Numerical evidence for unstable magnons at high fields in the Heisenberg antiferromagnet on the square lattice

Abstract

We find evidence for decaying magnons at strong magnetic field in the square lattice spin-1/2 Heisenberg antiferromagnet. The results are obtained using quantum Monte Carlo simulations combined with a Bayesian inference technique to obtain dynamics and are consistent with predictions from spin-wave theory.The square lattice spin-1/2 Heisenberg antiferromagnet ͑2DHAF͒ is the archetype quantum antiferromagnet and describes the magnetism of the mother compounds of the high-T c cuprate materials. 1 While the 2DHAF itself is rather well understood, 2 less is known when additional interactions are added. In this Rapid Communication we report on the nature of the excitations of the 2DHAF in an external magnetic field. Such a perturbation is highly relevant from an experimental point of view and has very interesting consequences.Adding a magnetic field introduces interactions among the magnon excitations of the pure 2DHAF. According to spin-wave theory these interactions will cause the magnons in certain regions of the Brillouin zone to be unstable at very high fields. 3 One should, however, note that spin-wave theory, which is an expansion in the parameter 1 / S, is not at all guaranteed to work for S =1/ 2. Furthermore the spinwave prediction involves certain assumptions as it is a selfconsistent calculation which neglects vertex corrections and renormalizes the spin-wave spectrum considerably. In addition there are also other theoretical predictions of what happens to the 2DHAF in a magnetic field: a scenario where the spin-1 excitation is viewed as a composite excitation of twodimensional spinons predicts additional bands of low-energy excitations at moderate values of the field. 4,5 Thus to settle the issue an independent calculation of the excitation spectrum of the 2DHAF in a magnetic field is needed. It is rather surprising that no such calculation has been performed before, given the prominence and simplicity of the model. In this Rapid Communication we use quantum Monte Carlo ͑QMC͒ simulations combined with a Bayesian inference technique to give a detailed and unbiased description of the excitation spectrum of the 2DHAF in a magnetic field. We find regions with broad spectral features at strong magnetic fields indicating decaying magnons consistent with spinwave theory, and we also show details of the spectrum in the decaying regions.In zero magnetic field the ground state of the 2DHAF is Néel ordered with a renormalized moment. Spin-wave theory explains very well the renormalized moment as well as the dispersion relation of the spin-1 excitations except for an anomaly occurring at ͑ ,0͒ ͑we use units where the lattice spacing a =1͒ where the dispersion softens and the spectrum broadens anomalously. [6][7][8] This anomaly at ͑ ,0͒ is, on the contrary, natural in a picture of the spin-1 excitation as a composite excitation of two spin-1/2 spinons that are excitations about a mean-field pi-flux state. 4 While this bound state has almost the same dispersion as predicted by spin-wave theory, it differs around ͑ ,0͒...

Field-induced decay dynamics in square-lattice antiferromagnets

“…In this case, magnons were shown to be overdamped in most of the Brillouin zone by both the spin-wave calculation, which used a different version of the SCBA, 16 and by the numerical QMC simulations. 17 Such a difference in the effect of magnon interaction between S = 1/2 and S ≥ 1 models deserves a separate discussion. We compare directly the imaginary part of the magnon self-energy at the quasiparticle pole, −ImΣ k (ǭ k ), for the S = 1/2 case obtained in Ref.…”

“…However, this consideration neglects the spectral weight redistribution. The analytical calculation 16 and the QMC study 17 have shown a significant non-Lorentzian broadening of the spectral lines, which takes the form of a double-peak structure in the dynamical susceptibility. Therefore, the overdamping in the S = 1/2 case is produced by two effects: broadening of the quasiparticle peak and spectral weight redistribution.…”

“…On the other hand, excitation spectrum and dynamical properties are expected to undergo rather dramatic transformation. [16][17][18] Following the prediction of the field-induced spontaneous magnon decays in Ref. 16, there is an ongoing search for suitable spin-1/2 square-lattice materials [2][3][4][5] to investigate such an effect.…”

Ab initiolow-energy dynamics of superfluid and solidH4e

“…Other methods have been proposed: the Average Spectrum Method 8 (ASM), which has been recently applied to lattice spin models 9 but also to realistic off-lattice systems 10 , the Stochastic Analytic Continuation (SAC) method 11 and also the spectral analysis described in Ref. 12.…”

Imaginary time correlations and the phaseless auxiliary field quantum Monte Carlo

“…As far as bosonic degrees of freedom are considered, QMC calculations allow static properties, energetics and structure functions, to be computed exactly [1][2][3][4][5][6] even for strongly correlated systems, for which analytic approaches yield only approximate results. Furthermore the possibility of reconstructing dynamical properties of bosonic systems, like excitation spectra and response functions, from imaginary time correlation functions has been explored with remarkable results [3,[7][8][9][10][11][12][13]. On the other hand, for fermionic degrees of freedom the situation is considerably complicated by the well-known sign problem [14,15]: computational cost increases exponentially with the system size.…”