Majorana Diagrammatics for Quantum Spin-1/2 Models
arXiv:2508.19734 · doi:10.21468/SciPostPhysCore.9.1.002
Abstract
A diagrammatic formalism for lattices of 1/2 is developed. It is based on an unconstrained mapping between spin and Majorana operators. This allows the use of standard tools of diagrammatic quantum many-body theory without requiring projections. We derive, in particular, the Feynman rules for the expansion around a color-preserving mean-field theory. We then present the numerical results obtained by computing the corrections up to second order for the Heisenberg model in one and two dimensions, showing that perturbative corrections are not only numerically important, but also qualitatively improve the results of mean-field theory. These results pave the way for the use of Majorana diagrammatic tools in theoretical and numerical studies of quantum spin systems.
29 pages, 10 figures
References in corpus (56)
- Anyons in an exactly solved model and beyond
- Quantum Orders and Symmetric Spin Liquids
- Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
- A Field Guide to Spin Liquids
- Susceptibility of the Spin 1/2 Heisenberg Antiferromagnetic Chain
- Polaron Problem by Diagrammatic Quantum Monte Carlo
- Spin liquid nature in the Heisenberg - triangular antiferromagnet
- Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
- Taming the dynamical sign problem in real-time evolution of quantum many-body problems
- Feynman diagrams versus Fermi-gas Feynman emulator
- Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
- Diagrammatic Monte Carlo
- Bold Diagrammatic Monte Carlo: When Sign Problem is Welcome
- Possible Realization of Odd Frequency Pairing in Heavy Fermion Compounds
- Mott insulating states with competing orders in the triangular lattice Hubbard model
- Determinant Diagrammatic Monte Carlo in the Thermodynamic Limit
- Extended crossover from Fermi liquid to quasi-antiferromagnet in the half-filled 2D Hubbard model
- Quantum Monte-Carlo for correlated out-of-equilibrium nanoelectronics devices
- New Fermionic Description of Quantum S = 1/2 Antiferromargnet
- Quantum Order: a Quantum Entanglement of Many Particles
- A Z spin-orbital liquid state in the square lattice Kugel-Khomskii model
- Bold Diagrammatic Monte Carlo Method Applied to Fermionized Frustrated Spins
- Shifted-Action Expansion and Applicability of Dressed Diagrammatic Schemes
- Frustrated Quantum Spins at finite Temperature: Pseudo-Majorana functional RG approach
- Spin-Ice State of the Quantum Heisenberg Antiferromagnet on the Pyrochlore Lattice
- Spin-spin correlators in Majorana representation
- SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
- Dynamics of Majorana-based qubits operated with an array of tunable gates
- Algorithmic Matsubara Integration for Hubbard-like models
- Spin dynamics from Majorana fermions
- Bold Diagrammatic Monte Carlo technique for frustrated spin systems
- Pseudo-fermion functional renormalization group for spin models
- Origin and fate of the pseudogap in the doped Hubbard model
- Real-frequency Diagrammatic Monte Carlo at Finite Temperature
- Majorana Fermion Representation For An Antiferromagnetic Spin-1/2 Chain
- Majorana representations of spin and an alternative solution of the Kitaev honeycomb model
- Majorana spin liquids and projective realization of SU(2) spin symmetry
- Dynamic Response of an Electron Gas: Towards the Exact Exchange-Correlation Kernel
- Renormalized perturbation theory at large expansion orders
- 50 years of quantum spin liquids
- Majorana spin liquid and dimensional reduction in Cs2CuCl4
- Analytical solution for time-integrals in diagrammatic expansions: application to real-frequency diagrammatic Monte Carlo
- Diagrammatic Monte Carlo procedure for the spin-charge transformed Hubbard model
- Efficient One-Loop-Renormalized Vertex Expansions with Connected Determinant Diagrammatic Monte Carlo
- From Popov-Fedotov trick to universal fermionization
- Quantum-to-classical correspondence in two-dimensional Heisenberg models
- Renormalized Perturbation Theory for Fast Evaluation of Feynman Diagrams on the Real Frequency Axis
- Spin-charge transformation of lattice fermion models: duality approach for diagrammatic simulation of strongly correlated systems
- Temperature flow in pseudo-Majorana functional renormalization for quantum spins
- Pfaffian formula for fermion parity fluctuations in a superconductor and application to Majorana fusion detection
- Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
- Pseudo-Majorana functional renormalization for frustrated XXZ spin-1/2 models with field or magnetization along the spin-Z direction at finite temperature
- Combinatorial summation of Feynman diagrams: Equation of state of the 2D SU(N) Hubbard model
- A Majorana Fermion t-J Model in One Dimension
- Evaluating second-order phase transitions with Diagrammatic Monte Carlo: Néel Transition in the doped three-dimensional Hubbard model
- Quantitative functional renormalization for three-dimensional quantum Heisenberg models