Quantum phase transition in the one-dimensional compass model

Abstract

We introduce a one-dimensional model which interpolates between the Ising model and the quantum compass model with frustrated pseudospin interactions σ z i σ z i+1 and σ x i σ x i+1 , alternating between even/odd bonds, and present its exact solution by mapping to quantum Ising models. We show that the nearest neighbor pseudospin correlations change discontinuosly and indicate divergent correlation length at the first order quantum phase transition. At this transition one finds the disordered ground state of the compass model with high degeneracy 2 × 2 N/2 in the limit of N → ∞.

Quantum Phase Transition in the One-Dimensional XZ Model

“…In the limit N → ∞ the lowest energies of periodic and antiperiodic QIM get equal at α = 1. For 0 < α ≤ 1 they are already two-and threefold degenerate, so when α = 1 the total degeneracy is 5 × 2 N , and the spin gap vanishes [8]. …”

“…The second method used for solving this problem provides more insight into the nature of the quantum phase transition as discussed in Ref. [8], while the first one is more flexible and may be generalized, for instance, to the ladder geometry.…”

“…The solution was described in detail in Ref. [8]. First step is to introduce the Jordan-Wigner (JW) transformation,…”

“…Recently we discussed the properties of the one--dimensional (1D) model that interpolates between the Ising and compass model [8]. The solution based on specific choice of interactions indicated divergences in correlation functions while approaching the transition point.…”

Quantum phase transitions in a generalized compass chain with three-site interactions

“…(1) interpolates between the Ising model at θ = 0 and the quantum compass model (QCM) at θ = π/2, in analogy to the 2D compass model [47]. The model was solved exactly and the ground state is found to have order along the easy axis as long as θ = π/2, whereas it becomes a highly disordered spinliquid ground state at θ = π/2 [48,49]. Here we introduce the XZY−YZX type of three-site interactions in addition,…”