Abstract
We derive flow equations for cold atomic gases with one macroscopically populated energy level. The generator is chosen such that the ground state decouples from all other states in the system as the renormalization group flow progresses. We propose a self-consistent truncation scheme for the flow equations at the level of three-body operators and show how they can be used to calculate the ground state energy of a general N-body system. Moreover, we provide a general method to estimate the truncation error in the calculated energies. Finally, we test our scheme by benchmarking to the exactly solvable Lieb–Liniger model and find good agreement for weak and moderate interaction strengths.
Highlights
The worlds of many- and few-body physics are generally far apart
The large number of degrees of freedom in many-body systems usually means that various approximations and/or large computational resources are needed to achieve this goal
There is an interesting class of systems that are in between these two extremes. These are finite systems in which the number of particles is sufficiently large for many-body phenomena, such as superfluidity or Bose–Einstein condensation, to emerge [1,2,3]; but they are still small enough to be within reach for numerically exact ab-initio calculations that use microscopic Hamiltonians
Summary
The worlds of many- and few-body physics are generally far apart. In the former, the number of particles is often infinite, while few-body systems normally do not contain more than a handful of particles. There is an interesting class of systems that are in between these two extremes These are finite systems in which the number of particles is sufficiently large for many-body phenomena, such as superfluidity or Bose–Einstein condensation, to emerge [1,2,3]; but they are still small enough to be within reach for numerically exact ab-initio calculations that use microscopic Hamiltonians. The investigation of such finite systems is crucial to understand how many-body phenomena arise from few-body body physics and microscopic interactions of the constituents
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