Fast Tensor Network Imaginary Time Evolution by Implicit Stepping on Logarithmic Grids
For researchers simulating quantum many-body systems, this method drastically accelerates imaginary time evolution, enabling access to large imaginary times with reduced computational cost.
The paper introduces a method for imaginary time evolution of matrix product states that uses logarithmic time grids and A-stable implicit time-stepping, achieving exponential reduction in time steps and several orders of magnitude speedup over standard methods, demonstrated on a Heisenberg spin chain and a single-site Anderson impurity model.
We present a new method for the efficient imaginary time evolution of quantum many-body wavefunctions represented by matrix product states (MPS). We first show that logarithmic time grids are sufficient to resolve long imaginary time dynamics, yielding an exponential reduction in the number of time steps compared with standard approaches. We then show that A-stable implicit time-stepping methods for ordinary differential equations allow stable propagation for any time step size. The resulting scheme requires only matrix-vector products and linear solves, standard operations in the MPS toolbox. We validate our approach with two examples: a Heisenberg spin chain, which we use to demonstrate a speedup of several orders of magnitude over the standard time-dependent variational principle method with uniform time steps, and a single-site Anderson impurity model with a metallic bath, for which propagation to large imaginary times allows one to observe the exponential dependence of the Kondo temperature on the interaction strength.