Ground states with cluster structures in a frustrated Heisenberg chain

Abstract

We examine the ground state of a Heisenberg model with arbitrary spin S on a one-dimensional lattice composed of diamond-shaped units. A unit includes two types of antiferromagnetic exchange interactions which frustrate each other. The system undergoes phase changes when the ratio $\lambda$ between the exchange parameters varies. In some phases, strong frustration leads to larger local structures or clusters of spins than a dimer. We prove for arbitrary S that there exists a phase with four-spin cluster states, which was previously found numerically for a special value of $\lambda$ in the S=1/2 case. For S=1/2 we show that there are three ground state phases and determine their boundaries.

4 pages, uses revtex.sty, 2 figures available on request from [email protected], to be published in J. Phys.: Cond. Matt

References in corpus (2)

• Spin-1/2 Heisenberg-Antiferromagnet on the Kagome Lattice: High Temperature Expansion and Exact Diagonalisation Studies
• Rigorous results on a first-order phase transition in antiferromagnetic spin-1/2 coupled chains

Cited by in corpus (75)

• Nature of the spin dynamics and 1/3 magnetization plateau in azurite
• Magnetic properties of the $S=1/2$ distorted diamond chain at T=0
• Geometric frustration in the class of exactly solvable Ising-Heisenberg diamond chains
• Thermal entanglement in exactly solvable Ising-XXZ diamond chain structure
• Magnetism and Thermodynamics of Spin-1/2 Heisenberg Diamond Chains in a Magnetic Field
• Universal properties of highly frustrated quantum magnets in strong magnetic fields
• Dynamic and thermodynamic properties of the generalised diamond chain model for azurite
• Ground state of an $S=1/2$ distorted diamond chain - model of $\mathrm{C}{\mathrm{u}}_3\mathrm{C}{\mathrm{l}}_6({\mathrm{H}}_2\mathrm{O}{)}_2\cdot 2{\mathrm{H}}_8{\mathrm{C}}_4\mathrm{S}{\mathrm{O}}_2$
• Sign-problem-free Monte Carlo simulation of certain frustrated quantum magnets
• Linear independence of localized magnon states
• Thermodynamic properties of highly frustrated quantum spin ladders: influence of many-particle bound states
• The antiferromagnetic spin 1/2 chain with competing dimers and plaquettes: Numerical versus exact results
• Magneto-thermal properties of the Heisenberg-Ising orthogonal-dimer chain with triangular XXZ-clusters
• Efficient Quantum Monte Carlo simulations of highly frustrated magnets: the frustrated spin-1/2 ladder
• Magnetization process of atacamite: a case of weakly coupled $S=1/2$ sawtooth chains
• Spontaneously magnetized Tomonaga-Luttinger liquid in frustrated quantum antiferromagnets
• Dynamics of the Distorted Diamond Chain
• Frustrated quantum Heisenberg antiferromagnets at high magnetic fields: Beyond the flat-band scenario
• Diamond chains with multiple-spin exchange interactions
• Spin frustration and fermionic entanglement in an exactly solved hybrid diamond chain with the localized Ising spins and mobile electrons
• Diversity of quantum ground states and quantum phase transitions of a spin-1/2 Heisenberg octahedral chain
• Static and Dynamic Magnetic Properties of Spin-1/2 Inequilateral Diamond-Chain Compounds $A_3$Cu${}_3$AlO${}_2$(SO${}_4$)${}_4$ ($A$=K, Rb, and Cs)
• Geometrical frustration of an extended Hubbard diamond chain in the quasi-atomic limit
• Exact non-magnetic ground state and residual entropy of S = 1/2 Heisenberg diamond spin lattices
• Frustrated magnetism of spin-1/2 Heisenberg diamond and octahedral chains as a statistical-mechanical monomer-dimer problem
• CaCu2(SeO3)2Cl2: spin-1/2 Heisenberg chain compound with complex frustrated interchain couplings
• Magneto-elastic couplings in the distorted diamond-chain compound azurite
• Exact spin-cluster ground states in a mixed diamond chain
• Low-energy structure of the intertwining double-chain ferrimagnets A_3_Cu_3_(PO_4_)_4_ (A=Ca,Sr,Pb)
• Ground-state phases of rung-alternated spin-1/2 Heisenberg ladder
