Computing vibrational eigenstates with tree tensor network states (TTNS)
We present how to compute vibrational eigenstates with tree tensor network states (TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on the density matrix renormalization group...
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| Veröffentlicht in: | The Journal of chemical physics 2019-11, Vol.151 (20), p.204102-204102 |
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| container_end_page | 204102 |
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| container_title | The Journal of chemical physics |
| container_volume | 151 |
| creator | Larsson, Henrik R. |
| description | We present how to compute vibrational eigenstates with tree tensor network states
(TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent
Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on
the density matrix renormalization group (DMRG). We apply this to compute the vibrational
spectrum of acetonitrile (CH3CN) to high accuracy and compare TTNSs with matrix
product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme
converges much faster than ML-MCTDH-based optimization. For this particular system, we
found no major advantage of the more general TTNS over MPS. We highlight that for both
TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of
required parameters. We furthermore propose a procedure to find good trees. |
| doi_str_mv | 10.1063/1.5130390 |
| format | Article |
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(TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent
Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on
the density matrix renormalization group (DMRG). We apply this to compute the vibrational
spectrum of acetonitrile (CH3CN) to high accuracy and compare TTNSs with matrix
product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme
converges much faster than ML-MCTDH-based optimization. For this particular system, we
found no major advantage of the more general TTNS over MPS. We highlight that for both
TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of
required parameters. We furthermore propose a procedure to find good trees.</description><identifier>ISSN: 0021-9606</identifier><identifier>EISSN: 1089-7690</identifier><identifier>DOI: 10.1063/1.5130390</identifier><identifier>CODEN: JCPSA6</identifier><language>eng</language><publisher>Melville: American Institute of Physics</publisher><subject>Acetonitrile ; Algorithms ; Eigenvectors ; Mathematical analysis ; Multilayers ; Optimization ; Tensors ; Time dependence</subject><ispartof>The Journal of chemical physics, 2019-11, Vol.151 (20), p.204102-204102</ispartof><rights>Author(s)</rights><rights>2019 Author(s). Published under license by AIP Publishing.</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c395t-758a0bc75540d8ca270a1116474d70d916b4d9f2faa65f305a93c2f6bb48f6963</citedby><cites>FETCH-LOGICAL-c395t-758a0bc75540d8ca270a1116474d70d916b4d9f2faa65f305a93c2f6bb48f6963</cites><orcidid>0000-0002-9417-1518</orcidid></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://pubs.aip.org/jcp/article-lookup/doi/10.1063/1.5130390$$EHTML$$P50$$Gscitation$$H</linktohtml><link.rule.ids>314,776,780,790,4497,27903,27904,76131</link.rule.ids></links><search><creatorcontrib>Larsson, Henrik R.</creatorcontrib><title>Computing vibrational eigenstates with tree tensor network states (TTNS)</title><title>The Journal of chemical physics</title><description>We present how to compute vibrational eigenstates with tree tensor network states
(TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent
Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on
the density matrix renormalization group (DMRG). We apply this to compute the vibrational
spectrum of acetonitrile (CH3CN) to high accuracy and compare TTNSs with matrix
product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme
converges much faster than ML-MCTDH-based optimization. For this particular system, we
found no major advantage of the more general TTNS over MPS. We highlight that for both
TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of
