Two soluble models of an antiferromagnetic chain

1961/12/01 by Elliott Lieb, Theodore Schultz, T. D. Schultz +2 · 4,332 citations
Physics and Astronomy · #Anisotropy #Antiferromagnetism #Condensed matter physics #Ground state #Heisenberg model #Isotropy #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Quantum mechanics #Spins #Statistical physics #Theoretical and Computational Physics

paper · doi:10.1016/0003-4916(61)90115-4

published in Annals of Physics 16(3), 407-466 (Elsevier BV)

openalex publication_date 1961/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/04

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• Magnetization plateau in the S=1 spin ladder with competing interactions
• Classification of gapped symmetric phases in one-dimensional spin systems
• Excitation spectrum gap and spin-wave velocity ofXXZHeisenberg chains: Global renormalization-group calculation
• Phase-induced transport in atomic gases: From superfluid to Mott insulator
• Complexity and Floquet dynamics: Nonequilibrium Ising phase transitions
• Probing topological states through the exact non-Markovian decoherence dynamics of a spin coupled to a spin bath in the real-time domain
• Finite-size scaling of the entanglement entropy of the quantum Ising chain with homogeneous, periodically modulated and random couplings
• Exact one- and two-site reduced dynamics in a finite-size quantum Ising ring after a quench: A semianalytical approach
• Quantum phase transitions in the exactly solved spin-1/2 Heisenberg–Ising ladder
• Entanglement spreading after a geometric quench in quantum spin chains
• Heterobimetallic Dy-Cu coordination compound as a classical-quantum ferrimagnetic chain of regularly alternating Ising and Heisenberg spins
• Magnetization distribution in the transverse Ising chain with energy flux
• Exact solution for a quantum compass ladder
• Scaling of macroscopic superpositions close to a quantum phase transition
• Optimal quasifree approximation: Reconstructing the spectrum from ground-state energies
• Speed and entropy of an interacting continuous time quantum walk
• Relation between two measures of entanglement in spin-1∕2and spinless fermion quantum chain systems
• On the application of the Non-linear sigma model to spin chains and spin ladders
• Dynamical critical properties of the random transverse-field Ising spin chain
• Localization properties of the disordered XY spin chain
• Beyond universal behavior in the one-dimensional chain with random nearest-neighbor hopping
• Twisted Boundary Condition and Lieb-Schultz-Mattis Ingappability for Discrete Symmetries
• RENORMALIZATION GROUP, HIDDEN SYMMETRIES AND APPROXIMATE WARD IDENTITIES IN THE XYZ MODEL
• Effective spin quantum phases in systems of trapped ions
• Closed hierarchy of Heisenberg equations in integrable models with Onsager algebra
• Single-particle spectral function of quarter-filled ladder systems
• Locally quasi-stationary states in noninteracting spin chains
• Giant rectification in segmented, strongly interacting spin chains despite the presence of perturbations
• Translational Symmetry and Microscopic Constraints on Symmetry-Enriched Topological Phases: A View from the Surface
• Uhlmann fidelity and fidelity susceptibility for integrable spin chains at finite temperature: exact results
• Equivalence of topological insulators and superconductors
• Entanglement entropy in multi-leg Kitaev ladders with interface defects
• PERFECT, EFFICIENT, STATE TRANSFER AND ITS APPLICATION AS A CONSTRUCTIVE TOOL
• Path-dependent scaling of geometric phase near a quantum multi-critical point
• Average eigenstate entanglement entropy of the XY chain in a transverse field and its universality for translationally invariant quadratic fermionic models
• Intertwined order in a frustrated four-leg t−J cylinder
• Observation of Strong and Weak Thermalization in a Superconducting Quantum Processor
• Anyonic Chains, Topological Defects, and Conformal Field Theory
• Fractional Quantum Hall Effect in Weyl Semimetals
• Linear energy bounds for Heisenberg spin systems
• A protocol for quantum energy distribution
• On the stability of topological phases on a lattice
• Time asymptotics and entanglement generation of Clifford quantum cellular automata
• Unquantized anomalies in topological semimetals
• High-fidelity entanglement purification using chains of atoms and optical cavities
• Some ground-state expectation values for the free parafermion Z ( N ) spin chain*
• Physics of symmetry protected topological phases involving higher symmetries and its applications
