Theory of topological defects and textures in two-dimensional quantum orders with spontaneous symmetry breaking

Journal Article · Fri May 24 00:00:00 EDT 2024 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.109.195165· OSTI ID:2477250

Wang, Yan-Qi ^[1]; Liu, Chunxiao ^[2]; Lu, Yuan-Ming ^[3]

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1. University of California, Berkeley, CA (United States); Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States); University of Maryland, College Park, MD (United States)
2. University of California, Berkeley, CA (United States)
3. The Ohio State University, Columbus, OH (United States)

In this article, we consider two-dimensional (2d) quantum many-body systems with long-range orders, where the only gapless excitations in the spectrum are Goldstone modes of spontaneously broken continuous symmetries. To understand the interplay between classical long-range order of local order parameters and quantum order of long-range entanglement in the ground states, we study the topological point defects and textures of order parameters in such systems. We show that the universal properties of point defects and textures are determined by the remnant symmetry enriched topological order in the symmetry-breaking ground states with a nonfluctuating order parameter, and provide a classification for their properties based on the inflation-restriction exact sequence. We highlight a few phenomena revealed by our theory framework. First, in the absence of intrinsic topological orders, we show a connection between the symmetry properties of point defects and textures to deconfined quantum criticality. Second, when the symmetry-breaking ground state has intrinsic topological orders, we show that the point defects can permute different anyons when braided around. They can also obey projective fusion rules in the sense that multiple vortices can fuse into an Abelian anyon, a phenomenon for which we coin “defect fractionalization.” Finally, we provide a formula to compute the fractional statistics and fractional quantum numbers carried by textures (skyrmions) in Abelian topological orders.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: National Science Foundation (NSF); USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE Office of Science (SC), High Energy Physics (HEP)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 2477250
• Alternate ID(s): OSTI ID: 2474385
• Journal Information: Physical Review. B, Journal Name: Physical Review. B Journal Issue: 19 Vol. 109; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
Defects
Fractionalization
Skyrmions
Strongly correlated systems
Symmetries in condensed matter
Topological phases of matter