required parameters. We furthermore propose a procedure to find good trees.</description><subject>Acetonitrile</subject><subject>Algorithms</subject><subject>Eigenvectors</subject><subject>Mathematical analysis</subject><subject>Multilayers</subject><subject>Optimization</subject><subject>Tensors</subject><subject>Time dependence</subject><issn>0021-9606</issn><issn>1089-7690</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2019</creationdate><recordtype>article</recordtype><recordid>eNqd0EFLwzAUB_AgCs7pwW9Q8LIJnS9JmzRHGeoE0YPzHNI2mZldM5N0w29v5waCR08P3vvxh_dH6BLDBAOjN3iSYwpUwBEaYChEypmAYzQAIDgVDNgpOgthCQCYk2yAZlO3WnfRtotkY0uvonWtahJtF7oNUUUdkq2N70n0Wiex3zmftDpunf9IDvfRfP78Oj5HJ0Y1QV8c5hC93d_Np7P06eXhcXr7lFZU5DHleaGgrHieZ1AXlSIcFMaYZTyrOdQCszKrhSFGKZYbCrkStCKGlWVWGCYYHaLRPnft3WenQ5QrGyrdNKrVrguSUAKUc5qRnl79oUvX-f69ncK9EULQXo33qvIuBK-NXHu7Uv5LYpC7TiWWh057e723obLxp6v_4Y3zv1Cua0O_ARBRg1Y</recordid><startdate>20191128</startdate><enddate>20191128</enddate><creator>Larsson, Henrik R.</creator><general>American Institute of Physics</general><scope>AAYXX</scope><scope>CITATION</scope><scope>8FD</scope><scope>H8D</scope><scope>L7M</scope><scope>7X8</scope><orcidid>https://orcid.org/0000-0002-9417-1518</orcidid></search><sort><creationdate>20191128</creationdate><title>Computing vibrational eigenstates with tree tensor network states (TTNS)</title><author>Larsson, Henrik R.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c395t-758a0bc75540d8ca270a1116474d70d916b4d9f2faa65f305a93c2f6bb48f6963</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2019</creationdate><topic>Acetonitrile</topic><topic>Algorithms</topic><topic>Eigenvectors</topic><topic>Mathematical analysis</topic><topic>Multilayers</topic><topic>Optimization</topic><topic>Tensors</topic><topic>Time dependence</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Larsson, Henrik R.</creatorcontrib><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><jtitle>The Journal of chemical physics</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Larsson, Henrik R.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Computing vibrational eigenstates with tree tensor network states (TTNS)</atitle><jtitle>The Journal of chemical physics</jtitle><date>2019-11-28</date><risdate>2019</risdate><volume>151</volume><issue>20</issue><spage>204102</spage><epage>204102</epage><pages>204102-204102</pages><issn>0021-9606</issn><eissn>1089-7690</eissn><coden>JCPSA6</coden><abstract>We present how to compute vibrational eigenstates with tree tensor network states
(TTNSs), the underlying ansatz behind the multilayer multiconfiguration time-dependent
Hartree (ML-MCTDH) method. The eigenstates are computed with an algorithm that is based on
the density matrix renormalization group (DMRG). We apply this to compute the vibrational
spectrum of acetonitrile (CH3CN) to high accuracy and compare TTNSs with matrix
product states (MPSs), the ansatz behind the DMRG. The presented optimization scheme
converges much faster than ML-MCTDH-based optimization. For this particular system, we
found no major advantage of the more general TTNS over MPS. We highlight that for both
TTNS and MPS, the usage of an adaptive bond dimension significantly reduces the amount of
required parameters. We furthermore propose a procedure to find good trees.</abstract><cop>Melville</cop><pub>American Institute of Physics</pub><doi>10.1063/1.5130390</doi><tpages>15</tpages><orcidid>https://orcid.org/0000-0002-9417-1518</orcidid><oa>free_for_read</oa></addata></record> |
| fulltext | fulltext |
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| ispartof | The Journal of chemical physics, 2019-11, Vol.151 (20), p.204102-204102 |
| issn | 0021-9606 1089-7690 |
| language | eng |
| recordid | cdi_scitation_primary_10_1063_1_5130390 |
| source | American Institute of Physics (AIP) Journals; Alma/SFX Local Collection |
| subjects | Acetonitrile Algorithms Eigenvectors Mathematical analysis Multilayers Optimization Tensors Time dependence |
| title | Computing vibrational eigenstates with tree tensor network states (TTNS) |
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