Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing

Phien, HN; Bengua, JA; Tuan, HD; Corboz, P; Orús, R

Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing

Phien, HN Bengua, JA

Tuan, HD

Corboz, P Orús, R

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Publication Type:: Journal Article
Citation:: Physical Review B - Condensed Matter and Materials Physics, 2015, 92 (3)
Issue Date:: 2015-07-24

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Field	Value	Language
dc.contributor.author	Phien, HN	en_US
dc.contributor.author	Bengua, JA https://orcid.org/0000-0001-9375-0449	en_US
dc.contributor.author	Tuan, HD https://orcid.org/0000-0003-0292-6061	en_US
dc.contributor.author	Corboz, P	en_US
dc.contributor.author	Orús, R	en_US
dc.date.issued	2015-07-24	en_US
dc.identifier.citation	Physical Review B - Condensed Matter and Materials Physics, 2015, 92 (3)	en_US
dc.identifier.issn	1098-0121	en_US
dc.identifier.uri	http://hdl.handle.net/10453/41666
dc.description.abstract	© 2015 American Physical Society. ©2015 American Physical Society. The infinite projected entangled pair states (iPEPS) algorithm [J. Jordan, Phys. Rev. Lett. 101, 250602 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.250602] has become a useful tool in the calculation of ground-state properties of two-dimensional quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings and (ii) improved overall stability. In addition, we extend the application of the local gauge fixing, successfully implemented for finite-size PEPS [M. Lubasch, Phys. Rev. B 90, 064425 (2014)PRBMDO1098-012110.1103/PhysRevB.90.064425], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method but also accelerates the convergence of the alternating least-squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground-state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.	en_US
dc.relation	http://purl.org/au-research/grants/arc/DP130104617
dc.relation.ispartof	Physical Review B - Condensed Matter and Materials Physics	en_US
dc.relation.isbasedon	10.1103/PhysRevB.92.035142	en_US
dc.subject.classification	Fluids & Plasmas	en_US
dc.title	Infinite projected entangled pair states algorithm improved: Fast full update and gauge fixing	en_US
dc.type	Journal Article
utslib.citation.volume	3	en_US
utslib.citation.volume	92	en_US
utslib.for	0903 Biomedical Engineering	en_US
utslib.for	0906 Electrical and Electronic Engineering	en_US
utslib.for	02 Physical Sciences	en_US
utslib.for	03 Chemical Sciences	en_US
utslib.for	09 Engineering	en_US
pubs.embargo.period	Not known	en_US
pubs.organisational-group	/University of Technology Sydney
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology
pubs.organisational-group	/University of Technology Sydney/Faculty of Engineering and Information Technology/School of Electrical and Data Engineering
pubs.organisational-group	/University of Technology Sydney/Students
utslib.copyright.status	open_access
pubs.issue	3	en_US
pubs.publication-status	Published	en_US
pubs.volume	92	en_US

Abstract:

© 2015 American Physical Society. ©2015 American Physical Society. The infinite projected entangled pair states (iPEPS) algorithm [J. Jordan, Phys. Rev. Lett. 101, 250602 (2008)PRLTAO0031-900710.1103/PhysRevLett.101.250602] has become a useful tool in the calculation of ground-state properties of two-dimensional quantum lattice systems in the thermodynamic limit. Despite its many successful implementations, the method has some limitations in its present formulation which hinder its application to some highly entangled systems. The purpose of this paper is to unravel some of these issues, in turn enhancing the stability and efficiency of iPEPS methods. For this, we first introduce the fast full update scheme, where effective environment and iPEPS tensors are both simultaneously updated (or evolved) throughout time. As we shall show, this implies two crucial advantages: (i) dramatic computational savings and (ii) improved overall stability. In addition, we extend the application of the local gauge fixing, successfully implemented for finite-size PEPS [M. Lubasch, Phys. Rev. B 90, 064425 (2014)PRBMDO1098-012110.1103/PhysRevB.90.064425], to the iPEPS algorithm. We see that the gauge fixing not only further improves the stability of the method but also accelerates the convergence of the alternating least-squares sweeping in the (either "full" or "fast full") tensor update scheme. The improvement in terms of computational cost and stability of the resulting "improved" iPEPS algorithm is benchmarked by studying the ground-state properties of the quantum Heisenberg and transverse-field Ising models on an infinite square lattice.

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