Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model

Abstract

We study the phase diagram of the antiferromagnetic $J_1$-$J_2$ Heisenberg model on the pyrochlore lattice with $S=1$ spins at zero and finite temperatures. We use a combination of complementary state-of-the-art quantum many-body approaches such as density matrix renormalization group (DMRG), density-matrix purification and pseudo-Majorana functional renormalization group (PMFRG). We present an efficient approach to preserve the applicability of the PMFRG for spin-1 systems at finite temperatures despite the inevitable presence of unphysical spin states. The good performance of our methods is first demonstrated for the nearest-neighbor pyrochlore Heisenberg model where the finite temperature behavior of the specific heat and uniform susceptibility show excellent agreement within PMFRG and density-matrix purification. Including an antiferromagnetic second neighbor coupling we find that the non-magnetic ground-state phase of the nearest neighbor model extents up to $J_2/J_1\sim 0.02$ within DMRG, beyond which magnetic $\mathbf{k}=0$ long-range order sets in. Our PMFRG calculations find the phase transition in a similar regime $J_2/J_1\sim 0.035(8)$ which, together with the DMRG result, provides a strong argument for the existence of a small but finite non-magnetic ground-state phase in the spin-1 pyrochlore Heisenberg model. We also discuss the origin of discrepancies between different versions of the functional renormalization group concerning the location of this phase transition.

arXiv comment13 pages, 10 figures

References in corpus (35)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• Time-dependent variational principle for quantum lattices
• Unifying time evolution and optimization with matrix product states
• Time-evolution methods for matrix-product states
• Computational Studies of Quantum Spin Systems
• Quantum Excitations in Quantum Spin Ice
• Spin Ice, Fractionalization and Topological Order
• New Trends in Density Matrix Renormalization
• Finite Temperature Density Matrix Renormalization using an enlarged Hilbert space
• Frustrated quantum rare-earth pyrochlores
• A Strictly Single-Site DMRG Algorithm with Subspace Expansion
• The $S=1/2$ Kagome Heisenberg Antiferromagnet Revisited
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study
• The pyrochlore S=1/2 Heisenberg antiferromagnet at finite temperature
• Error estimates for extrapolations with matrix-product states
• Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach
• Possible inversion symmetry breaking in the $S=1/2$ pyrochlore Heisenberg magnet
• Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet
• Pseudo-fermion functional renormalization group for spin models
• Chiral spin states in the pyrochlore Heisenberg magnet: Fermionic mean-field theory and variational Monte Carlo calculations
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Adapting Planck's route to investigate the thermodynamics of the spin-half pyrochlore Heisenberg antiferromagnet
• Thermodynamics of the pyrochlore-lattice quantum Heisenberg antiferromagnet
• Theory of antiferromagnetic Heisenberg spins on breathing pyrochlore lattice
• Abundance of hard-hexagon crystals in the quantum pyrochlore antiferromagnet
• The spin-1/2 Heisenberg antiferromagnet on the pyrochlore lattice: An exact diagonalisation study
• Enhanced symmetry-breaking tendencies in the $S=1$ pyrochlore antiferromagnet
• Taming pseudo-fermion functional renormalization for quantum spins: Finite-temperatures and the Popov-Fedotov trick
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Temperature flow in pseudo-Majorana functional renormalization for quantum spins

Cited by in corpus (1)

• Mapping the Phase Diagram of a Frustrated Magnet: Degeneracies, Flat Bands, and Canting Cycles on the Pyrochlore Lattice