Semi-Dirac spin liquids and frustrated quantum magnetism on the trellis lattice

Abstract

Geometrical frustration in quantum magnets provides a fertile setting for unconventional phases of matter, including quantum spin liquids (QSLs). The trellis lattice, with its complex site arrangements and edge-sharing triangular motifs, presents a promising platform for such physics. In this work, we undertake a comprehensive classification of all fully symmetric QSLs on the trellis lattice using the projective symmetry group approach within the Abrikosov-fermion representation. We find 7 U(1) and 25 $Z_2$ short-ranged Ansätze and analyze the phase diagram in the mean-field parameter space, uncovering both gapped and Dirac QSLs as well as a semi-Dirac spin liquid that emerges at the level of projective symmetry group classification and mean-field band structure, in which the spinon dispersion is linear along one momentum direction but quadratic along the orthogonal one. We demonstrate that such dispersions can occur only at high-symmetry points in the Brillouin zone with $C_{2v}$ little groups and analyze their characteristic correlation signatures. Moreover, by optimizing over all symmetry-allowed mean-field states, we map out a phase diagram -- featuring six distinct phases -- of the nearest-neighbor Heisenberg Hamiltonian on the trellis lattice. Among these, we find four quasi-one-dimensional QSL phases, one dimer phase, and one Dirac QSL phase. Going beyond mean field, we also assess equal-time and dynamical spin structure factors of these phases using density-matrix renormalization group and Keldysh pseudofermion functional renormalization group calculations and compare qualitative momentum-space features of these spectra with those obtained at the mean-field level. Finally, we identify four cuprate and vanadate compounds as promising experimental realizations and provide spectroscopic predictions, based on first-principles Hamiltonians, as a guide for neutron-scattering studies.

arXiv comment46 pages, 16 figures, 10 tables

References in corpus (144)

