In these lecture notes we give a technical overview of tangent-space methods for matrix product states in the thermodynamic limit. We introduce the manifold of uniform matrix product states, show how to compute different types of observables, and discuss the concept of a tangent space. We explain how to variationally optimize ground-state approximations, implement real-time evolution and describe elementary excitations for a given model Hamiltonian. Also, we explain how matrix product states approximate fixed points of one-dimensional transfer matrices. We show how all these methods can be translated to the language of continuous matrix product states for one-dimensional field theories. We conclude with some extensions of the tangent-space formalism and with an outlook to new applications.
Cited by 3
Victor V. Albert, Asymptotics of quantum channels: conserved quantities, an adiabatic limit, and matrix product states
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Laurens Vanderstraeten et al., Simulating excitation spectra with projected entangled-pair states
Phys. Rev. B 99, 165121 (2019) [Crossref]
Román Orús, Tensor networks for complex quantum systems
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- Austrian Science Fund (FWF) (through Organization: Fonds zur Förderung der wissenschaftlichen Forschung / FWF Austrian Science Fund [FWF])
- European Research Council [ERC]
- Fonds Wetenschappelijk Onderzoek (FWO) (through Organization: Fonds voor Wetenschappelijk Onderzoek - Vlaanderen / Research Foundation - Flanders [FWO])