Spectrum of a Magnetized Strong-Leg Quantum Spin Ladder

Inelastic neutron scattering is used to measure the spin excitation spectrum of the Heisenberg $S=1/2$ ladder material $({\mathrm{C}}_7{\mathrm{H}}_{10}\mathrm{N}{)}_2{\mathrm{CuBr}}_4$ in its entirety, both in the gapped spin liquid and the magnetic field-induced Tomonaga-Luttinger spin liquid regimes. A fundamental change of the spin dynamics is observed between these two regimes. Density matrix renormalization group calculations quantitatively reproduce and help understand the observed commensurate and incommensurate excitations. The results validate long-standing quantum field-theoretical predictions but also test the limits of that approach.

Figure 1

(a) Time-of-flight inelastic neutron scattering spectrum measured on DIMPY in zero applied field ($E_i=4.2\mathrm{meV}$). (b) A DMRG calculation of the same spectrum, folded with the known resolution function of the neutron instrument for a direct comparison with experiment.

Figure 2

Spin excitations in DIMPY at $H=2.55\mathrm{T}$. Inelastic neutron data were measured at $T=70\mathrm{mK}$ in the low-resolution [(a) $E_i=4.2\mathrm{meV}$] and high-resolution [(b) $E_i=2.2\mathrm{meV}$] modes. (c),(d) Numerical DMRG calculations, convoluted with experimental resolution. Dashed lines indicate the onset of the elastic line in the experiment. Solid lines indicate the low-energy magnon excitations with relativistic dispersion.

Figure 3

Spectrum of DIMPY at $H=7\mathrm{T}$. (a)–(d) and dashed lines: Same as in Fig. 2. Lines are linear fits to the dispersion of the gapless excitations. Symbols with arrows are specific features predicted by a QFT mapping of the ladder model [13], as described in the text.

Figure 4

Calculated components of the $H=7\mathrm{T}$ excitation spectrum of DIMPY, classified by their spin projection quantum number (top to bottom) and parity with respect to ladder-leg interchange (left, asymmetric; right, symmetric). Lines and symbols are as in Fig. 3.