SAMOP 2023 – scientific programme

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QI: Fachverband Quanteninformation

QI 13: Quantum Simulation

QI 13.7: Talk

Tuesday, March 7, 2023, 12:30–12:45, F428

Time Evolution of Matrix Product States Using Adaptive Subspace Expansion — •Tizian Blatz, Sebastian Paeckel, and Martin Grundner — Arnold Sommerfeld Center of Theoretical Physics, Department of Physics, University of Munich, Theresienstrasse 37, 80333 Munich, Germany

Today's advances in experimentally realizable ultracold-atom-based quantum simulators are tied to the evolution of computational methods ranging from phenomenological approaches to full quantum state descriptions. Matrix product states (MPS) are a prominent numerical state class that has gained popularity due to the success of density-matrix renormalization group (DMRG) algorithms for ground state search. Beyond the ground state, accessing dynamic quantities and finite-temperature states realized in experiments requires methods for a state's evolution in time. Here, we present recent advances in MPS time-evolution methods based on the time-dependent variational principle (TDVP) accompanied by a subspace expansion prescription. Compared to the current state of the art, this method excels in describing challenging initial conditions, global quenches, and long (effective) interaction ranges, which are common, in particular, in (quasi) two-dimensional ultracold-atom setups. We highlight both technical aspects of the method as well as prospective use cases in the cold-atom context.