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Tangent-space methods for uniform matrix product states

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arxiv 1810.07006 v3 pith:HY53ELXC submitted 2018-10-16 cond-mat.str-el cond-mat.stat-mechquant-ph

Laurens Vanderstraeten , Jutho Haegeman , Frank Verstraete This is my paper · ORCID
classification cond-mat.str-elcond-mat.stat-mechquant-ph
keywords matrixproductstatesmethodstangent-spaceexplainone-dimensionaluniform
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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.

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Cited by 3 Pith papers

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    Matrix product state simulations of real-time scattering in Ising Field Theory reproduce perturbative results near free fermion and E8 limits and support a conjectured crossover in high-energy elastic versus inelastic...

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    A well-organized five-lecture review of tensor networks (MPS/PEPS/MPO) covering algorithms, phase classification, string-nets, strange correlators, and dualities; it contains no new research results.

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