• Measurement-Based Quantum Computation
• Symmetry-protected non-Fermi liquids, kagome spin liquids, and the chiral Kondo lattice model
• Dynamics of entanglement in a two-dimensional spin system
• Properties and application of SO(3) Majorana representation of spin: Equivalence with Jordan-Wigner transformation and exact Z2 gauge theories for spin models
• Phases of one-dimensional SU(N) cold atomic Fermi gases—From molecular Luttinger liquids to topological phases
• Spin chain model for correlated quantum channels
• Simulating spin systems with Majorana networks
• Gapless spin liquids in disguise
• Note on generalized symmetries, gapless excitations, generalized symmetry protected topological states, and anomaly
• Jordan-Wigner approach tothe frustrated spin one-half XXZ chain
• Interplay of quantum criticality and geometric frustration in columbite
• Testing forZ2topological order in variational wave functions for spin liquids
• Quantum Geometry of Finite XY Chains: A Comparison of Neveu-Schwarz and Ramond Sectors
• Integrability test for spin chains
• Single-copy entanglement in critical quantum spin chains
• Effects of dynamical paths on the energy gap and the corrections to the free energy in path integrals of mean-field quantum spin systems
• Quantum transitions of the isotropicXYmodel with long-range interactions on the inhomogeneous periodic chain
• Competing quantum phases of hard-core bosons with tilted dipole-dipole interaction
• Thermal canting of spin-bond order
• Dissipation-Induced Deviations from Kibble-Zurek Scaling in Non-Hermitian Quantum Annealing
• Deconfined quantum criticality in SU(3) antiferromagnets on the triangular lattice
• Correlation functions of the XX Heisenberg magnet and random walks of vicious walkers
• Higher-Form Anomalies Imply Intrinsic Long-Range Entanglement
• Local spin operators for fermion simulations
• Localization transition in incommensurate non-Hermitian systems
• Possible phases of the spin-12 XXZ model on a honeycomb lattice by boson-vortex duality
• Determinant representation for correlation functions of spin-1/2 XXX and XXZ Heisenberg magnets
• Low-energy properties of regularly depleted spin ladders
• Non-local spacetime supersymmetry on the lattice
• Calculation of multi-fractal dimensions in spin chains. [europepmc]
• Loschmidt echo in many-spin systems: contrasting time scales of local and global measurements. [europepmc]
• Majorana zero modes and long range edge correlation in interacting Kitaev chains: analytic solutions and density-matrix-renormalization-group study. [europepmc]
• Defects in Quantum Computers. [europepmc]
• Universality in volume-law entanglement of scrambled pure quantum states. [europepmc]
• Finite temperature quantum annealing solving exponentially small gap problem with non-monotonic success probability. [europepmc]
• Multipartite Entanglement at Finite Temperature. [europepmc]
• Unifying description of competing orders in two-dimensional quantum magnets. [europepmc]
• Probing the Possibilities of Ergodicity in the 1D Spin-1/2 XY Chain with Quench Dynamics. [europepmc]
• SU (2) Decomposition for the Quantum Information Dynamics in 2 d -Partite Two-Level Quantum Systems. [europepmc]
• Uncomputability of phase diagrams. [europepmc]
• Thermal Robustness of Entanglement in a Dissipative Two-Dimensional Spin System in an Inhomogeneous Magnetic Field. [europepmc]
• Experimental realization of a 3D random hopping model. [europepmc]
• Integrable quantum many-body sensors for AC field sensing. [europepmc]
• Control of structure and spin texture in the van der Waals layered magnet CrSBr. [europepmc]
• Simulating groundstate and dynamical quantum phase transitions on a superconducting quantum computer. [europepmc]
• Anti-Zeno purification of spin baths by quantum probe measurements. [europepmc]
• Entanglement asymmetry as a probe of symmetry breaking. [europepmc]
• Bath Engineering Enhanced Quantum Critical Engines. [europepmc]
• Implementation of the Projective Quantum Eigensolver on a Quantum Computer. [europepmc]
• Resilience of quantum spin fluctuations against Dzyaloshinskii-Moriya interaction. [europepmc]
• Monte Carlo Based Techniques for Quantum Magnets with Long-Range Interactions. [europepmc]
• Reviving the Lieb-Schultz-Mattis theorem in open quantum systems. [europepmc]
• Spin excitations in nanographene-based antiferromagnetic spin-1/2 Heisenberg chains. [europepmc]
• Dynamics of decoherence in a noisy driven environment. [europepmc]