Effective many-body interactions in one-dimensional dilute Bose gases
Institute of High Technologies, T. Shevchenko National University, Kyiv 03022, Ukraine
Institute of Magnetism NAS of Ukraine and MES of Ukraine, Kyiv 03142, Ukraine
Received March 25, 2020, published online June 22, 2020
We propose a new method of constructing the effective theory for a multicomponent low-dimensional dilute Bose gas. The method is based on obtaining and solving renormalization group equations for all many-body interactions of density-density type in the one-loop approximation. In contrast to the standard approach based on two-body interactions, our method does not rely on the introduction of density-dependent infrared cutoff, and is able to reproduce exactly the leading term in the energy density of the one-dimensional dilute Bose gas, and to obtain the next term with the error of less than 2%.