Thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain

Abstract

The thermodynamics of finite open antiferromagnetic XXZ chains is studied using field theory, Bethe Ansatz and quantum Monte Carlo methods. For the susceptibility a parameter-free result as a function of the number of sites L and temperature T beyond the scaling limit is derived. The limiting cases T/J >> 1/L (J being the exchange constant), where the boundary correction shows a logarithmically suppressed Curie behaviour, and T/J << 1/L, where a crossover to the ground state behaviour takes place, are discussed in detail. Based on this analysis we present a simple formula for the averaged susceptibility of a spin-1/2 chain doped with non-magnetic impurities. We show that the effective Curie constant has a highly non-trivial temperature dependence and shows scaling in the low-temperature limit. Finally, corrections due to intra- and interchain couplings and implications for experiments on Sr_2 Cu_{1-x}Pd_x O_{3+δ} and related compounds are discussed.

arXiv comment30 pages, 11 figures

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• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Purification and many-body localization in cold atomic gases
• Interacting bosons in one dimension and Luttinger liquid theory
• Thermodynamics of multiferroic spin chains
• Surface free energy of the open XXZ spin-1/2 chain
• The even-odd effect in short antiferromagnetic Heisenberg chains
• Spin pseudogap in Ni-doped SrCuO2
• Transport and scattering in inhomogeneous quantum wires
• Finite-size effects in the quasi-one-dimensional quantum magnets Sr${}_2$CuO${}_3$, Sr${}_2$Cu${}_{0.99}$M${}_{0.01}$O${}_3$ (M = Ni, Zn), and SrCuO${}_2$
• Tunable Kondo screening length at a Y-junction of three inhomogenous spin chains
• Exact boundary free energy of the open XXZ chain with arbitrary boundary conditions
• Spin exchange dominated by charge fluctuations of the Wigner lattice in the newly synthesized chain cuprate Na5Cu3O6
• NMR Response in quasi one-dimensional Spin-1/2 Antiferromagnets
• Electron scattering from domain walls in ferromagnetic Luttinger liquids
• Site Dilution in the Half-Filled One-Band Hubbard Model: Ring Exchange, Charge Fluctuations and Application to La2Cu_{1-x}(Mg/Zn)_xO4
• Specific heat of segmented Heisenberg quantum spin chains in (Yb_{1-x}Lu_x)_4As_3
• Edge effects in the two-dimensional spin-1/2 Heisenberg antiferromagnet
• Low-energy local density of states of the 1D Hubbard model
• The Two-Band Luttinger Liquid with Spin-Orbit Coupling: Applications to Monatomic Chains on Surfaces
• Spin wave calculation of the field-dependent magnetization pattern around an impurity in Heisenberg antiferromagnets
• Spin pseudogap in the $S=\frac{1}{2}$ chain material Sr${}_2$CuO${}_3$ with impurities
• The dynamic structure factor in impurity-doped spin chains
• Magnetic ordering in the ultra-pure site-diluted spin chain materials SrCu${}_{1-x}$Ni${}_x$O${}_2$
• Quantum critical dynamics and scaling in one-dimensional antiferromagnets
• Kondo Length in Bosonic Lattices
• LT-scaling in depleted quantum spin ladders
• Boundary logarithmic corrections to the dynamical correlation functions of one-dimensional spin-1/2 chains
• Scattering of spinon excitations by potentials in the 1D Heisenberg model