Print Email Facebook Twitter Matrix Product State Simulations of Spin Chains at Finite Temperatures using State Purification Title Matrix Product State Simulations of Spin Chains at Finite Temperatures using State Purification Author Ates, Matthijs (TU Delft Technology, Policy and Management; TU Delft Applied Sciences) Contributor Thijssen, J.M. (mentor) Budko, N.V. (mentor) Otte, A.F. (mentor) Dubbeldam, J.L.A. (mentor) Degree granting institution Delft University of Technology Programme Applied Mathematics | Applied Physics Date 2022-10-13 Abstract The aim of this thesis is to simulate quantum spin chains at a finite temperature. This has been achieved by using purification to write the incoherent thermal states of the spin chain as pure states, after which the matrix product state (MPS) formalism to simulate the spin chain. The influence of temperature on the spin chain has been tested by comparing chain magnetization to the strength of the external magnetic field at different temperatures. Real time evolution has also been applied under the assumption that the time evolution is adiabatic. The results have been compared to the analytical solution found by directly calculating the density matrix. The model is very accurate for imaginary time evolution, which is required to evolve the system to the desired temperature. During real time evolution the results oscillate slightly around the analytical solution, which remains constant. This oscillation is a consequence of model truncation and the Suzuki-Trotter approximation. The effect of allocating more numerical resources to limit this phenomenon is explored, and a method to increase reachable timescales by decreasing entanglement growth in the chain over time is tested and verified. Subject spin chainsMatrix Product Statesstate purificationMPSTEBDfinite temperatures To reference this document use: http://resolver.tudelft.nl/uuid:a204bc58-d73c-437e-8eb5-4e375e3a075d Part of collection Student theses Document type bachelor thesis Rights © 2022 Matthijs Ates Files PDF BEP_Ates_final.pdf 3.55 MB Close viewer /islandora/object/uuid:a204bc58-d73c-437e-8eb5-4e375e3a075d/datastream/OBJ/view