ultracold spinor bosons

“…In our PIMD simulation, the number of beads used decreases as temperature increases to ensure numerical stability and assure convergence. Compared with two dimensions with P = 12/T beads in the usual case 30,32,34 , it is worthy to point out that many more beads are needed to assure accuracy and convergence, because the size of phase space has been greatly enlarged compared with two dimensional case. Based on the relation ∆β = β/P and the fact that the evolution operator has been expanded to an order of O(∆β 2 ), we would like to keep ∆β a constant with different β, which leads to the choice P=70/T.…”

“…30 , path integral molecular dynamics (PIMD) and the recursion formula are generalized to calculate Green's function and momentum distribution of single-component bosons. Other recent advances include the application of PIMD to supersolid phase in high-pressure deuterium 31 and bosons in singular magnetic field 32 , and the generalization of PIMD to spin-polarized fermions [33][34][35] . In particular, PIMD was used most recently to consider the fermion sign problem for large fermion system 35 .…”

“…The purpose of the present work is to develop PIMD for two-component bosons with the same intracomponent and intercomponent interaction, and it is straightforward to generalize our method to different intracomponent and intercomponent interactions. Different from previous PIMD simulation 29,30,[32][33][34][35] for identical particles in two dimensions, here we consider spinor bosons in three dimensions and study the number of beads (in PIMD simulation) needed in numerical simulation to achieve numerical convergence. As an example, we consider the thermodynamics of two-component bosons in a three-dimensional harmonic trap.…”