Quasiparticles governing the zero-temperature dynamics of the one-dimensional spin-1/2 Heisenberg antiferromagnet in a magnetic field

Abstract

The Tϭ0 dynamical properties of the one-dimensional ͑1D͒ sϭ 1 2 Heisenberg antiferromagnet in a uniform magnetic field are studied via the Bethe ansatz for cyclic chains of N sites. The ground state at magnetization 0ϽM z ϽN/2, which can be interpreted as a state with 2M z spinons or as a state of N/2ϪM z magnons, is reconfigured here as the vacuum for a different species of quasiparticles, the psinons and antipsinons. We investigate three kinds of quantum fluctuations, namely the spin fluctuations parallel and perpendicular to the direction of the applied magnetic field and the dimer fluctuations. The dynamically dominant excitation spectra are found to be sets of collective excitations composed of two quasiparticles excited from the psinon vacuum in different configurations. The Bethe ansatz provides a framework for ͑i͒ the characterization of the new quasiparticles in relation to the more familiar spinons and magnons, ͑ii͒ the calculation of spectral boundaries and densities of states for each continuum, ͑iii͒ the calculation of transition rates between the ground state and the dynamically dominant collective excitations, ͑iv͒ the prediction of line shapes for dynamic structure factors relevant for experiments performed on a variety of quasi-1D antiferromagnetic compounds, including KCuF 3 ,

Field-Induced Quantum Criticality and Universal Temperature Dependence of the Magnetization of a Spin-1/2Heisenberg Chain

“…In 1D spin systems that are gapped at zero field, such as spin-1 Haldane chains and spin-1/2 two-leg ladders, an additional QCP exists -the lower critical field H c , at which a quantum phase transition takes place from a gapped, disordered state to a TLL. Near H s and H c , an effective description of the TLL is given in terms of interacting magnons -quasiparticles carrying spin 1 [4,5]; the ground states in the regions H ≥ H s and H ≤ H c can be considered vacuums, in which excitations are respectively S z = −1 and S z = 1 magnons [6].…”

Spin Chain in Magnetic Field: Limitations of the Large-N Mean-Field Theory

“…Ref. [9,17]). It is then only when H z ≥ H cr z that another simple analytical approach becomes valid the well-known linear spin-wave approximation which works well for spin ground states with long range magnetic order [11,18].…”

How to Calculate Correlation Functions of Heisenberg Chains

“…What saves the day is that the number of states over which we have to sum can be vastly reduced [19,20,21,22].…”