DOI: 10.1088/1742-5468/2005/09/p09012. Mapping local Hamiltonians of fermions to local Hamiltonians of spins

Mapping local Hamiltonians of fermions to local Hamiltonians of spins

10.1088/1742-5468/2005/09/p09012

Crossref journal-article

IOP Publishing

Journal of Statistical Mechanics: Theory and Experiment (266)

Abstract

We show how to map local fermionic problems onto local spin problems on a lattice in any dimension. The main idea is to introduce auxiliary degrees of freedom, represented by Majorana fermions, which allow us to extend the Jordan–Wigner transformation to dimensions higher than one. We also discuss the implications of our results in the numerical investigation of fermionic systems.

Bibliography

Verstraete, F., & Cirac, J. I. (2005). Mapping local Hamiltonians of fermions to local Hamiltonians of spins. Journal of Statistical Mechanics: Theory and Experiment, 2005(09), P09012âP09012.

Authors 2

F Verstraete (first)
J I Cirac (additional)

References 24 Referenced 153

10.1007/BF01331938 / Z. Phys. (1928)
10.1006/aphy.2002.6254 / Ann. Phys., NY (2002)
{'year': '2004', 'key': '3-1'} (2004)
10.1103/PhysRevLett.88.011602 / Phys. Rev. Lett. (2002)
10.1103/PhysRevB.67.245316 / Phys. Rev. (2003)
10.1103/PhysRevD.68.065003 / Phys. Rev. (2003)
10.1103/PhysRevB.71.045110 / Phys. Rev. (2005)
{'year': '2004', 'key': '8-1'} (2004)
10.1016/j.aop.2004.07.001 / Ann. Phys., NY (2005)
{'year': '2004', 'key': '10-1'} (2004)
10.1103/PhysRevLett.71.666 / Phys. Rev. Lett. (1993)
10.1016/0550-3213(94)90402-2 / Nucl. Phys. (1994)
10.1103/PhysRevD.50.3987 / Phys. Rev. (1994)
10.1103/PhysRevLett.90.227902 / Phys. Rev. Lett. (2003)
10.1103/PhysRevLett.94.060503 / Phys. Rev. Lett. (2005)
10.1016/j.physleta.2005.01.060 / Phys. Lett. (2005)
{'year': '2005', 'key': '17-1'} (2005)
10.1103/PhysRevA.65.042101 / Phys. Rev. (2002)
10.1103/PhysRevLett.92.060402 / Phys. Rev. Lett. (2004)
10.1016/S0003-4916(02)00018-0 / Ann. Phys., NY (2003)
10.1103/PhysRevB.41.9377 / Phys. Rev. (1990)
10.1103/RevModPhys.47.773 / Rev. Mod. Phys. (1975)
{'year': '2005', 'key': '23-1'} (2005)
{'year': '2005', 'key': '24-1'} (2005)

Dates

Type	When
Created	19 years, 11 months ago (Sept. 29, 2005, 11:13 p.m.)
Deposited	8 months, 3 weeks ago (Dec. 12, 2024, 6:14 a.m.)
Indexed	1 week, 2 days ago (Aug. 26, 2025, 2:36 a.m.)
Issued	20 years ago (Sept. 1, 2005)
Published	20 years ago (Sept. 1, 2005)
Published Online	19 years, 11 months ago (Sept. 29, 2005)
Published Print	20 years ago (Sept. 1, 2005)

Funders 0

None

BibTeX

@article{Verstraete_2005, title={Mapping local Hamiltonians of fermions to local Hamiltonians of spins}, volume={2005}, ISSN={1742-5468}, url={http://dx.doi.org/10.1088/1742-5468/2005/09/p09012}, DOI={10.1088/1742-5468/2005/09/p09012}, number={09}, journal={Journal of Statistical Mechanics: Theory and Experiment}, publisher={IOP Publishing}, author={Verstraete, F and Cirac, J I}, year={2005}, month=sep, pages={P09012–P09012} }

