Making Trotters Sprint: A Variational Imaginary Time Ansatz for Quantum Many-body Systems

Understand

We introduce a variational wavefunction for many-body ground states that involves imaginary time evolution with two different Hamiltonians in an alternating fashion with variable time intervals.

• We successfully apply the ansatz on the one- and two-dimensional transverse-field Ising model and systematically study its scaling for the one-dimensional model at criticality.
• We find the total imaginary time required scales logarithmically with system size, in contrast to the linear scaling in conventional Quantum Monte Carlo.
• We suggest this is due to unique dynamics permitted by alternating imaginary time evolution, including the exponential growth of bipartite entanglement.