Instabilities of a U(1) quantum spin liquid in disordered non-Kramers pyrochlores

Abstract

Quantum spin liquids (QSLs) are exotic phases of matter exhibiting long-range entanglement and supporting emergent gauge fields. A vigorous search for experimental realizations of these states has identified several materials with properties hinting at QSL physics. A key issue in understanding these QSL candidates is often the interplay of weak disorder of the crystal structure with the spin liquid state. It has recently been pointed out that in at least one important class of candidate QSLs - pyrochlore magnets based on non-Kramers ions such as Pr${}^{3+}$ or Tb${}^{3+}$- structural disorder can actually promote a $U(1)$ QSL ground state. Here we set this proposal on a quantitative footing by analyzing the stability of the QSL state in the minimal model for these systems: a random transverse field Ising model. We consider two kinds of instability, which are relevant in different limits of the phase diagram: condensation of spinons and confinement of the $U(1)$ gauge fields. Having obtained stability bounds on the QSL state we apply our results directly to the disordered candidate QSL Pr${}_2$Zr${}_2$O${}_7$. We find that the available data for currently studied samples of Pr${}_2$Zr${}_2$O${}_7$ is most consistent with it a ground state outside the spin liquid regime, in a paramagnetic phase with quadrupole moments near saturation due to the influence of structural disorder.

Significant revisions including new calculation of confinement instability of the QSL. Accepted for publication in Physical Review Letters

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• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
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• Pyrochlore U(1) spin liquid of mixed symmetry enrichments in magnetic fields
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• Thermodynamics of the dipole-octupole pyrochlore magnet Ce${}_2$Hf${}_2$O${}_7$ in applied magnetic fields
• Traversing the pyrochlore stability diagram; microwave-assisted synthesis and discovery of mixed B-site Ln${}_2$InSbO${}_7$ family
• Revisiting spin ice physics in the ferromagnetic Ising pyrochlore Pr${}_2$Sn${}_2$O${}_7$
• 2-Form U(1) Spin Liquids: Classical Model and Quantum Aspects
• Collective magnetic state induced by charge disorder in the non-Kramers rare-earth pyrochlore Tb${}_2$ScNbO${}_7$
• L-based numerical linked cluster expansion for square lattice models
• Quantum Spin Liquids in Pyrochlore Magnets With Non-Kramers Local Moments
• Confinement, reduced entanglement, and spin-glass order in a random quantum spin-ice model
• Influence of controlled disorder on the dipolar spin ice state of Ho-based pyrochlores
• Quantum Spin Liquids Stabilized by Disorder in Non-Kramers Pyrochlores
• Magnetostriction in the $J$-$K$-$\Gamma$ model: Application of the numerical linked cluster expansion
• Random Transverse Field Effects on Magnetic Noise in Spin Systems
• Excitation spectrum and low-temperature magnetism in disordered defect-fluorite Ho2Zr2O7
• Disorder-induced proximate quantum spin ice phase in Pr2Sn2O7