JSON

{
  "indexed": {
    "date-parts": [
      [
        2025,
        8,
        26
      ]
    ],
    "date-time": "2025-08-26T06:36:34Z",
    "timestamp": 1756190194292,
    "version": "3.30.2"
  },
  "reference-count": 24,
  "publisher": "IOP Publishing",
  "issue": "09",
  "license": [
    {
      "start": {
        "date-parts": [
          [
            2005,
            9,
            29
          ]
        ],
        "date-time": "2005-09-29T00:00:00Z",
        "timestamp": 1127952000000
      },
      "content-version": "vor",
      "delay-in-days": 28,
      "URL": "https://iopscience.iop.org/page/copyright"
    },
    {
      "start": {
        "date-parts": [
          [
            2005,
            9,
            29
          ]
        ],
        "date-time": "2005-09-29T00:00:00Z",
        "timestamp": 1127952000000
      },
      "content-version": "tdm",
      "delay-in-days": 28,
      "URL": "https://iopscience.iop.org/info/page/text-and-data-mining"
    }
  ],
  "content-domain": {
    "domain": [
      "iopscience.iop.org"
    ],
    "crossmark-restriction": false
  },
  "published-print": {
    "date-parts": [
      [
        2005,
        9,
        1
      ]
    ]
  },
  "abstract": "<jats:p>We show how to map local fermionic problems onto local spin problems on a lattice in any\ndimension. The main idea is to introduce auxiliary degrees of freedom, represented by\nMajorana fermions, which allow us to extend the Jordan\u2013Wigner transformation to\ndimensions higher than one. We also discuss the implications of our results in the numerical\ninvestigation of fermionic systems.</jats:p>",
  "DOI": "10.1088/1742-5468/2005/09/p09012",
  "type": "journal-article",
  "created": {
    "date-parts": [
      [
        2005,
        9,
        30
      ]
    ],
    "date-time": "2005-09-30T03:13:52Z",
    "timestamp": 1128050032000
  },
  "page": "P09012-P09012",
  "update-policy": "https://doi.org/10.1088/crossmark-policy",
  "source": "Crossref",
  "is-referenced-by-count": 153,
  "title": "Mapping local Hamiltonians of fermions to local Hamiltonians of spins",
  "prefix": "10.1088",
  "volume": "2005",
  "author": [
    {
      "given": "F",
      "family": "Verstraete",
      "sequence": "first",
      "affiliation": []
    },
    {
      "given": "J I",
      "family": "Cirac",
      "sequence": "additional",
      "affiliation": []
    }
  ],
  "member": "266",
  "published-online": {
    "date-parts": [
      [
        2005,
        9,
        29
      ]
    ]
  },
  "reference": [
    {
      "key": "1-1",
      "doi-asserted-by": "publisher",
      "first-page": "631",
      "DOI": "10.1007/BF01331938",
      "volume": "47",
      "year": "1928",
      "journal-title": "Z. Phys.",
      "ISSN": "https://id.crossref.org/issn/1434-6001",
      "issn-type": "print"
    },
    {
      "key": "2-1",
      "doi-asserted-by": "publisher",
      "first-page": "210",
      "DOI": "10.1006/aphy.2002.6254",
      "volume": "298",
      "year": "2002",
      "journal-title": "Ann. Phys., NY",
      "ISSN": "https://id.crossref.org/issn/0003-4916",
      "issn-type": "print"
    },
    {
      "year": "2004",
      "key": "3-1"
    },
    {
      "key": "4-1",
      "doi-asserted-by": "publisher",
      "first-page": "011602",
      "DOI": "10.1103/PhysRevLett.88.011602",
      "volume": "88",
      "year": "2002",
      "journal-title": "Phys. Rev. Lett.",
      "ISSN": "https://id.crossref.org/issn/0031-9007",
      "issn-type": "print"
    },
    {
      "key": "5-1",
      "doi-asserted-by": "publisher",
      "first-page": "245316",
      "DOI": "10.1103/PhysRevB.67.245316",
      "volume": "67",
      "year": "2003",
      "journal-title": "Phys. Rev.",
      "ISSN": "https://id.crossref.org/issn/0163-1829",
