Interactions and the θ [theta] term in one-dimensional gapped systems
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Author(s)
Mulligan, Michael
Date Issued
May 2011
Journal
Physical review B
Publisher
American Physical Society
Citation
Mulligan, Michael. “Interactions and the Θ [theta] Term in One-dimensional Gapped Systems.” Physical Review B 83.20 (2011) : n. pag. ©2011 American Physical Society
Version
Final published version
Abstract
We study how the θ [theta] term is affected by interactions in certain one-dimensional gapped systems that preserve charge conjugation, parity, and time-reversal invariance. We exploit the relation between the chiral anomaly of a fermionic system and the classical shift symmetry of its bosonized dual. The vacuum expectation value of the dual boson is identified with the value of the θ [theta] term for the corresponding fermionic system. Two (related) examples illustrate the identification. We first consider the massive Luttinger liquid and find the θ [theta] term to be insensitive to the strength of the interaction. Next we study the continuum limit of the Heisenberg XXZ spin-1/2 chain, perturbed by a second nearest-neighbor spin interaction. For a certain range of the XXZ anisotropy, we find that we can tune between two distinct sets of topological phases by varying the second nearest-neighbor coupling. In the first we find the standard vacua at θ=0,π [theta = 0, pi], while the second contains vacua that spontaneously break charge conjugation and parity with fractional θ/π=1/2,3/2 [0/pi = 1/2, 3/2]. We also study quantized pumping in both examples following recent work.
MIT Department
Massachusetts Institute of Technology. Center for Theoretical Physics
Massachusetts Institute of Technology. Laboratory for Nuclear Science
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DOI of Published Version
https://doi.org/10.1103/PhysRevB.83.205110
