An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
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| Main Authors: | , , , , |
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| Format: | Preprint |
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2023
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| _version_ | 1866916387188899840 |
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| author | Naumann, Jan Weerda, Erik Lennart Rizzi, Matteo Eisert, Jens Schmoll, Philipp |
| author_facet | Naumann, Jan Weerda, Erik Lennart Rizzi, Matteo Eisert, Jens Schmoll, Philipp |
| contents | Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2308_12358 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation Naumann, Jan Weerda, Erik Lennart Rizzi, Matteo Eisert, Jens Schmoll, Philipp Strongly Correlated Electrons Computational Physics Quantum Physics Tensor networks capture large classes of ground states of phases of quantum matter faithfully and efficiently. Their manipulation and contraction has remained a challenge over the years, however. For most of the history, ground state simulations of two-dimensional quantum lattice systems using (infinite) projected entangled pair states have relied on what is called a time-evolving block decimation. In recent years, multiple proposals for the variational optimization of the quantum state have been put forward, overcoming accuracy and convergence problems of previously known methods. The incorporation of automatic differentiation in tensor networks algorithms has ultimately enabled a new, flexible way for variational simulation of ground states and excited states. In this work we review the state-of-the-art of the variational iPEPS framework, providing a detailed introduction to automatic differentiation, a description of a general foundation into which various two-dimensional lattices can be conveniently incorporated, and demonstrative benchmarking results. |
| title | An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation |
| topic | Strongly Correlated Electrons Computational Physics Quantum Physics |
| url | https://arxiv.org/abs/2308.12358 |