抄録
We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.
| 本文言語 | English |
|---|---|
| 論文番号 | 221601 |
| ジャーナル | Physical review letters |
| 巻 | 121 |
| 号 | 22 |
| DOI | |
| 出版ステータス | Published - 2018 11月 27 |
ASJC Scopus subject areas
- 物理学および天文学（全般）
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Symmetry Breaking and Lattice Kirigami. / Castro, Eduardo V.; Flachi, Antonino; Ribeiro, Pedro; Vitagliano, Vincenzo.
In: Physical review letters, Vol. 121, No. 22, 221601, 27.11.2018.研究成果: Article › 査読
}
TY - JOUR
T1 - Symmetry Breaking and Lattice Kirigami
AU - Castro, Eduardo V.
AU - Flachi, Antonino
AU - Ribeiro, Pedro
AU - Vitagliano, Vincenzo
N1 - Funding Information: In this Letter we have looked at symmetry breaking in the Hubbard model on a curved 2D manifold constructed by taking the continuum limit of a flat hexagonal lattice deformed by insertion of a defect. The two important features of the story turn out to be the increasing (or decreasing) curvature near the defect and the boundary conditions along the cut. The latter can be assimilated by a nondynamical gauge field. As an example, we have considered the staggered magnetization, the order parameter associated with the discrete sublattice symmetry. Numerical results have shown a surprising increase of the order parameter as the locally curved region is approached. This behavior has been explained by the competition between the effect of curvature and of the emergent gauge field (i.e., boundary conditions) modulated by the conical structure. What we have seen here should be generic and should be expected to occur for different QFT phases and different lattice structures as long as the same geometrical traits are maintained. Here, we have ignored fluctuations of the order parameter; thus, the system is always in the ordered state. However, the way R ˜ and the emergent gauge field appear in the determinant suggests an analogous suppression to what we find here of the onset of a metallic phase. An intriguing possibility is to consider a multidefect configuration and look for arrangements where the competition between the geometry-induced gauge fields and curvature can be adjusted to produce specific order parameter profiles. The effect of curvature on the spontaneous breaking of sublattice symmetry could be used to shed light on the question regarding the semimetal-insulator phase transition in graphene: even though graphene is predicted to be very close to the transition point [40,58] , no experimental signature of the insulating behavior has been found in flat graphene so far [59] . Another promising route in graphene would be the combination of curvature with adatom adsorption in order to enhance symmetry breaking, in particular of magnetic order [60] . Cosmic strings in cosmology [61] or their condensed matter analogue (in liquid crystals, for example [62,63] ) offer a straightforward application of our results. In this case the effect discussed here should locally trigger fermion condensation and offer a mechanism for inducing a superconducting phase at the string. Finally, it is tempting to relate the present ideas to gravity at the Planck scale, where spacetime may be discrete and the presence of defects could cause local changes in the lattice geometry and topology similar to those described here, triggering a form of graviton condensation in the vicinity of these spacetime glitches. We acknowledge the support of the Japanese Ministry of Education, Culture, Sports, Science Program for the Strategic Research Foundation at Private Universities “Topological Science” (Grant No. S1511006) and of JSPS KAKENHI Grant No. 18K03626 for A. F.; the JSPS (Grant No. P17763) for V. V.; the FCT-Portugal (Grant No. UID/CTM/04540/2013) for E. V. C. and P. R.; and the Investigador FCT program (Contract No. IF/00347/2014) for P. R. A. F. is grateful to A. Beekman, K. Fukushima, T. Fujimori, M. Nitta, and R. Yoshii for discussions on various aspects of symmetry breaking and geometry, and to A. Beekman for his feedback on the manuscript. [1] 1 N. D. Birrel and P. 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PY - 2018/11/27
Y1 - 2018/11/27
N2 - We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.
AB - We consider an interacting quantum field theory on a curved two-dimensional manifold that we construct by geometrically deforming a flat hexagonal lattice by the insertion of a defect. Depending on how the deformation is done, the resulting geometry acquires a locally nonvanishing curvature that can be either positive or negative. Fields propagating on this background are forced to satisfy boundary conditions modulated by the geometry and that can be assimilated by a nondynamical gauge field. We present an explicit example where curvature and boundary conditions compete in altering the way symmetry breaking takes place, resulting in a surprising behavior of the order parameter in the vicinity of the defect. The effect described here is expected to be generic and of relevance in a variety of situations.
UR - http://www.scopus.com/inward/record.url?scp=85057847797&partnerID=8YFLogxK
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U2 - 10.1103/PhysRevLett.121.221601
DO - 10.1103/PhysRevLett.121.221601
M3 - Article
C2 - 30547615
AN - SCOPUS:85057847797
VL - 121
JO - Physical Review Letters
JF - Physical Review Letters
SN - 0031-9007
IS - 22
M1 - 221601
ER -