Tangent-space methods for uniform matrix product states

By L. Vanderstraeten, J. Haegeman, Frank Verstraete. SciPost Physics Lecture Notes, 2018

211 citations recorded by the source corpus.

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.

Subfields: Atomic and Molecular Physics, and Optics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/588b1dbbc9c5bec99280039be70680f786ee6292

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Atomic and Molecular Physics, and Optics

1. Frank Verstraete
2. M. Fishman
3. Norbert Schuch
4. E. Stoudenmire
5. Suguru Endo
6. I. Cirac
7. S. White
8. Simon C. Benjamin

In Numerical Analysis

1. M. Fishman
2. E. Stoudenmire
3. S. White
4. Ying Li
5. Frank Verstraete
6. Simon C. Benjamin

In Statistical and Nonlinear Physics

1. E. Stoudenmire
2. Norbert Schuch
3. S. White
4. M. Fishman
5. Suguru Endo
6. Xiao Yuan
7. Simon C. Benjamin
8. Ying Li

Citations in the corpus

• Time-evolution methods for matrix-product states (2019, unknown): “Future developments While one should of course not lose sight of new alternative methods to evaluate excitation spectra[87–91] or Green’s functions[92], the direct evaluation of real-time observables will always find interesting applications.”
• Matrix product states and projected entangled pair states: Concepts, symmetries, theorems (2020, methodology): “Given a specific MPS on the manifold, we can associate a linear subspace to it, namely the tangent space on the manifold (Haegeman et al., 2011; Vanderstraeten et al., 2018).”
• The ITensor Software Library for Tensor Network Calculations (2020, methodology): “Other techniques for computing excited states are planned in the future, such as the quasiparticle MPS ansatz [26,27].”
• Theory of variational quantum simulation (2018, methodology): “Variational simulation is a widely used technique in many-body physics [1–7] and chemistry [8–10].”