Numerical treatment of spin systems with unrestricted spin length $S$: A functional renormalization group study

Abstract

We develop a generalized pseudo-fermion functional renormalization group (PFFRG) approach that can be applied to arbitrary Heisenberg models with spins ranging from the quantum case $S=1/2$ to the classical limit $S\to \infty$. Within this framework, spins of magnitude $S$ are realized by implementing $M=2S$ copies of spin-1/2 degrees of freedom on each lattice site. We confirm that even without explicitly projecting onto the highest spin sector of the Hilbert space, ground states tend to select the largest possible local spin magnitude. This justifies the average treatment of the pseudo fermion constraint in previous spin-1/2 PFFRG studies. We apply this method to the antiferromagnetic $J_1$-$J_2$ honeycomb Heisenberg model with nearest neighbor $J_1>0$ and second neighbor $J_2>0$ interactions. Mapping out the phase diagram in the $J_2/J_1$-$S$ plane we find that upon increasing $S$ quantum fluctuations are rapidly decreasing. In particular, already at $S=1$ we find no indication for a magnetically disordered phase. In the limit $S\to \infty$, the known phase diagram of the classical system is exactly reproduced. More generally, we prove that for $S\to \infty$ the PFFRG approach is identical to the Luttinger-Tisza method.

14 pages, 13 figures

References in corpus (10)

• Exact evolution equation for the effective potential
• Physical realization of a quantum spin liquid based on a novel frustration mechanism
• Weak plaquette valence bond order in the $S=1/2$ honeycomb $J_1-J_2$ Heisenberg model
• Plaquette valence-bond ordering in J_1-J_2 Heisenberg antiferromagnet on the honeycomb lattice
• Exotic disordered phases in the quantum $J_1-J_2$ model on the honeycomb lattice
• Competing magnetic orders and spin liquids in two- and three-dimensional kagome systems: A pseudo-fermion functional renormalization group perspective
• Intertwined nematic orders in a frustrated ferromagnet
• Functional-renormalization-group analysis of Dzyaloshinsky-Moriya and Heisenberg spin interactions on the kagome lattice
• Nematic and supernematic phases in Kagome quantum antiferromagnets under a magnetic field
• Fermionic theory for quantum antiferromagnets with spin S > 1/2

Cited by in corpus (52)

• Evidence for a three-dimensional quantum spin liquid in PbCuTe${}_2$O${}_6$
• Quantum spin liquids in frustrated spin-1 diamond antiferromagnets
• Quantum and Classical Phases of the Pyrochlore Heisenberg Model with Competing Interactions
• Fingerprints of Kitaev physics in the magnetic excitations of honeycomb iridates
• Breathing chromium spinels: a showcase for a variety of pyrochlore Heisenberg Hamiltonians
• Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach
• Spin-orbit entangled j=1/2 moments in Ba${}_2$CeIrO${}_6$ -- a frustrated fcc quantum magnet
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite
• Signatures of a gearwheel quantum spin liquid in a spin-$\frac{1}{2}$ pyrochlore molybdate Heisenberg antiferromagnet
• Multiloop functional renormalization group approach to quantum spin systems
• Magnetic field induced quantum spin liquid in the two coupled trillium lattices of K${}_2$Ni${}_2$(SO${}_4$)${}_3$
• Stability of the spiral spin liquid in MnSc${}_2$S${}_4$
• Characterization of quantum spin liquids and their spinon band structures via functional renormalization
• TMDs as a platform for spin liquid physics: A strong coupling study of twisted bilayer WSe${}_2$
• Absence of long-range order in a triangular spin system with dipolar interactions
• Pseudo-fermion functional renormalization group for spin models
• Rise and fall of plaquette order in Shastry-Sutherland magnet revealed by pseudo-fermion functional renormalization group
• Functional renormalization group approach to SU(N) Heisenberg models: Real-space RG at arbitrary N
• Pinwheel valence-bond-crystal ground state of the spin-$\frac{1}{2}$ Heisenberg antiferromagnet on the $shuriken$ lattice
• Classical spiral spin liquids as a possible route to quantum spin liquids
• Dimerization tendencies of the pyrochlore Heisenberg antiferromagnet: A functional renormalization group perspective
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Functional renormalization group approach to SU(N) Heisenberg models: Momentum-space RG for the large-N limit
• Functional renormalization group study of the Kitaev-$\Gamma$ model on the honeycomb lattice and emergent incommensurate magnetic correlations
• Quantum effects on unconventional pinch point singularities
• Emergence and stability of spin-valley entangled quantum liquids in moiré heterostructures
• Ground-state phase diagram of spin-$S$ Kitaev-Heisenberg models
• Functional renormalization group for frustrated magnets with nondiagonal spin interactions
• Quantum paramagnetism and helimagnetic orders in the Heisenberg model on the body centered cubic lattice
• Effects of two-loop contributions in the pseudofermion functional renormalization group method for quantum spin systems
• Classical and quantum phases of the pyrochlore $S=1/2$ magnet with Heisenberg and Dzyaloshinskii-Moriya interactions
• Renormalization group analysis of dipolar Heisenberg model on square lattice
• Cluster functional renormalization group and absence of a bilinear spin liquid in the $J_1$-$J_2$-Heisenberg model
• 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
• Semiclassical theory for liquid-like behaviour of the frustrated magnet ${\mathrm{Ca}}_{10}{\mathrm{Cr}}_7{\mathrm{O}}_{28}$
• Affine lattice construction of spiral surfaces in classical Heisenberg models
• Benchmark Calculations of Multiloop Pseudofermion fRG
• Feasibility of Kitaev quantum spin liquids in ultracold polar molecules
• Spin functional renormalization group for the $J_1{J}_2{J}_3$ quantum Heisenberg model
• Bilinear Majorana representations for spin operators with spin magnitudes $S>1/2$
• Phase diagram of the $J_1$-$J_2$ quantum Heisenberg model for arbitrary spin
• A pseudofermion functional renormalization group study of dipolar-octupolar pyrochlore magnets
• Pseudo-fermion functional renormalization group with magnetic fields
• Ground States of Heisenberg Spin Clusters from Projected Hartree-Fock Theory
• The SpinParser software for pseudofermion functional renormalization group calculations on quantum magnets
• Quantum effects on pyrochlore higher-rank U(1) spin liquids: Pinch-line singularities, spin nematics, and connections to oxide materials
• ${\mathbb{Z}}_2$ vortices in the ground states of classical Kitaev-Heisenberg models
• Unconventional orders in the maple-leaf ferro-antiferromagnetic Heisenberg model
• Phase diagram of the antiferromagnetic $J_1$-$J_2$ spin-$1$ pyrochlore Heisenberg model
• Quantitative functional renormalization for three-dimensional quantum Heisenberg models
• A quantum Monte Carlo algorithm for arbitrary high-spin Hamiltonians