Simulation of Finite Temperature Dynamics using Purification MPS

Finite temperature dynamics are difficult to study using Matrix Product States due to the complexity of representing a thermal density matrix. One method for studying systems at finite temperature is to use a purification, in which a mixed density matrix is represented by a pure state MPS at the cost of enlarging the Hilbert space by the addition of ancilla degrees of freedom. In a purification, there exists a gauge freedom as the represented density matrix is invariant under unitary transformations on the ancilla degrees of freedom. In this work, we optimize the purification and exploit this gauge freedom to minimize the entanglement of the purification MPS. Using a global isometry generating procedure recently introduced (arXiv:1902.05100) for a class of 2D tensor network states, we investigate the feasibility of projecting out ancilla degrees of freedom suitably unentangled from the system, which yields a more compact purification representation that is more efficiently simulated.