Geometric frustration in spin systems offers potential routes to realize unusual phases of matter. The authors consider emergent quantum spin liquids of interacting $S=1/2$ moments on the pyrochlore lattice with a breathing anisotropy, where two inequivalent sets of tetrahedra are present. They classify possible ${\mathbb{Z}}_{2}$ and U(1) quantum spin liquids in this system and find a small number of physically motivated candidates. In particular, two degenerate U(1) spin liquids are identified for the antiferromagnetic Heisenberg model. The degeneracy is robust with respect to tuning the breathing anisotropy, but it can be lifted by a finite Dzyaloshinskii-Moriya interaction. The effect of gauge fluctuations in a gapless U(1) spin liquid is investigated for comparison with future experiments.Geometric frustration in spin systems offers potential routes to realize unusual phases of matter. The authors consider emergent quantum spin liquids of interacting $S=1/2$ moments on the pyrochlore lattice with a breathing anisotropy, where two inequivalent sets of tetrahedra are present. They classify possible ${\mathbb{Z}}_{2}$ and U(1) quantum spin liquids in this system and find a small number of physically motivated candidates. In particular, two degenerate U(1) spin liquids are identified for the antiferromagnetic Heisenberg model. The degeneracy is robust with respect to tuning the breathing anisotropy, but it can be lifted by a finite Dzyaloshinskii-Moriya interaction. The effect of gauge fluctuations in a gapless U(1) spin liquid is investigated for comparison with future experiments.

arXiv:2207.13105Physical review. B./Physical review. BOct 4, 202215 citations

Spin- 12 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalization study

V. Ravi Chandra, Jyotisman Sahoo

We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants ${J}_{1}$ and ${J}_{2}$ for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra ( ${J}_{2}=0$ ) to a correlated state at ${J}_{1}={J}_{2}$ . We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near ${J}_{1}={J}_{2}$ to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at ${J}_{1}={J}_{2}$ .We present exact diagonalization calculations for the spin-1/2 nearest-neighbor antiferromagnet on the pyrochlore lattice. We study a section of the lattice in the [111] direction and analyze the Hamiltonian of the breathing pyrochlore system with two coupling constants ${J}_{1}$ and ${J}_{2}$ for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (${J}_{2}=0$) to a correlated state at ${J}_{1}={J}_{2}$. We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near ${J}_{1}={J}_{2}$ to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at ${J}_{1}={J}_{2}$.

arXiv:1710.11316Physical review. B./Physical review. BApr 12, 201819 citations

Geometric frustration in spin systems offers potential routes to realize unusual phases of matter. The authors consider emergent quantum spin liquids of interacting

S=1/2

moments on the pyrochlore lattice with a breathing anisotropy, where two inequivalent sets of tetrahedra are present. They classify possible

{\mathbb{Z}}_{2}

and U(1) quantum spin liquids in this system and find a small number of physically motivated candidates. In particular, two degenerate U(1) spin liquids are identified for the antiferromagnetic Heisenberg model. The degeneracy is robust with respect to tuning the breathing anisotropy, but it can be lifted by a finite Dzyaloshinskii-Moriya interaction. The effect of gauge fluctuations in a gapless U(1) spin liquid is investigated for comparison with future experiments.

{J}_{1}

and

{J}_{2}

for tetrahedra of different orientations and investigate the evolution of the system from the limit of disconnected tetrahedra (

{J}_{2}=0

) to a correlated state at

{J}_{1}={J}_{2}

. We evaluate the low-energy spectrum, two and four spin correlations, and spin chirality correlations for a system size of up to 36 sites. The model shows a fast decay of spin correlations and we confirm the presence of several singlet excitations below the lowest magnetic excitation. We find chirality correlations near

{J}_{1}={J}_{2}

to be small at the length scales available at this system size. Evaluation of dimer-dimer correlations and analysis of the nature of the entanglement of the tetrahedral unit shows that the triplet sector of the tetrahedron contributes significantly to the ground-state entanglement at

{J}_{1}={J}_{2}