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arXiv · 1804.04130

$Z_2$ fractionalized phases of a solvable, disordered, $t$-$J$ model

Wenbo Fu·Yingfei Gu·Subir Sachdev·Grigory Tarnopolsky
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Abstract

We describe the phases of a solvable $t$-$J$ model of electrons with infinite-range, and random, hopping and exchange interactions, similar to those in the Sachdev-Ye-Kitaev models. The electron fractionalizes, as in an `orthogonal metal', into a fermion $f$ which carries both the electron spin and charge, and a boson $ϕ$. Both $f$ and $ϕ$ carry emergent $\mathbb{Z}_2$ gauge charges. The model has a phase in which the $ϕ$ bosons are gapped, and the $f$ fermions are gapless and critical, and so the electron spectral function is gapped. This phase can be considered as a toy model for the underdoped cuprates. The model also has an extended, critical, `quasi-Higgs' phase where both $ϕ$ and $f$ are gapless, and the electron operator $\sim f ϕ$ has a Fermi liquid-like $1/τ$ propagator in imaginary time, $τ$. So while the electron spectral function has a Fermi liquid form, other properties are controlled by $\mathbb{Z}_2$ fractionalization and the anomalous exponents of the $f$ and $ϕ$ excitations. This `quasi-Higgs' phase is proposed as a toy model of the overdoped cuprates. We also describe the critical state separating these two phases.

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Wenbo Fu, Yingfei Gu, Subir Sachdev, Grigory Tarnopolsky. 2018-04-11. $Z_2$ fractionalized phases of a solvable, disordered, $t$-$J$ model. https://doi.org/10.1103/physrevb.98.075150

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