Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.Yb_{2}Ti_{2}O_{7} is a celebrated example of a pyrochlore magnet with highly frustrated, anisotropic exchange interactions. To date, attention has largely focused on its unusual, static properties, many of which can be understood as coming from the competition between different types of magnetic order. Here we use inelastic neutron scattering with exceptionally high energy resolution to explore the dynamical properties of Yb_{2}Ti_{2}O_{7}. We find that spin correlations exhibit dynamical scaling, analogous to behavior found near to a quantum critical point. We show that the observed scaling collapse can be explained within a phenomenological theory of multiple-phase competition, and confirm that a scaling collapse is also seen in semiclassical simulations of a microscopic model of Yb_{2}Ti_{2}O_{7}. These results suggest that dynamical scaling may be general to systems with competing ground states.

arXiv:2202.11085Physical Review LettersNov 15, 202213 citations

Electron correlations in the Hubbard model on the planar pyrochlore lattice

Akihisa Koga, Takuya Yoshioka, Norio Kawakami +1 more

Physica C SuperconductivityMar 31, 20072 citations

Quantum disorder in the two-dimensional pyrochlore Heisenberg antiferromagnet

S. E. Palmer, J. T. Chalker

We present the results of an exact diagonalization study of the spin- $1/2$ Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low-energy spectra for systems of up to 24 spins, we find that all clusters studied have nondegenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of nonmagnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short ranged, and we suggest that the ground state is magnetically disordered.We present the results of an exact diagonalization study of the spin-$1/2$ Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low-energy spectra for systems of up to 24 spins, we find that all clusters studied have nondegenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of nonmagnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short ranged, and we suggest that the ground state is magnetically disordered.

arXiv:cond-mat/0102447Physical review. B, Condensed matterAug 7, 200153 citations

Electron correlations in the Hubbard model on the planar pyrochlore lattice

Masahisa Koga, Akihisa Koga

Jan 1, 20070 citations

Order, disorder, and monopole confinement in the spin- 12 XXZ model on a pyrochlore tube

Chunhan Feng, Alexander Wietek, Edwin Miles Stoudenmire +1 more

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction ${J}_{z}$ and a transverse exchange interaction ${J}_{x}$ , on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When ${J}_{z}$ is antiferromagnetic ( ${J}_{z}>0$ ) and ${J}_{x}$ is ferromagnetic ( ${J}_{x}<0$ ), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$ . For ${J}_{z}<0$ and ${J}_{x}>0$ , spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a nondegenerate ground state with no broken symmetries and a robust energy gap. The low-energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|{J}_{x}|$ , we study the confinement of monopole-antimonopole pairs and find that the confinement length scale is larger for ${J}_{x}<0$ than for ${J}_{x}>0$ , although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction ${J}_{z}$ and a transverse exchange interaction ${J}_{x}$, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When ${J}_{z}$ is antiferromagnetic (${J}_{z}>0$) and ${J}_{x}$ is ferromagnetic (${J}_{x}<0$), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at $T=0$. For ${J}_{z}<0$ and ${J}_{x}>0$, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a nondegenerate ground state with no broken symmetries and a robust energy gap. The low-energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small $|{J}_{x}|$, we study the confinement of monopole-antimonopole pairs and find that the confinement length scale is larger for ${J}_{x}<0$ than for ${J}_{x}>0$, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.

arXiv:2203.00032Physical review. B./Physical review. BAug 18, 20224 citations

From Two Dimensional Correlations to a Disordered Ground State in the XY Pyrochlore, Yb

_2

_2

_7

We present the results of an exact diagonalization study of the spin-

1/2

Heisenberg antiferromagnet on a two-dimensional version of the pyrochlore lattice, also known as the square lattice with crossings or the checkerboard lattice. Examining the low-energy spectra for systems of up to 24 spins, we find that all clusters studied have nondegenerate ground states with total spin zero, and big energy gaps to states with higher total spin. We also find a large number of nonmagnetic excitations at energies within this spin gap. Spin-spin and spin-Peierls correlation functions appear to be short ranged, and we suggest that the ground state is magnetically disordered.

We study the ground state and thermodynamic properties of the spin-half XXZ model, with an Ising interaction

{J}_{z}

and a transverse exchange interaction

{J}_{x}

, on a pyrochlore tube obtained by joining together elementary cubes in a one-dimensional array. Periodic boundary conditions in the transverse directions ensure that the bulk of the system consists of corner-sharing tetrahedra, with the same local geometry as the pyrochlore lattice. We use exact diagonalization, the density matrix renormalization group (DMRG), and minimally entangled typical thermal states (METTS) methods to study the system. When

{J}_{z}

is antiferromagnetic (

{J}_{z}>0

) and

{J}_{x}

is ferromagnetic (

{J}_{x}<0

), we find a transition from a spin liquid to an XY ferromagnet, which has power-law correlations at

T=0

. For

{J}_{z}<0

and

{J}_{x}>0

, spin-two excitations are found to have lower energy than spin-one at the transition away from the fully polarized state, showing evidence for incipient spin-nematic order. When both interactions are antiferromagnetic, we find a nondegenerate ground state with no broken symmetries and a robust energy gap. The low-energy spectra evolve smoothly from predominantly Ising to predominantly XY interactions. In the spin-liquid regime of small

|{J}_{x}|

, we study the confinement of monopole-antimonopole pairs and find that the confinement length scale is larger for

{J}_{x}<0

than for

{J}_{x}>0

, although both length scales are very short. These results are consistent with a local spin-liquid phase for the Heisenberg antiferromagnet with no broken symmetries.