Symmetric U(1) and ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice

Journal Article · Mon Aug 02 00:00:00 EDT 2021 · Physical Review. B

DOI:https://doi.org/10.1103/physrevb.104.054401· OSTI ID:1817427

Liu, Chunxiao  ^[1]; Halász, Gábor B.  ^[2]; Balents, Leon  ^[3]

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1. Univ. of California, Santa Barbara, CA (United States)
2. Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States). Materials Science & Technology Division; Quantum Science Center, Oak Ridge, TN (United States); Univ. of California, Santa Barbara, CA (United States)
3. Univ. of California, Santa Barbara, CA (United States); USA and Canadian Institute for Advanced Research, Toronto, ON (Canada)

The geometrically frustrated three-dimensional pyrochlore lattice has been long predicted to host a quantum spin liquid, an intrinsic long-range entangled state with fractionalized excitations. To date, most proposals for pyrochlore materials have focused on quantum spin ice, a U(1) quantum spin liquid whose only low energy excitations are emergent photons of Maxwell type. Here, we explore the possibility of finding pyrochlore quantum spin liquids whose low energy theories go beyond this standard one. We give a complete classification of symmetric $\mathrm{U}\left(1\right)$ and ${\mathbb{Z}}_2$ spin liquids on the pyrochlore lattice within the projective symmetry group framework for fermionic spinons. We find 18 $\mathrm{U}\left(1\right)$ spin liquids and 28 ${\mathbb{Z}}_2$ spin liquids that preserve pyrochlore space-group symmetry while, upon further imposing time-reversal symmetry, the numbers of classes become 16 and 48, respectively. For each class, the most general symmetry-allowed spinon mean-field Hamiltonian is given. Interestingly, we find that several U(1) spin liquid classes possess an unusual gapless multi-nodal-line structure (“nodal star”) in the spinon bands, which is protected by the projective actions of the threefold rotation and screw symmetries of the pyrochlore space group. Through a simple model, we study the effect of gauge fluctuations on such a nodal star spin liquid and propose that the leading terms in the low temperature specific heat have the scaling form $C/T~\sqrt{T}+\sqrt{T}/lnT$, in contrast to the form $C/T~T^2$ of the standard U(1) pyrochlore spin liquid with gapped spinons.

• Research Organization: Oak Ridge National Laboratory (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE Office of Science (SC), Basic Energy Sciences (BES); National Science Foundation (NSF)
• Grant/Contract Number: AC05-00OR22725; FG02-08ER46524; PHY-1748958
• OSTI ID: 1817427
• Journal Information: Physical Review. B, Vol. 104, Issue 5; ISSN 2469-9950
• Publisher: American Physical Society (APS)
• Country of Publication: United States
• Language: English

Related Subjects

75 CONDENSED MATTER PHYSICS
SUPERCONDUCTIVITY AND SUPERFLUIDITY
crystal symmetry
fractionalization
frustrated magnetism
magnetism
quantum spin liquid
spin liquid