Complex Langevin dynamics and supersymmetric quantum mechanics

Abstract

Using complex Langevin method we probe the possibility of dynamical supersymmetry breaking in supersymmetric quantum mechanics models with complex actions. The models we consider are invariant under the combined operation of parity and time reversal, in addition to supersymmetry. When actions are complex traditional Monte Carlo methods based on importance sampling fail. Models with dynamically broken supersymmetry can exhibit sign problem due to the vanishing of the partition function. Complex Langevin method can successfully evade the sign problem. Our simulations suggest that complex Langevin method can reliably predict the absence or presence of dynamical supersymmetry breaking in these one-dimensional models with complex actions.

Quantum computing for lattice supersymmetry

“…where 𝑚 is the mass while the coefficients 𝑔 and 𝜇 control the strength of interactions between the boson and fermion. For non-zero values of 𝑔 and 𝜇, this system is expected to exhibit dynamical supersymmetry breaking [7]. In Fig.…”

“…This is one of the simplest superpotentials to consider since 𝑊 ( q) = 𝑚 and the bosons and fermions do not interact. No dynamical supersymmetry breaking is expected for this superpotential [7]. The energy spectrum as a function of the cutoff determined via exact diagonalization is plotted in Fig.…”

“…where 𝑚 is the mass of the boson and the coefficient 𝑔 dictates the strength of the interaction between the boson and fermion. For any value of 𝑔 the AHO is also expected to preserve supersymmetry [7].…”

“…This system was recently studied with classical-computing lattice methods by Refs. [6][7][8], which explored dynamical supersymmetry breaking for different superpotentials. Similar supersymmetric matrix models are also under consideration as targets for quantum computing [9][10][11].…”

Complex Langevin simulations for $PT$-symmetric models

“…(The zero-and one-dimensional cousins of this model were studied recently in Refs. [12,13].) We add fermions to the Lagrangian and consider the simplest two-dimensional supersymmetric quantum field theory, the N = 1 Wess-Zumino model.…”