Tangent-space methods for uniform matrix product states
Laurens Vanderstraeten, Jutho Haegeman, Frank Verstraete
SciPost Phys. Lect. Notes 7 (2019) · published 15 January 2019
- doi: 10.21468/SciPostPhysLectNotes.7
- Submissions/Reports
Abstract
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.
TY - JOUR
PB - SciPost Foundation
DO - 10.21468/SciPostPhysLectNotes.7
TI - Tangent-space methods for uniform matrix product states
PY - 2019/01/15
UR - https://www.scipost.org/SciPostPhysLectNotes.7
JF - SciPost Physics Lecture Notes
JA - SciPost Phys. Lect. Notes
SP - 7
A1 - Vanderstraeten, Laurens
AU - Haegeman, Jutho
AU - Verstraete, Frank
AB - 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.
ER -
@Article{10.21468/SciPostPhysLectNotes.7,
title={{Tangent-space methods for uniform matrix product states}},
author={Laurens Vanderstraeten and Jutho Haegeman and Frank Verstraete},
journal={SciPost Phys. Lect. Notes},
pages={7},
year={2019},
publisher={SciPost},
doi={10.21468/SciPostPhysLectNotes.7},
url={https://scipost.org/10.21468/SciPostPhysLectNotes.7},
}
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Authors / Affiliations: mappings to Contributors and Organizations
See all Organizations.- 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])