Comment on “Unique Translation between Hamiltonian Operators and Functional Integrals”

We re-examine the 1/S-correction to the self-energy of the gapless magnon of a D-dimensional quantum Heisenberg antiferromagnet in a uniform magnetic field h using a hybrid approach between 1/S-expansion and non-linear sigma model, where the Holstein-Primakoff bosons are expressed in terms of Hermitian field operators representing the uniform and the staggered components of the spin-operators [N. Hasselmann and P. Kopietz, Europhys. Lett. 74, 1067 (2006)]. By integrating over the field associated with the uniform spin-fluctuations we obtain the effective action for the staggered spin-fluctuations on the lattice, which contains fluctuations on all length scales and does not have the cutoff ambiguities of the non-linear sigma model. We show that in dimensions D ≤ 3 the magnetic field dependence of the spin-wave velocityc−(h) is non-analytic in h 2 , withc−(h)−c−(0) ∝ h 2 ln |h| in D = 3, andc−(h) −c−(0) ∝ |h| in D = 2. The frequency dependent magnon self-energy is found to exhibit an even more singular magnetic field dependence, implying a strong momentum dependence of the quasi-particle residue of the gapless magnon. We also discuss the problem of spontaneous magnon decay and show that in D > 1 dimensions the damping of magnons with momentum k is proportional to |k| 2D−1 if spontaneous magnon decay is kinematically allowed.

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Comment on “Unique Translation between Hamiltonian Operators and Functional Integrals”

Cited by 2 publications

References 4 publications

Functional Renormalization Group and the Transition in⁴He

Functional Renormalization Group and the Transition in⁴He

Quantum Heisenberg antiferromagnets in a uniform magnetic field: Nonanalytic magnetic field dependence of the magnon spectrum

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Comment on “Unique Translation between Hamiltonian Operators and Functional Integrals”

Cited by 2 publications

References 4 publications

Functional Renormalization Group and the Transition in4He

Functional Renormalization Group and the Transition in4He

Quantum Heisenberg antiferromagnets in a uniform magnetic field: Nonanalytic magnetic field dependence of the magnon spectrum

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Functional Renormalization Group and the Transition in⁴He

Functional Renormalization Group and the Transition in⁴He