Flow equations for cold Bose gases

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.

References in corpus (5)

• The density-matrix renormalization group in the age of matrix product states
• The Magnus expansion and some of its applications
• Recent developments in no-core shell-model calculations
• In-Medium Similarity Renormalization Group for Nuclei
• Analytical approach to the Bose polaron problem in one dimension

Cited by in corpus (9)

• Few-body Bose gases in low dimensions -- a laboratory for quantum dynamics
• Impurities in a one-dimensional Bose gas: the flow equation approach
• Magnetic impurity in a one-dimensional few-fermion system
• In-medium bound states of two bosonic impurities in a one-dimensional Fermi gas
• A modular implementation of an effective interaction approach for harmonically trapped fermions in 1D
• Artificial atoms from cold bosons in one dimension
• Comparison of renormalized interactions using one-dimensional few-body systems as a testbed
• Emergence of a Bose polaron in a small ring threaded by the Aharonov-Bohm flux
• Generalized Gross-Pitaevskii Equation for 2D Bosons with Attractive Interactions