From Two Dimensional Correlations to a Disordered Ground State in the XY Pyrochlore, Yb $_2$ Ti $_2$ O $_7$ From Two Dimensional Correlations to a Disordered Ground State in the XY Pyrochlore, Yb$_2$Ti$_2$O$_7$

Kate A. Ross

Bulletin of the American Physical SocietyMar 21, 20110 citations

Quantum spin state in a spin-1/2 breathing pyrochlore antiferromagnet

Kenta Kimura, Satoru Nakatsuji, T. Kimura

Bulletin of the American Physical SocietyMar 3, 20150 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

Computing Effective Hamiltonians of Doped and Frustrated Antiferromagnets By Contractor Renormalization

Assa Auerbach

A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high‐Tc cuprates. For the S = 1/2 Pyrochlore and Kagomé antiferromagnets, the effective hamiltonians predict spin‐disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.A review of the Contractor Renormalization (CORE) method, as a systematic derivation of the low energy effective hamiltonian, is given, with emphasis on its differences and advantages over traditional perturbative (weak/strong links) real space RG. For the low energy physics of the 2D Hubbard model, we derive the plaquette bosons (projected SO(5)) model which connects the microscopic model to phases and phenomenology of high‐Tc cuprates. For the S = 1/2 Pyrochlore and Kagomé antiferromagnets, the effective hamiltonians predict spin‐disordered, lattice symmetry breaking, ground states with a large density of low energy singlets as found by exact diagonalization of small clusters.

arXiv:cond-mat/0510738AIP conference proceedingsJan 1, 20062 citations

Large-scale calculation of ferromagnetic spin systems on the pyrochlore lattice

Konstantin S Soldatov, Konstantin Valentinovich Nefedev, Yukihiro Komura +1 more

arXiv:1612.08312Physics Letters ADec 24, 20168 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.