Correlated spin liquids in the quantum kagome antiferromagnet at finite field: a renormalisation group analysis

Abstract

We analyse the antiferromagnetic spin-$1/2$ XXZ model on the kagome lattice at finite external magnetic field with the help of a nonperturbative zero-temperature renormalization group (RG) technique. Following the work of Kumar \emph{et al} (Phys. Rev. B {\bf 90}, 174409 (2014)), we use a Jordan-Wigner transformation to map the spin problem into one of spinless fermions (spinons) in the presence of a statistical gauge field, and with nearest-neighbour interactions. While the work of Kumar \emph{et al} was confined mostly to the plateau at $1/3$-filling (magnetisation per site) in the XY regime, we analyse the role of inter-spinon interactions in shaping the phases around this plateau in the entire XXZ model. The RG phase diagram obtained contains three spin liquid phases whose position is determined as a function of the exchange anisotropy and the energy scale for fluctuations arising from spinon scattering. Two of these spins liquids are topologically ordered states of matter with gapped, degenerate states on the torus. The gap for one of these phases corresponds to the one-spinon band gap of the Azbel-Hofstadter spectrum for the XY part of the Hamiltonian, while the other arises from two-spinon interactions. The Heisenberg point of this problem is found to lie within the interaction gapped spin liquid phase, in broad agreement with a recent experimental finding. The third phase is an algebraic spin liquid with a gapless Dirac spectrum for spinon excitations, and possess properties that show departures from the Fermi liquid paradigm. The three phase boundaries correspond to critical theories, and meet at a $SU(2)$-symmetric multicritical point. This special critical point agrees well with the gap-closing transition point predicted by Kumar \emph{et al}. We discuss the relevance of our findings to various recent experiments, as well as results obtained from other theoretical analyses.

arXiv comment35 pages, 7 figures, 63 references

References in corpus (52)

• Berry Phase Effects on Electronic Properties
• Electronic Structure of Pyrochlore Iridates: From Topological Dirac Metal to Mott Insulator
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Fractionalized excitations in the spin liquid state of a kagomé lattice antiferromagnet
• Identifying Topological Order by Entanglement Entropy
• Dirac Fermions in Solids - from High Tc cuprates and Graphene to Topological Insulators and Weyl Semimetals
• Non-Fermi liquid behaviour of electrons in the half-filled honeycomb lattice (A renormalization group approach)
• Marginal Fermi liquid behavior from 2d Coulomb interaction
• Commensurability, excitation gap and topology in quantum many-particle systems on a periodic lattice
• Gapless spin-liquid ground state in the $S=1/2$ kagome antiferromagnet
• First excitations of the spin 1/2 Heisenberg antiferromagnet on the kagomé lattice
• Evidence for a Gapped Spin-Liquid Ground State in a Kagome Heisenberg Antiferromagnet
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Properties of an algebraic spin liquid on the kagome lattice
• Controlling frustrated liquids and solids with an applied field in a kagome Heisenberg antiferromagnet
• Relativistic Mott criticality in graphene
• The magnetic groundstate of an experimental $S=1/2$ kagomé antiferromagnet
• Magnetization plateaus in frustrated antiferromagnetic quantum spin models
• Theta-terms in nonlinear sigma-models
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• Gapped spin liquid with ${\mathbb{Z}}_2$-topological order for kagome Heisenberg model
• Gapless spin liquid ground state in the S=1/2 vanadium oxyfluoride kagome antiferromagnet [NH4]2[C7H14N][V7O6F18]
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Numerical study of magnetization plateaux in the spin-1/2 kagome Heisenberg antiferromagnet
• Pressure- and Field-Tuning the Magnetostructural Phases of Mn3O4: Raman Scattering and X-Ray Diffraction Studies
• Spin-S Kagome quantum antiferromagnets in a field with tensor networks
• Fractionalization, topological order, and quasiparticle statistics
• One-Third Magnetization Plateau with a Preceding Novel Phase in Volborthite
• Quantum kagome antiferromagnet in a magnetic field: Low-lying non-magnetic excitations versus valence-bond crystal order
• Algebraic vortex liquid theory of a quantum antiferromagnet on the kagome lattice
• Lattice Twisting Operators and Vertex Operators in Sine-Gordon Theory in One Dimension
• The mother of all states of the kagome quantum antiferromagnet
• Spin liquid phase in a $S=1/2$ quantum magnet on the kagome lattice
• Magnetization Plateaus in the Spin-1/2 Kagome Antiferromagnets: Volborthite and Vesignieite
• Thermodynamics of Spin-1/2 Kagomé Heisenberg Antiferromagnet: Algebraic Paramagnetic Liquid and Finite-Temperature Phase Diagram
• Observation of a Transient Magnetization Plateau in a Quantum Antiferromagnet on the Kagome Lattice
• Chiral spin liquids on the kagome Lattice
• Pseudo-magnetic catalysis of the time-reversal symmetry breaking in graphene
• Chern-Simons theory of the magnetization plateaus of the spin-1/2 quantum XXZ Heisenberg model on Kagome Lattice
• Universality, marginal operators, and limit cycles
• Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model
• Spin dynamics in the high-field phases of volborthite
• Insulator, conductor and commensurability: a topological approach
• The spin-1/2 Kagome XXZ model in a field: competition between lattice nematic and solid orders
• Classification of symmetry fractionalization in gapped ${\mathbb{Z}}_2$ spin liquids
• Microscopic theory of the nearest-neighbor valence bond sector of the spin-1/2 kagome antiferromagnet
• Orbital and spin ordering physics of the Mn${}_3$O${}_4$ spinel
• Magnetization plateaus of an easy-axis Kagomé antiferromagnet with extended interactions
• Spin-1/2 Heisenberg antiferromanget on kagome: a $Z_2$ spin liquid with fermionic spinons
• The mobility of dual vortices in honeycomb, square, triangular, Kagome and dice lattices
• Numerical evidence for a chiral spin liquid in the XXZ antiferromagnetic Heisenberg model on the kagome lattice at $m=\frac{2}{3}$ magnetization

Cited by in corpus (14)

• Scaling theory for Mott-Hubbard transitions
• Unveiling the Kondo cloud: unitary RG study of the Kondo model
• Magnetisation plateaux of the quantum pyrochlore Heisenberg antiferromagnet
• Holographic unitary renormalization group for correlated electrons -- II: insights on fermionic criticality
• Holographic unitary renormalization group for correlated electrons -- I: a tensor network approach
• Fermionic criticality is shaped by Fermi surface topology: a case study of the Tomonaga-Luttinger liquid
• Origin of Topological Order in a Cooper Pair Insulator
• Holographic entanglement renormalisation of topological order in a quantum liquid
• Frustration shapes multi-channel Kondo physics: a star graph perspective
• Universal entanglement signatures of quantum liquids as a guide to fermionic criticality
• Mott Criticality as the Confinement Transition of a Pseudogap-Mott Metal
• Kondo frustration via charge fluctuations: a route to Mott localisation
• Holographic entanglement renormalisation for fermionic quantum matter
• Unveiling topological order through multipartite entanglement