      "issn-type": "print"
    },
    {
      "key": "6-1",
      "doi-asserted-by": "publisher",
      "first-page": "065003",
      "DOI": "10.1103/PhysRevD.68.065003",
      "volume": "68",
      "year": "2003",
      "journal-title": "Phys. Rev.",
      "ISSN": "https://id.crossref.org/issn/0556-2821",
      "issn-type": "print"
    },
    {
      "key": "7-1",
      "doi-asserted-by": "publisher",
      "first-page": "045110",
      "DOI": "10.1103/PhysRevB.71.045110",
      "volume": "71",
      "year": "2005",
      "journal-title": "Phys. Rev."
    },
    {
      "year": "2004",
      "key": "8-1"
    },
    {
      "key": "9-1",
      "doi-asserted-by": "publisher",
      "first-page": "1",
      "DOI": "10.1016/j.aop.2004.07.001",
      "volume": "316",
      "year": "2005",
      "journal-title": "Ann. Phys., NY",
      "ISSN": "https://id.crossref.org/issn/0003-4916",
      "issn-type": "print"
    },
    {
      "year": "2004",
      "key": "10-1"
    },
    {
      "key": "11-1",
      "doi-asserted-by": "publisher",
      "first-page": "666",
      "DOI": "10.1103/PhysRevLett.71.666",
      "volume": "71",
      "year": "1993",
      "journal-title": "Phys. Rev. Lett.",
      "ISSN": "https://id.crossref.org/issn/0031-9007",
      "issn-type": "print"
    },
    {
      "key": "12-1",
      "doi-asserted-by": "publisher",
      "first-page": "443",
      "DOI": "10.1016/0550-3213(94)90402-2",
      "volume": "424",
      "year": "1994",
      "journal-title": "Nucl. Phys.",
      "ISSN": "https://id.crossref.org/issn/0550-3213",
      "issn-type": "print"
    },
    {
      "key": "13-1",
      "doi-asserted-by": "publisher",
      "first-page": "3987",
      "DOI": "10.1103/PhysRevD.50.3987",
      "volume": "50",
      "year": "1994",
      "journal-title": "Phys. Rev.",
      "ISSN": "https://id.crossref.org/issn/0556-2821",
      "issn-type": "print"
    },
    {
      "key": "14-1",
      "doi-asserted-by": "publisher",
      "first-page": "227902",
      "DOI": "10.1103/PhysRevLett.90.227902",
      "volume": "90",
      "year": "2003",
      "journal-title": "Phys. Rev. Lett.",
      "ISSN": "https://id.crossref.org/issn/0031-9007",
      "issn-type": "print"
    },
    {
      "key": "15-1",
      "doi-asserted-by": "publisher",
      "first-page": "060503",
      "DOI": "10.1103/PhysRevLett.94.060503",
      "volume": "94",
      "year": "2005",
      "journal-title": "Phys. Rev. Lett.",
      "ISSN": "https://id.crossref.org/issn/0031-9007",
      "issn-type": "print"
    },
    {
      "key": "16-1",
      "doi-asserted-by": "publisher",
      "first-page": "22",
      "DOI": "10.1016/j.physleta.2005.01.060",
      "volume": "337",
      "year": "2005",
      "journal-title": "Phys. Lett.",
      "ISSN": "https://id.crossref.org/issn/0375-9601",
      "issn-type": "print"
    },
    {
      "year": "2005",
      "key": "17-1"
    },
    {
      "key": "18-1",
      "doi-asserted-by": "publisher",
      "first-page": "042101",
      "DOI": "10.1103/PhysRevA.65.042101",
      "volume": "65",
      "year": "2002",
      "journal-title": "Phys. Rev.",
      "ISSN": "https://id.crossref.org/issn/1050-2947",
      "issn-type": "print"
    },
    {
      "key": "19-1",
      "doi-asserted-by": "publisher",
      "first-page": "060402",
      "DOI": "10.1103/PhysRevLett.92.060402",
      "volume": "92",
      "year": "2004",
      "journal-title": "Phys. Rev. Lett.",
      "ISSN": "https://id.crossref.org/issn/0031-9007",
      "issn-type": "print"
    },
    {
      "key": "20-1",
      "doi-asserted-by": "publisher",
      "first-page": "2",
      "DOI": "10.1016/S0003-4916(02)00018-0",
      "volume": "303",
      "year": "2003",
      "journal-title": "Ann. Phys., NY",
      "ISSN": "https://id.crossref.org/issn/0003-4916",
