Efficient Study of Finite Temperature Dynamics using Isometrically Compressed Purification MPS

A standard approach for studying quantum systems at finite temperature is to represent the thermal density matrix as a purification matrix product state (MPS), a pure state with additional ancilla degrees of freedom. The increased bond dimension due to the ancilla degrees of freedom makes the study of low temperature physics computationally expensive. Here, inspired by the unitary gauge freedom on the ancilla legs and algorithms introduced in the context of two-dimensional isometric tensor networks, we demonstrate that the ancillas can be dynamically discarded as the purification MPS is cooled from infinite temperature towards the ground state. This approach produces a lower bond dimension purification MPS than achievable with existing methods. Coupled with a novel sampling scheme to extract independently distributed computational-basis "snapshots" from a purification MPS, this method can be used to simulate and benchmark cold atom and quantum computing experiments in which individual atoms/qubits are projectively measured.