• The density-matrix renormalization group
• Quantum Spin Liquids
• The ITensor Software Library for Tensor Network Calculations
• Quantum Orders and Symmetric Spin Liquids
• Observation of tunable bandgap and anisotropic Dirac semimetal state in black phosphorus
• Probing Topological Spin Liquids on a Programmable Quantum Simulator
• Topological classification of crystalline insulators through band structure combinatorics
• Projected wavefunction study of Spin-1/2 Heisenberg model on the Kagome lattice
• Finite-Size Scaling of the Ground State Parameters of the Two-Dimensional Heisenberg Model
• Long range Neel order in the triangular Heisenberg model
• Variational study of triangular lattice spin-1/2 model with ring exchanges and spin liquid state in κ-(ET)_2 Cu_2 (CN)_3
• Pressure-Induced Zero-Gap Semiconducting State in Organic Conductor $\alpha$-(BEDT-TTF)${}_2$I${}_3$ Salt
• Spin-ladders with spin gaps: A description of a class of cuprates
• Merging of Dirac points in a two-dimensional crystal
• Thermodynamics and spin gap of the Heisenberg ladder calculated by the look-ahead Lanczos algorithm
• Gapless spin-liquid phase in the kagome spin-1/2 Heisenberg antiferromagnet
• Properties of an algebraic spin liquid on the kagome lattice
• Topological creation and destruction of edge states in photonic graphene
• Spin liquid nature in the Heisenberg $J_1$-$J_2$ triangular antiferromagnet
• A new magnetic field dependence of Landau levels on a graphene like structure
• Spin Liquid States on the Triangular and Kagome Lattices: A Projective Symmetry Group Analysis of Schwinger Boson States
• Density matrix renormalization group algorithms with a single center site
• Tight-binding modeling and low-energy behavior of the semi-Dirac point
• Toward a realistic description of multilayer black phosphorus: from $GW$ approximation to large-scale tight-binding simulations
• Phase Diagram of a Frustrated Quantum Antiferromagnet on the Honeycomb Lattice: Magnetic Order versus Valence-Bond Crystal formation
• Spin-Liquid phase of the Multiple-Spin Exchange Hamiltonian on the Triangular Lattice
• Experimental signatures of a three-dimensional quantum spin liquid in effective spin-1/2 Ce2Zr2O7 pyrochlore
• Topological transition of Dirac points in a microwave experiment
• Spin correlations in the algebraic spin liquid - implications for high Tc superconductors
• Doping a spin-orbit Mott Insulator: Topological Superconductivity from the Kitaev-Heisenberg Model and possible application to (Na2/Li2)IrO3
• Projected wave function study of Z2 spin liquids on the kagome lattice for the spin-1/2 quantum Heisenberg antiferromagnet
• Global Phase Diagram of Competing Ordered and Quantum Spin Liquid Phases on the Kagomé Lattice
• Dirac Spin Liquid on the Spin-1/2 Triangular Heisenberg Antiferromagnet
• Wallpaper Fermions and the Nonsymmorphic Dirac Insulator
• J_1-J_2 frustrated two-dimensional Heisenberg model: Random phase approximation and functional renormalization group
• Z2 spin liquid in S=1/2 Heisenberg model on Kagome lattice: A projective symmetry group study of Schwinger-fermion mean-field states
• Confinement of fractional quantum number particles in a condensed matter system
• Absence of magnetic thermal conductivity in the quantum spin liquid candidate YbMgGaO4
• Vanishing spin gap in a competing spin-liquid phase in the kagome Heisenberg antiferromagnet
• Tilted and type-III Dirac cones emerging from flat bands in photonic orbital graphene
• Functional renormalization group for the anisotropic triangular antiferromagnet
• One- and Two-Triplon Spectra of a Cuprate Ladder
• Schwinger Boson Mean Field Theories of Spin Liquid States on Honeycomb Lattice: Projective Symmetry Group Analysis and Critical Field Theory
• Unifying Description of Competing Orders in Two Dimensional Quantum Magnets
• Two-Dimensional Dirac Fermions Protected by Space-Time Inversion Symmetry in Black Phosphorus
• A quantum liquid of magnetic octupoles on the pyrochlore lattice
• First-principles determination of Heisenberg Hamiltonian parameters for the spin-1/2 kagome antiferromagnet ZnCu3(OH)6Cl2
• Projective symmetry group classification of chiral spin liquids
• Dynamical structure factor of the $J_1-J_2$ Heisenberg model on the triangular lattice: magnons, spinons, and gauge fields
• Emergence of a Chern-insulating state from a semi-Dirac dispersion
• Exchange interactions and magnetic properties of the layered vanadates CaV2O5, MgV2O5, CaV3O7 and CaV4O9
• Quantum spin liquid in the Ising triangular-lattice antiferromagnet neodymium heptatantalate
• Gapless chiral spin liquid in a kagome Heisenberg model
• Continuum of quantum fluctuations in a three-dimensional $S=1$ Heisenberg magnet
• Valence-bond crystal in the extended kagome spin-1/2 quantum Heisenberg antiferromagnet: A variational Monte Carlo approach
• Emergent non-Fermi liquid at the quantum critical point of a topological phase transition in two dimensions
• Variational Monte Carlo study of chiral spin liquid in the extended Heisenberg model on the Kagome lattice
• $Z_2$ spin liquid and chiral antiferromagnetic phase in Hubbard model on the honeycomb lattice: duality between Schwinger-fermion and Schwinger-boson representations
• Spin liquids on a honeycomb lattice: Projective Symmetry Group study of Schwinger fermion mean-field theory
• Photoinduced Chern insulating states in semi-Dirac materials
• A semi-Dirac point in the Hofstadter spectrum
• Observation of quasi-two-dimensional Dirac fermions in ZrTe5
• Quantum s = 1/2 Antiferromagnets on Archimedean Lattices: The Route from Semiclassical Magnetic Order to Nonmagnetic Quantum States
• Spectral Properties of Magnetic Excitations in Cuprate Two-Leg Ladder Systems
• Hidden-Symmetry-Protected Topological Semimetals on a Square Lattice
• Thermal conductivity of the quantum spin liquid candidate EtMe3Sb[Pd(dmit)2]2: No evidence of mobile gapless excitations
• The case for a U(1)${}_{\pi }$ Quantum Spin Liquid Ground State in the Dipole-Octupole Pyrochlore Ce${}_2$Zr${}_2$O${}_7$
• Site dilution of quantum spins in the honeycomb lattice
• From Spin Glass to Quantum Spin Liquid Ground States in Molybdate Pyrochlores