• Cluster-based Haldane phases, bound magnon crystals and quantum spin liquids of a mixed spin-1 and spin-1/2 Heisenberg octahedral chain
• Magnetic properties of the quantum spin-1/2 XX diamond chain: The Jordan-Wigner approach
• Magnetoelastic and structural properties of azurite Cu3(CO3)2(OH)2 from neutron scattering and muon spin rotation
• Exact Realization of a Quantum-Dimer Model in Heisenberg Antiferromagnets on a Diamond-Like Decorated Lattice
• Quantum Phase Transitions in Alternating-Bond Mixed Diamond Chains with Spins 1 and 1/2
• Ground-state phase diagram and thermodynamics of coupled trimer chains
• Frustrated spin ladder with alternating spin-1 and spin-1/2 rungs
• Magnetic field - temperature phase diagram of ferrimagnetic alternating chains: spin-wave theory from a fully polarized vacuum
• Selection of factorizable ground state in a frustrated spin tube: Order by disorder and hidden ferromagnetism
• Semiquantitative theory for high-field low-temperature properties of a distorted diamond spin chain
• One-dimensional spin pyrochlore lattice: exact ground state and elementary excitations
• Effective low-energy description of almost Ising-Heisenberg diamond chain
• Ground State Phase Diagram of S=1 Diamond Chains
• Magnetic phase separation in a frustrated ferrimagnetic chain under a magnetic field
• Nontrivial ferrimagnetism of the Heisenberg model on the Union Jack strip lattice
• Ground States of Spin-1/2 Heisenberg Antiferromagnets with Frustration on a Diamond-Like Decorated Square Lattice
• Disordered ground states in a quantum frustrated spin chain with side chains
• Quantum Rotors on the AB${}_2$ Chain with Competing Interactions
• Multiple frustration-induced plateaus in a magnetization process of the mixed spin-1/2 and spin-3/2 Ising-Heisenberg diamond chain
• The Thermodynamic Limit of Spin Systems on Random Graphs
• Designs of magnetic atom-trap lattices for quantum simulation experiments
• The role of density-dependent magnon hopping and magnon-magnon repulsion in ferrimagnetic spin-(1/2, $S$) chains in a magnetic field
• Ground-State Phases of Anisotropic Mixed Diamond Chains with Spins 1 and 1/2
• Ground-State Phases of Alternating-Bond S = 1 Diamond Chains
• All product eigenstates in Heisenberg models from a graphical construction
• Exact ground states of frustrated quantum spin systems consisting of spin-dimer units
• Ground State Phases of Distorted $S=1$ Diamond Chains
• BaCu3O4: High Temperature Magnetic Order in One-Dimensional S=1/2 Diamond-Chains
• Emergence of a Dimer-Dimer Interaction in the Low-Energy Effective Quantum-Dimer Model of a Diamond-Like-Decorated Square-Lattice Heisenberg Antiferromagnets with Further Neighbor Couplings
• Infinite Series of Ferrimagnetic Phases Emergent from the Gapless Spin Liquid Phase of Mixed Diamond Chains
• Coupled Cluster Treatment of the Alternating Bond Diamond Chain
• Scaling Property of the F-AF Spin Chain Near the Exactly Solvable Point
• Phase Diagram of the 1/2-1/2-1-1 Spin Chain by the Nonlinear Sigma Model
• Macroscopic degeneracy of ground state in the frustrated Heisenberg diamond chain
• Dimer-Monomer Ground State for Extended Spin-1/2 Diamond Chain
• XXZ-Ising model on the triangular kagome lattice with spin-1 on the decorated trimers
• Ground-State Phase Diagram of (1/2,1/2,1) Mixed Diamond Chains
• Trimers in the Extended Hubbard Model
• Quantum phase with spontaneous translational symmetry breaking in an extended diamond chain
• First Order Transitions Between the Gapped Spin-Liquid and Ferrimagnetic Phases in (1/2,1/2,1) Mixed Diamond Chains with Bond Alternation
• Magnetization of electronic ground states in frustrated superstable graphs
• Quantum Phase Transitions of the Distorted Diamond Spin Chain
• Tree-Graph Based Construction of Quantum Spin Models with Exact Ground State
• Ground-State Phase Diagram of (1/2,1/2,1) Mixed Diamond Chains with Single-Site Anisotropy
• Phase diagram and macroscopic ground state degeneracy of frustrated spin-1/2 anisotropic Heisenberg model on diamond-decorated lattices