Magnetic field induced bound states in spin-$\frac{1}{2}$ ladders

TL;DR

This paper investigates magnetic field-induced bound states in spin-1/2 ladders, explaining experimental mode splittings in BPCB through DMRG and analytical methods, revealing bound states with field-independent binding energy.

Contribution

It introduces a theoretical framework showing bound states are generically present in spin ladders above the critical field, matching experimental observations in BPCB.

Findings

Bound states exist near k=0 above Hc1 in spin ladders.

Binding energy of these states is field-independent.

Intensity of bound states increases with magnetic field.

Abstract

Motivated by the intriguing mode splittings in a magnetic field recently observed with inelastic neutron scattering in the spin ladder compound (C$_5$H$_{12}$N)$_2$CuBr$_4$ (BPCB), we investigate the nature of the spin ladder excitations using DMRG and analytical arguments. Starting from the fully frustrated ladder, for which we derive the low-energy spectrum, we show that bound states are generically present close to $k=0$ in the dynamical structure factor of spin ladders above $H_{c 1}$, and that they are characterized by a field-independent binding energy and an intensity that grows with $H-H_{c 1}$. These predictions are shown to explain quantitatively the split modes observed in BPCB.