Interacting Bosons at Finite Angular Momentum Via Complex Langevin

Abstract

Quantum field theories with a complex action suffer from a sign problem in stochastic nonperturbative treatments, making many systems of great interest-such as polarized or mass-imbalanced fermions and QCD at finite baryon density-extremely challenging to treat numerically. Another such system is that of bosons at finite angular momentum; experimentalists have successfully achieved vortex formation in ultracold bosonic atoms, and have measured quantities of interest such as density profiles and the moment of inertia. However, the treatment of superfluids requires the use of complex bosons, making the usual numerical methods unusable. In this work, we apply complex Langevin, a method that has gained much attention in lattice QCD, to the calculation of basic properties of interacting bosons at finite angular momentum. We show preliminary results for the angular momentum and moment of inertia and benchmark calculations in the noninteracting limit.

Complex Langevin simulations and the QCD phase diagram: recent developments

“…Additional uses of complex Langevin outside of QCD related models include superstring-inspired models [32] and quantum many-body studies: rotating bosons [33,34], spin-orbit coupled bosons [35], fermions with repulsive interactions [36], non-zero polarisation [37,38], mass imbalance [39,40], and to determine their virial coefficients [41].…”

Thermodynamics of spin-orbit-coupled bosons in two dimensions from the complex Langevin method

“…One alternative in this scenario is the complex Langevin technique, which has been used to study theories with sign problems such as those with repulsive interactions [24] as well as polarized [25,26] and massimbalanced fermions [27] (see Ref. [28] for a review), finite density QCD with staggered quarks [29][30][31][32], random matrix models [33,34], rotating bosons [35,36], superstringinspired matrix models [37], among others.…”

A lattice pairing-field approach to ultracold Fermi gases

“…Such theories are known to have a sign problem on a spacetime lattice. In order to deal with this sign problem, we employ the complex Langevin (CL) approach, which has been employed before to study relativistic as well as non-relativistic complex scalar field theories [53][54][55]. Moreover, the CL approach has been successfully applied to compute properties of ultracold Fermi gases described by the Hamilton operator (1), see Refs.…”