Topological to magnetically ordered quantum phase transition in antiferromagnetic spin ladders with long-range interactions

Abstract

We study a generalized quantum spin ladder with staggered long range interactions that decay as a power-law with exponent \alphaα. Using large scale quantum Monte Carlo (QMC) and density matrix renormalization group (DMRG) simulations, we show that this model undergoes a transition from a rung-dimer phase characterized by a non-local string order parameter, to a symmetry broken N'eel phase. We find evidence that the transition is second order. In the magnetically ordered phase, the spectrum exhibits gapless modes, while excitations in the gapped phase are well described in terms of triplons – bound states of spinons across the legs. We obtain the momentum resolved spin dynamic structure factor numerically and find a well defined triplon band that evolves into a gapless magnon dispersion across the transition. We further discuss the possibility of deconfined criticality in this model.

Continuously varying critical exponents in long-range quantum spin ladders

“…Note, the Hamiltonian in Ref. [72] corresponds to H ▷◁ at λ = 1. In the limit of isolated rung dimers λ = 0, the ground state is given exactly by the product state of rung singlets…”

“…Previous studies of the spin-1/2 Heisenberg chain [41,42,45,49] and the two-leg ladder H ▷◁ for λ = 1 [72] with unfrustrated long-range interactions deduced a quantum phase transition towards Néel order with broken SU(2)-symmetry and thus circumventing the HMW theorem [67][68][69][70][71]. Further, Goldstone's theorem states that the spontaneous breaking of a continuous symmetry gives rise to massless Nambu-Goldstone modes [83][84][85], however, the same restriction applies and the theorem loses its validity in the presence of long-range interactions.…”

“…The HMW theorem can be circumvented when unfrustrated long-range interactions are sufficiently strong, giving rise to a quantum phase transition to a Néel state with broken SU(2)-symmetry [36,41,42,45,47,49,66]. Interestingly, beyond the chain geometry, a recent work [72] has studied an antiferromagnetic quasi one-dimensional two-leg quantum spin ladder with unfrustrated long-range Heisenberg interactions. Here, an exotic deconfined quantum critical point between the gapped short-range isotropic ladder with a non-local string order parameter and the Néel state with broken SU(2)-symmetry has been suggested [72].…”

“…Interestingly, beyond the chain geometry, a recent work [72] has studied an antiferromagnetic quasi one-dimensional two-leg quantum spin ladder with unfrustrated long-range Heisenberg interactions. Here, an exotic deconfined quantum critical point between the gapped short-range isotropic ladder with a non-local string order parameter and the Néel state with broken SU(2)-symmetry has been suggested [72]. The proposed transition goes therefore even beyond the established scenario of deconfined quantum criticality between two ordered phases with local order parameters [49,[73][74][75][76].…”

“…We stress that the model studied in Ref. [72] is contained as one specific parameter line λ = 1 in our twodimensional quantum phase diagram. From our findings and physical arguments we conclude that the investigated long-range Heisenberg quantum spin ladders do not show deconfined criticality.…”