      "issn-type": "print"
    },
    {
      "key": "21-1",
      "doi-asserted-by": "publisher",
      "first-page": "9377",
      "DOI": "10.1103/PhysRevB.41.9377",
      "volume": "41",
      "year": "1990",
      "journal-title": "Phys. Rev.",
      "ISSN": "https://id.crossref.org/issn/0163-1829",
      "issn-type": "print"
    },
    {
      "key": "22-1",
      "doi-asserted-by": "publisher",
      "first-page": "773",
      "DOI": "10.1103/RevModPhys.47.773",
      "volume": "47",
      "year": "1975",
      "journal-title": "Rev. Mod. Phys.",
      "ISSN": "https://id.crossref.org/issn/0034-6861",
      "issn-type": "print"
    },
    {
      "year": "2005",
      "key": "23-1"
    },
    {
      "year": "2005",
      "key": "24-1"
    }
  ],
  "container-title": "Journal of Statistical Mechanics: Theory and Experiment",
  "original-title": [],
  "link": [
    {
      "URL": "https://iopscience.iop.org/article/10.1088/1742-5468/2005/09/P09012",
      "content-type": "text/html",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://iopscience.iop.org/article/10.1088/1742-5468/2005/09/P09012/pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "text-mining"
    },
    {
      "URL": "https://iopscience.iop.org/article/10.1088/1742-5468/2005/09/P09012/pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "syndication"
    },
    {
      "URL": "https://iopscience.iop.org/article/10.1088/1742-5468/2005/09/P09012/pdf",
      "content-type": "application/pdf",
      "content-version": "vor",
      "intended-application": "similarity-checking"
    }
  ],
  "deposited": {
    "date-parts": [
      [
        2024,
        12,
        12
      ]
    ],
    "date-time": "2024-12-12T11:14:00Z",
    "timestamp": 1734002040000
  },
  "score": 1,
  "resource": {
    "primary": {
      "URL": "https://iopscience.iop.org/article/10.1088/1742-5468/2005/09/P09012"
    }
  },
  "subtitle": [],
  "short-title": [],
  "issued": {
    "date-parts": [
      [
        2005,
        9,
        1
      ]
    ]
  },
  "references-count": 24,
  "journal-issue": {
    "issue": "09",
    "published-online": {
      "date-parts": [
        [
          2005,
          9,
          29
        ]
      ]
    },
    "published-print": {
      "date-parts": [
        [
          2005,
          9,
          1
        ]
      ]
    }
  },
  "URL": "http://dx.doi.org/10.1088/1742-5468/2005/09/P09012",
  "relation": {},
  "ISSN": [
    "1742-5468"
  ],
  "subject": [],
  "container-title-short": "J. Stat. Mech.",
  "published": {
    "date-parts": [
      [
        2005,
        9,
        1
      ]
    ]
  },
  "assertion": [
    {
      "value": "Mapping local Hamiltonians of fermions to local Hamiltonians of spins",
      "name": "article_title",
      "label": "Article Title"
    },
    {
      "value": "Journal of Statistical Mechanics: Theory and Experiment",
      "name": "journal_title",
      "label": "Journal Title"
    },
    {
      "value": "paper",
      "name": "article_type",
      "label": "Article Type"
    },
    {
      "value": "IOP Publishing Ltd",
      "name": "copyright_information",
      "label": "Copyright Information"
    },
    {
      "value": "2005-08-25",
      "name": "date_received",
      "label": "Date Received",
      "group": {
        "name": "publication_dates",
        "label": "Publication dates"
      }
    },
    {
      "value": "2005-09-17",
      "name": "date_accepted",
      "label": "Date Accepted",
      "group": {
        "name": "publication_dates",
        "label": "Publication dates"
      }
    },
    {
      "value": "2005-09-29",
      "name": "date_epub",
      "label": "Online publication date",
      "group": {
        "name": "publication_dates",
        "label": "Publication dates"
      }
    }
  ]
}