Geometry and the hidden order of Luttinger liquids: the universality of squeezed space

Kruis, H. V., McCulloch, I. P., Nussinov, Z. and Zaanen, J. (2004) Geometry and the hidden order of Luttinger liquids: the universality of squeezed space. Physical Review B, 70 7: 075109.1-075109.21. doi:10.1103/PhysRevB.70.075109

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Author Kruis, H. V.
McCulloch, I. P.
Nussinov, Z.
Zaanen, J.
Title Geometry and the hidden order of Luttinger liquids: the universality of squeezed space
Journal name Physical Review B   Check publisher's open access policy
ISSN 1098-0121
Publication date 2004-08
Sub-type Article (original research)
DOI 10.1103/PhysRevB.70.075109
Open Access Status File (Publisher version)
Volume 70
Issue 7
Start page 075109.1
End page 075109.21
Total pages 21
Place of publication College Park, MD, United States
Publisher American Physical Society
Language eng
Formatted abstract
We present the case where Luttinger liquids are characterized by a form of hidden order which is similar, but distinct in some crucial regards, to the hidden order characterizing spin-1 Heisenberg chains. We construct a string correlator for the Luttinger liquid which is similar to the string correlator constructed by den Nijs and Rommelse for the spin chain. We reanalyze the spin one chain, introducing a precise formulation of the geometrical principle behind the so-called "squeezed space" construction, to demonstrate that the physics at long wavelength can be reformulated in terms of a Z2 gauge theory. Peculiarly, the normal spin chain lives at infinite gauge coupling where it is characterized by deconfinement. We identify the microscopic conditions required for confinement thereby identifying a novel phase of the spin chain. We demonstrate that the Luttinger liquid can be approached in the same general framework. The difference from the spin chain is that the gauge sector is critical in the sense that the Luttinger liquid is at the phase boundary where the Z2 local symmetry emerges. In addition, the "matter" (spin) sector is also critical. We evaluate the string correlator analytically for the strongly coupled Hubbard model and we further demonstrate that the squeezed space structure is still present even in the noninteracting fermion gas. This adds new insights to the meaning of bosonization. These structures are hard wired in the mathematical structure of bosonization and this becomes obvious by considering string correlators. Numerical results are presented for the string correlator using a non-abelian version of the density matrix renormalization group algorithm, confirming in detail the expectations following from the theory. We conclude with some observations regarding the generalization of bosonization to higher dimensions.
Keyword Luttinger liquids
Heisenberg chains
Q-Index Code C1
Q-Index Status Provisional Code
Institutional Status Non-UQ

Document type: Journal Article
Sub-type: Article (original research)
Collection: School of Mathematics and Physics
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Citation counts: TR Web of Science Citation Count  Cited 20 times in Thomson Reuters Web of Science Article | Citations
Scopus Citation Count Cited 16 times in Scopus Article | Citations
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