Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

Abstract. We use the exact determinantal representation derived by Kitanine, Maillet, and Terras for matrix elements of local spin operators between Bethe wave functions of the one-dimensional s = 1 2 Heisenberg model to calculate and numerically evaluate transition rates pertaining to dynamic spin structure factors. For real solutions z1, . . . , zr of the Bethe ansatz equations, the size of the determinants is of order r ×r. We present applications to the zero-temperature spin fluctuations parallel and perpendicular to an external magnetic field.

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“…. as predicted [7,8]. At the upper band edge, the transition rates approach zero in what looks like a linear trend.…”

Section: Applicationsmentioning

confidence: 81%

Transition rates via Bethe ansatz for the spin-½ Heisenberg chain

Biegel¹,

Karbach²,

Müller³

2002

Europhys. Lett.

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“…Of course, the dressed charge ξ has to be calculated numerically. Alternatively, similar results can be obtained by numerical calculations on the basis of the Bethe ansatz equations for finite systems and (37), however involving an explicit extrapolation analysis with the usual disadvantages, see [33] and for finite external fields [34].…”

Section: Correlation Functionsmentioning

confidence: 83%

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

1998

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We present numerical and analytical results for the thermodynamical properties of the spin-1/2 Heisenberg chain at arbitrary external magnetic field. Special emphasis is placed on logarithmic corrections in the susceptibility and specific heat at very low temperatures (T /J = 10 −24 ) and small fields. A longstanding controversy about the specific heat is resolved. At zero temperature the spin-Peierls exponent is calculated in dependence on the external magnetic field. This describes the energy response of the system to commensurate and incommensurate modulations of the lattice. The exponent for the spin gap in the incommensurate phase is given.

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“…As ͉q͉ increases from q s toward , S Ϫϩ (q) increases gradually and at an accelerated rate. The value at the zone boundary diverges in the thermodynamic limit: S Ϫϩ ( )ϳN 1Ϫ1/ , with an exponent (M z /N) that assumes the value 14,15 ͑ 1/4͒ϭ1.53122 . .…”

Section: ͑7͒mentioning

confidence: 99%

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

2002

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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 ,

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Critical properties of the one-dimensional spin-1/2 antiferromagnetic Heisenberg model in the presence of a uniform field

Cited by 35 publications

References 15 publications

Transition rates via Bethe ansatz for the spin-½ Heisenberg chain

Transition rates via Bethe ansatz for the spin-½ Heisenberg chain

The spin-1/2 Heisenberg chain: thermodynamics, quantum criticality and spin-Peierls exponents

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

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