Decay of quasiparticles in quantum spin liquids

Abstract

Magnetic excitations are studied in gapped quantum spin systems, for which spontaneous twomagnon decays are allowed by symmetry. Interaction between one-and two-particle states acquires nonanalytic frequency and momentum dependence near the boundary of two-magnon continuum. This leads to a termination point of single-particle branch for one-dimensional systems and to strong suppression of quasiparticle weight in two dimensions. The momentum dependence of the decay rate is calculated in arbitrary dimensions and effect of external magnetic field is discussed.PACS numbers: 75.10. Jm, 75.10.Pq, 78.70.Nx A number of magnetic materials with quantum disordered, or spin-liquid, ground states have been discovered in the past two decades. The well-known examples include the spin-Peierls compound CuGeO 3 , 1 dimer systems Cs 3 Cr 2 Br 9 2 and TlCuCl 3 , 3 integer-spin antiferromagnetic chains, 4 and many others. Common property of all these systems is presence of a spin gap in the excitation spectrum, which separates a singlet, S = 0 ground state from S = 1 quasiparticles. The lowenergy triplet of magnons can be split due to intrinsic anisotropies or under applied magnetic field. Recent neutron experiments 5,6 on two organic spin-gap materials PHCC and IPA-CuCl 3 have revealed drastic transformation of triplet quasiparticles undergoing at high energies. Upon entering two-magnon continuum, see Fig. 1, spontaneous (T = 0) decay of a magnon into a pair of quasiparticles becomes possible, which leads to a rapid decrease in the quasiparticle life-time in the former case 5 and complete disappearance of the single-particle branch in the latter system. 6 Quasiparticle instability is well documented for another type of quantum liquid-superfluid 4 He. Predicted by Pitaevskii nearly fifty years ago, 7,8,9 this instability was later confirmed by neutron scattering measurements. 10,11 In liquid helium, interaction between one-and two-particle states is enhanced in the vicinity of a decay threshold by a large density of roton states and leads to avoided crossing: the single-particle branch flattens at energies below twice the roton energy and ceases to exist completely above that energy scale.The aim of present article is to investigate similar effects in quantum spin liquids. We consider an isotropic spin system with a quantum disordered ground state, which is separated by a finite gap ∆ from low-energy spin-1 excitations. A bare dispersion of propagating triplets is given by ε(p). Bosonic operators t pα and t † pα destroy and create a quasiparticle with momentum p in one of the three polarizations α = x, y, z. Interaction between one-and two-particle states is, generally, described by two types of cubic vertices shown in Fig. 2a,b. In superfluid 4 He presence of such particle non-conserving processes is determined by a Bose condensate, which absorbs or emits an extra particle. 8,12 In quantum spin systems with singlet ground states one finds a more diverse situation. Symmetry of a majority of low-dimensional dimer systems, like, fo...

Quasiparticle-continuum level repulsion in a quantum magnet

“…Furthermore, these branches remain resolution-limited in energy at all wavevectors, but terminate abruptly inside the continuum. This is a spectacular example of a spontaneous quasiparticle breakdown, where the decay channels are so effective that an appropriate description of the system in terms of quasiparticles does not exist 4,24 . To understand this behaviour quantitatively, we have extended the BOT to include anharmonic (both cubic and quartic) interaction terms.…”

Microscopic model for Bose-Einstein condensation and quasiparticle decay

“…Such systems are of great current interest because they allow for the study of Bose-Einstein condensation of triplons and of the massless excitations above this condensate [8,9]. Additionally, they represent gapped quantum liquids known to display considerable quasiparticle decay [13][14][15][16].…”

“…Diagrammatic approaches are able to capture the qualitative features but may encounter difficulties in the quantitative description in the regime of strong merging where the sharp mode dissolves completely in the continuum because this is a strong coupling phenomenon [13,14]. Unitary transformations also face difficulties when modes of finite life-time occur [16].…”

“…Theoretically as well, there is rising interest in the understanding and quantitative description of this phenomenon for gapped triplons [13][14][15][16] as well as for gapless magnons [17][18][19].…”

Field-induced decay dynamics in square-lattice antiferromagnets

“…31,32 Similar effects in quantum magnets have started to attract attention only recently. 9,16,26,[33][34][35][36] Appearance of spontaneous twomagnon decays for the SAFM is controlled by the energy conservation law:…”