Field-Theoretic Simulations of Fully-Fluctuating Spin Lattices at Finite Temperature

We explore the equilibrium behavior of quantum spin-1/2 lattice models at finite temperature using approximation-free field-theoretic methods.  Other exact methods for simulating spins, such as quantum Monte Carlo or Density Matrix Renormalization Group (DMRG), either crumble under the sign problem inherent to many frustrated spin models or are limited to low site densities and 1D-like geometries, respectively. To overcome these challenges, this work presents a new approach that 1) makes an exact transformation from spins to Schwinger Bosons and 2) leverages our previous numerical framework that uses complex Langevin dynamics to sample fluctuating bosonic coherent states field theories at finite temperature both efficiently and accurately. We apply this approach to fully-fluctuating quantum Heisenberg models and validate our results by comparison with single spin and 1D spin chain references. We display the method’s ability to predict thermodynamic averages at finite temperature and discuss numerical stability limitations.