Confinement of fractional quantum number particles in a condensed-matter system

Abstract

The idea of confinement states that in certain systems constituent particles can be discerned only indirectly being bound by an interaction whose strength increases with increasing particle separation. Though the most famous example is the confinement of quarks to form baryons and mesons in (3+1)-dimensional Quantum Chromodynamics, confinement can also be realized in condensed matter physics systems such as spin-ladders which consist of two spin-1/2 antiferromagnetic chains coupled together by spin exchange interactions. Excitations of individual chains (spinons) carrying spin S=1/2, are confined even by an infinitesimal interchain coupling. The realizations studied so far cannot illustrate this process due to the large strength of their interchain coupling which leaves no energy window for the spinon excitations of individual chains. Here we present neutron scattering experiments for a weakly-coupled ladder material. At high energies the spectral function approaches that of individual chains; at low energies it is dominated by spin 0,1 excitations of strongly-coupled chains.The experiments presented in this paper illustrate the condensed matter realization of the confinement idea. The original and most popularized form of this idea comes from particle theory, more specifically from the theory of strong interactions. It is suggested that heavy particles (baryons and mesons) are made of quarks. The latter particles possess properties (more precisely, quantum numbers) which cannot be directly observed, such as fractional electric charge (±2e/3,±e/3). In a similar fashion in spin ladders excitations of individual spin-1/2 chains (spinons) carry quantum numbers which which are forbidden as soon as the chains are coupled. Quarks are held together by the Yang-Mills (or colour) gauge field which quanta are called gluons. As for any gauge field at smallest distances this interaction obeys the Coulomb law, but at larger distances instead of decreasing it progressively increases due to the gluon-gluon interaction. The popular image is of gluon field lines sticking together and creating some kind of "string" between the quarks. This picture is very appealing since quarks being just end points of a string can under no circumstances appear as individual particles provided the string has a finite tension. Even if one allows the string to snap, none of its pieces can have just one end and hence single quarks still cannot appear. A finite string tension generates an effective potential between the quarks which grows with distance leading to their confinement. Since such a potential well apparently contains infinite number of energy levels, corresponding to different internal energies and hence by the E = mc 2 relation to different particles masses, one would imagine that there is an infinite number of particles with the same quantum numbers, but different masses. This picture is oversimplified, however, failing to take into account the quantum nature of the gluon

Field-Induced Magnonic Liquid in the 3D Spin-Dimerized AntiferromagnetSr3Cr2O8Wang1, Quintero-Castro2, Жерлицын3 et al. 2016Phys. Rev. Lett.182801View full textAdd to dashboardCite

“…Due to enhanced quantum fluctuations and reduced dimensionality, the low-dimensional quantum magnets host very often exotic quantum states of matter [1][2][3][4][5][6][7][8][9][10][11][12][13] . Especially for the one-dimensional (1D) spin systems, realization of novel quantum spin states is not only of lively experimental interest [7][8][9][10]12,13 but also a constant focus of theoretical study 1,2,[14][15][16][17] , since quantitative description of the elementary excitations can be provided by rigorous theoretical approaches and precise comparisons between theoretical predictions and experimental results can be made [7][8][9][10]12,13,15 .…”

“…Confinement of the fractional spinon excitations can be even realized 9,10,[19][20][21][22] as an analogy with quark confinement in particle physics 23 . The concept of spinon confinement is illustrated in [ Fig.…”

Single to Multiquasiparticle Excitations in the Itinerant Helical MagnetCeRhIn5

“…Analogous classic examples of this cross section are found in model insulating low spin chains. [48][49][50][51][52][53][54] We now investigate whether the two component lineshape found here can be understood in terms of a single and multiparticle parameterization.…”

Numerical simulations and magnetism

“…In this case, the dynamical structure factor shows no coherent excitation but an incoherent spectrum called two-spinon continuum, which reflects the range of energies corresponding to the different spinon pairs. Experimental evidence of the two-spinon continuum has been recently reported in quasi-1D systems such as CuP zN [12] or CDC [13], and the quantum spin ladder (C 5 D 12 N ) 2 CuBr 4 [14], as well as in more complex spin-half compounds like the square ladder CaCu 2 O 3 [15], or the two-dimensional triangular lattice Cs 2 CuCl 4 [16].…”