Isometric tensor network representations of two-dimensional thermal states
Wilhelm Kadow, Frank Pollmann, Michael Knap
Abstract
Tensor networks provide a useful tool to describe low-dimensional complex many-body systems. Finding efficient algorithms to use these methods for finite-temperature simulations in two dimensions is a continuing challenge. Here, we use the class of recently introduced isometric tensor network states, which can also be directly realized with unitary gates on a quantum computer. We utilize a purification ansatz to efficiently represent thermal states of the transverse field Ising model. By performing an imaginary-time evolution starting from infinite temperature, we find that this approach offers a different way with low computational complexity to represent states at finite temperatures.
Topics & Concepts
AnsatzTensor (intrinsic definition)Unitary stateIsing modelImaginary timePhysicsOperator (biology)Class (philosophy)QuantumTensor fieldComputer scienceStatistical physicsTheoretical physicsQuantum mechanicsMathematicsExact solutions in general relativityPure mathematicsQuantum statistical mechanicsArtificial intelligenceChemistrySupersymmetric quantum mechanicsGeneRepressorPolitical scienceBiochemistryLawTranscription factorQuantum many-body systemsPhysics of Superconductivity and MagnetismQuantum and electron transport phenomena