Post-Matrix Product State Methods: To tangent space and beyond

Abstract

We develop in full detail the formalism of tangent states to the manifold of matrix product states, and show how they naturally appear in studying time-evolution, excitations and spectral functions. We focus on the case of systems with translation invariance in the thermodynamic limit, where momentum is a well defined quantum number. We present some new illustrative results and discuss analogous constructions for other variational classes. We also discuss generalizations and extensions beyond the tangent space, and give a general outlook towards post matrix product methods.

40 pages, 8 figures

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• Lieb-Robinson bounds and the generation of correlations and topological quantum order
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• Holographic quantum states
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• Quantum spin nematics, dimerization, and deconfined criticality in quasi-one dimensional spin-1 magnets
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Cited by in corpus (147)

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• Information geometry and local asymptotic normality for multi-parameter estimation of quantum Markov dynamics
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• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
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• High Harmonic Generation in Two-Dimensional Mott Insulators
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