Fractional charges in pyrochlore lattices

The "spin ice" state found in the rare earth pyrochlore magnets Ho2Ti2O7 and Dy2Ti2O7 offers a beautiful realisation of classical magnetostatics, complete with magnetic monopole excitations. It has been suggested that in "quantum spin ice" materials, quantum-mechanical tunnelling between different ice configurations could convert the magnetostatics of spin ice into a quantum spin liquid which realises a fully dynamical, latticeanalogue of quantum electromagnetism. Here we explore how such a state might manifest itself in experiment, within the minimal microscopic model of a such a quantum spin ice. We develop a lattice field theory for this model, and use this to make explicit predictions for the dynamical structure factor which would be observed in neutron scattering experiments on a quantum spin ice. We find that "pinch points", which are the signal feature of a classical spin ice, fade away as a quantum ice is cooled to its zero-temperature ground state. We also make explicit predictions for the ghostly, linearly dispersing magnetic excitations which are the "photons" of this emergent electromagnetism. The predictions of this field theory are shown to be in quantitative agreement with Quantum Monte Carlo simulations at zero temperature.

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“…(40)], and to expressions for the equal-time structure factor at finite temperatures derived from S αβ spin (k, ω) [Eq. (89)].…”

Section: A Temperature Dependence Of Structure Factorsmentioning

confidence: 99%

“…This suggests a simple diagnostic for a quantum spin ice in quasi-elastic neu- [Eq. (40)], for comparison with neutron scattering experiments on a powder sample of a quantum spin ice. Results are plotted for temperatures ranging from T = 0 to T = 1.0ca…”

Section: A Temperature Dependence Of Structure Factorsmentioning

confidence: 99%

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

2012

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“…. } up to order β 6 . By applying the mapping between the aformentioned one-dimensional fermionic and spin models, we obtain the expansion of the HFE of the fermionic spinless Hubbard model also up to order β 6 .…”

Section: Introductionmentioning

confidence: 99%

The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime

Silva¹,

Thomaz²,

Rojas³

2015

Condens. Matter Phys.

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We found that when the spinless model is off the half-filling regime (µ V ), the Helmholtz free energy (HFE) can be written as two β-expansions: one expansion comes from the half-filling configuration and another one that depends on the parameter x = µ − V . We show numerically that the chemical potential as a function of temperature satisfies a relation similar to the one derived from the particle-hole symmetry of the fermionic spinless model. We extend the β-expansion of the HFE of the one-dimensional fermionic spinless Hubbard model up to order β 8 .

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“…It has been noticed that hopping of fermions from site to site in frustrated lattices can lead, under certain conditions, to fractionalization of the fermionic charge in a rather natural way. 4,5 The motion of spinless fermions ͑or hardcore bosons͒ on a lattice can be mapped to an Ising spin problem or to a dimer configuration for any given lattice geometry and filling fraction as we will see in the next paragraph. The addition of a fermion ͑or boson͒ leads to a flip of an Ising spin or, equivalently, to a new dimer.…”

Section: Introductionmentioning

confidence: 99%

Classical correlations of defects in lattices with geometrical frustration in the motion of a particle

2006

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We map certain highly correlated electron systems on lattices with geometrical frustration in the motion of added particles or holes to the spatial defect-defect correlations of dimer models in different geometries. These models are studied analytically and numerically. We consider different coverings for four different lattices: square, honeycomb, triangular, and diamond. In the case of a hard-core dimer covering, we verify the existing results for square and triangular lattices and obtain new ones for the honeycomb and diamond lattices while in the case of a loop covering we obtain new numerical results for all the lattices and use the existing analytical Liouville field theory for the case of a square lattice. The results show power-law correlations for the square and honeycomb lattices, while exponential decay with distance is found for the triangular lattice and exponential decay with the inverse distance on the diamond lattice. We relate this fact to the lack of bipartiteness of the triangular lattice and in the latter case to the three dimensionality of the diamond. The connection of our findings to the problem of fractionalized charge in such lattices is pointed out.

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Fractional charges in pyrochlore lattices

Cited by 67 publications

References 15 publications

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

Seeing the light: Experimental signatures of emergent electromagnetism in a quantum spin ice

The β-expansion of the D=1 fermionic spinless Hubbard model off the half-filling regime

Classical correlations of defects in lattices with geometrical frustration in the motion of a particle

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