• Magnetic properties of the S=1/2 quasi-one-dimensional antiferromagnet CaCu2O3
• Semi-Dirac Transport and Anisotropic Localization in Polariton Honeycomb Lattices
• SU(2)-invariant spin liquids on the triangular lattice with spinful Majorana excitations
• Symmetric $Z_2$ spin liquids and their neighboring phases on triangular lattice
• Phase diagram of a distorted kagome antiferromagnet and application to Y-kapellasite
• Quantum Multicriticality near the Dirac-Semimetal to Band-Insulator Critical Point in Two Dimensions: A Controlled Ascent from One Dimension
• Low temperature broken symmetry phases of spiral antiferromagnets
• Semi-Dirac Semimetal in Silicene Oxide
• Spin dynamics of SrCu${}_2$O${}_3$ and the Heisenberg ladder
• The spin-half Heisenberg antiferromagnet on two Archimedian lattices: From the bounce lattice to the maple-leaf lattice and beyond
• Dirac point metamorphosis from third-neighbor couplings in graphene
• Persistence of the gapless spin liquid in the breathing kagome Heisenberg antiferromagnet
• Pseudo-fermion functional renormalization group for spin models
• Electronic structure and exchange interactions of the ladder vanadates CaV2O5 and MgV2O5
• Valence-bond crystals in the kagome spin-1/2 Heisenberg antiferromagnet: a symmetry classification and projected wave function study
• The spin-1/2 Heisenberg antiferromagnet on a 1/7-depleted triangular lattice: Ground-state properties
• Influence of an inter-chain coupling on spiral ground-state correlations in frustrated spin-1/2 J1-J2 Heisenberg chains
• Disappearance of the Spin Gap in a Zn doped 2-Leg Ladder Compound Sr(Cu1-xZnx)2O3
• Magnetic bound states in the quarter-filled ladder system ${\alpha }^{\prime }-Na{V}_2{O}_5$}
• Magnetic properties of the coupled ladder system MgV${}_2$O${}_5$
• Gutzwiller-projected states for the $J_1$-$J_2$ Heisenberg model on the kagome lattice: achievements and pitfalls
• Pinch-points to half-moons and up in the stars: the kagome skymap
• Competing quantum paramagnetic ground states of the Heisenberg antiferromagnet on the star lattice
• Another Exact Ground State of a 2D Quantum Antiferromagnet
• Quantum effects on unconventional pinch point singularities
• Anisotropic effects in two-dimensional materials
• Schwinger boson spin liquid states on square lattice
• Quantum Monte Carlo Simulation of the Trellis Lattice Heisenberg Model for SrCu${}_2$O${}_3$ and CaV${}_2$O${}_5$
• Raman Scattering from Magnetic Excitations in the Spin Ladder Compounds CaV2O5 and MgV2O5
• Quantum Criticality of Semi-Dirac Fermions in 2+1 Dimensions
• The planar pyrochlore antiferromagnet: A large-N analysis
• Phase Diagram of the S = 1/2 Frustrated Coupled Ladder System
• Semi-Dirac Fermions in a Topological Metal
• Static and dynamical signatures of Dzyaloshinskii-Moriya interactions in the Heisenberg model on the kagome lattice
• The observation of quantum fluctuations in a kagome Heisenberg antiferromagnet
• SU(2)-invariant Majorana spin liquid with stable parton Fermi surfaces in an exactly solvable model
• Hidden symmetry and protection of Dirac points on the honeycomb lattice
• 50 years of quantum spin liquids
• Candidate quantum disordered intermediate phase in the Heisenberg antiferromagnet on the maple-leaf lattice
• Curie-law crossover in spin liquids
• Coupling, merging, and splitting Dirac points by electron-electron interaction
• Gapless spin liquids in disguise
• Phase diagram of the $J$-$J_d$ Heisenberg Model on the Maple-Leaf Lattice: Neural networks and density matrix renormalization group
• Classification of quantum phases for the star-lattice antiferromagnet via a projective symmetry group analysis
• Magnetic order in ferromagnetically coupled spin ladders
• Noncoplanar orders and quantum disordered states in maple-leaf (anti)ferromagnets
• Field-Induced Quantum Criticality of Systems with Ferromagnetically Coupled Structural Spin Units
• Coulomb interactions and renormalization of semi-Dirac fermions near a topological Lifshitz transition
• Symmetry protected gapless $Z_2$ spin liquids
• Fermionic criticality of anisotropic nodal point semimetals away from the upper critical dimension: exact $1/N_f$ exponents
• Electronic Density of States of a $U\left(1\right)$ Quantum Spin Liquid with Spinon Fermi Surface. I. Orbital Magnetic Field Effects
• Schwinger boson symmetric spin liquids of Shastry-Sutherland model
• Coulomb interactions in systems of generalized semi-Dirac fermions
• Monopole excitations in the $U(1)$ Dirac spin liquid on the triangular lattice
• Tunable Dirac points in a two-dimensional non-symmorphic wallpaper group lattice
• Candidate quantum spin liquids on the maple-leaf lattice
• Stability of zero energy Dirac touchings in the honeycomb Hofstadter problem
• Quantum phase diagram of a frustrated spin-1/2 system on a Trellis Ladder
• Projective symmetry group classification of Abrikosov fermion mean-field ansätze on the square-octagon lattice
• Kitaev model on Hurwitz hyperbolic tilings: A non-Abelian gapped chiral spin liquid
• Hyperbolic Spin Liquids
• Chiral Gapless Spin Liquid in Hyperbolic Space
• Dynamical response theory of interacting Majorana fermions and its application to generic Kitaev quantum spin liquids in a field
• Piercing the Dirac spin liquid: From a single monopole to chiral states
• Engineering frustrated Rydberg spin models by graphical Floquet modulation
• Antiferromagnetic long range order in the uniform resonating valence bond state on square lattice
• Nature of Topological Phase Transition of Kitaev Quantum Spin Liquids
• Kitaev model in regular hyperbolic tilings
• Effects of interladder couplings in the trellis lattice
• Microscopic lattice model for quartic semi-Dirac fermions in two dimensions
• Learning topological states from randomized measurements using variational tensor network tomography
• Two-Dimensionality of Magnetic Excitations on the Trellis Lattice: (La,Sr,Ca)${}_{14}$Cu${}_{24}$O${}_{41}$ and SrCu${}_2$O${}_3$
• Spin ladder compound Pb(0.55)Cd(0.45)V(2)O(5): synthesis and investigation
• Melting of Ferromagnetic Order on a Trellis Ladder
• Keldysh pseudo-fermion functional renormalization group for quantum magnetism

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