Microscopic model for Bose-Einstein condensation and quasiparticle decay

Abstract

Abstract. -Sufficiently dimerized quantum antiferromagnets display elementary S = 1 excitations, triplon quasiparticles, protected by a gap at low energies. At higher energies, the triplons may decay into two or more triplons. A strong enough magnetic field induces Bose-Einstein condensation of triplons. For both phenomena the compound IPA-CuCl3 is an excellent model system. Nevertheless no quantitative model was determined so far despite numerous studies. Recent theoretical progress allows us to analyse data of inelastic neutron scattering (INS) and of magnetic susceptibility to determine the four magnetic couplings J1 ≈ −2.3 meV, J2 ≈ 1.2 meV, J3 ≈ 2.9 meV and J4 ≈ −0.3 meV. These couplings determine IPA-CuCl3 as system of coupled asymmetric S = 1/2 Heisenberg ladders quantitatively. The magnetic field dependence of the lowest modes in the condensed phase as well as the temperature dependence of the gap without magnetic field corroborate this microscopic model.Low-dimensional antiferromagnetic quantum spin systems display various fascinating properties, e.g., spinPeierls transition [1, 2], appearance of a Haldane gap for integer spins [3,4], high-temperature superconductivity upon doping [5], and the Bose-Einstein condensation (BEC) in spin-dimer systems [6][7][8][9], where the latter one is characterized by a phase transition from a non-magnetic phase to a long-range antiferromagnetically ordered gapless phase at a critical magnetic field H c1 .Another fascinating phenomenon recently observed in low-dimensional antiferromagnets is the decay of their elementary S = 1 excitations, triplons [10], at higher energies so that the triplons exist only in a restricted part of the Brillouin zone [11,12]. 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].The description of quasiparticle decay faces an intrinsic difficulty. The merging of the long-lived, infinitely sharp elementary triplon with a multitriplon continuum requires to describe the resulting resonance and its edges precisely. This is still a challenge for numerical approaches such as exact diagonalization or dynamic density-matrix (a) fischer@fkt.physik.tu-dortmund.de (b) goetz.uhrig@tu-dortmund.de renormalization [20]. 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].A crucial step in the understanding of both phenomena is to identify a suitable experimental system. The best studied candidate for the BEC in coupled spin-dimer systems is TlCuCl 3 . Unfortunately, recent research suggests that the high field spectrum remains gapped [21,22] in contrast to what is expected from a phase where a continuous s...

Low-temperature spin dynamics in the TmFeO3 orthoferrite with a non-Kramers ion

“…In recent years, a wide variety of spin-1/2 and spin-1 quantum many-particle models with exotic disordered ground states have been extensively developed [1]. Accordingly, theoretical studies examined key concepts for exotic quantum matter, as for instance, a quantum spin liquid [2], fractional excitations (spinons) and their confinement [3][4][5], quantum criticality [1,6], and Bose-Einstein condensation [7][8][9]. For a long time, the search for a physical realization of novel quantum phases was mainly limited by materials with 3d transition metals, mostly Cu 2+ or Co 2+ , as a magnetic ion.…”

Symmetric and asymmetric excitations of a strong-leg quantum spin ladder

“…Lately, a lot of effort was put in the study of dimerized strong-rung spin-ladders, such as e.g. the organometallic compounds (CH 3 ) 2 CHNH 3 CuCl 3 (IPA-CuCl 3 ) 10,13,14 or (C 5 H 12 N) 2 CuBr 4 (BPCP) 6,7,15,16 . In this coupling limit, the zero-field excitation spectrum is dominated by gapped but hardly mobile dimer triplet excitations on the rung.…”

Bose–Einstein condensation of triplons with a weakly broken U(1) symmetry

“…Open questions include the possibility to observe macroscopic quantum phenomena such as superfluidity or Josephson effects [41]. Therefore, a possible future extension of the present approach in the spirit of a bond operator formalism [42] or a microscopic model as proposed by Fischer et al [43] would be desirable. The third and fourth order terms may be further simplified by using the approximation given in equation (17) as: with m m = S + S -= S -S -( ) X X , .…”