Experimental observation of Bethe strings

Abstract

Almost a century ago, string states-complex bound states of magnetic excitations-were predicted to exist in one-dimensional quantum magnets. However, despite many theoretical studies, the experimental realization and identification of string states in a condensed-matter system have yet to be achieved. Here we use high-resolution terahertz spectroscopy to resolve string states in the antiferromagnetic Heisenberg-Ising chain SrCoVO in strong longitudinal magnetic fields. In the field-induced quantum-critical regime, we identify strings and fractional magnetic excitations that are accurately described by the Bethe ansatz. Close to quantum criticality, the string excitations govern the quantum spin dynamics, whereas the fractional excitations, which are dominant at low energies, reflect the antiferromagnetic quantum fluctuations. Today, Bethe's result is important not only in the field of quantum magnetism but also more broadly, including in the study of cold atoms and in string theory; hence, we anticipate that our work will shed light on the study of complex many-body systems in general.

Magnetic phase diagram of the quantum spin chain compound SrCo2V2O8: a single-crystal neutron diffraction study

“…Concomitantly, the continuum spectrum is replaced by a series of discrete spinon bound states. It has been found that the spinon confinement can be significantly tuned by applying a magnetic field [3][4][5][6][7].…”

“…Recently, the weakly coupled quantum spin chain compound SrCo 2 V 2 O 8 has raised much attention due to the exotic magnetism that it hosts, including the magnetic-field-induced order-disorder transition [11], spinon confinement [5,12] and Bethe strings [7]. This compound crystallizes in a body-centred tetragonal lattice (space group I4 1 cd), in which 4-fold screw chains of CoO 6 -octahedra run along the crystallographic c-axis [13,14].…”

“…The Co 2+ ion (3d 7 ) has an effective spin of 1/2 because of the octahedral distortion and spin-orbit coupling [15,16]. The intrachain spin interactions in SrCo 2 where J>0 is the nearest-neighbour (NN) antiferromagnetic (AFM) exchange constant, ò is the anisotropy parameter, and g z is the component of the Landé g-tensor along the chain direction [5,7,12]. This Hamiltonian can be exactly solved by the Bethe ansatz [17].…”

“…This Hamiltonian can be exactly solved by the Bethe ansatz [17]. The anisotropy in SrCo 2 V 2 O 8 is Ising-like (ò<1) [5,7,[12][13][14], for which the XXZ model predicts a Néel type AFM ground state. A spin disordered state, described as a Tomonaga-Luttinger liquid (TLL), can be induced above a critical magnetic field.…”

Dissociation of One-Dimensional Matter-Wave Breathers due to Quantum Many-Body Effects

“…For attractive interactions with g < 0, there are also eigenstates in the form of one or several several stringsbound states of several particles, i.e., quantum solitons [24,25,44]. Although they remained a theoretical concept since they were introduced, very recently similar states-the Bethe strings-have been directly observed in an antiferromagnetic Heisenberg-Ising chain [45]. A superposition of strings with different velocities may remain localized for a finite time, so that it carries over into a MF multisoliton (breather) in the limit of N → ∞ [26][27][28].…”