Quantum entanglement in theS=1∕2spin ladder with ring exchange

Abstract

In this paper we study the concurrence and the block-block entanglement in the S = 1/2 spin ladder with four-spin ring exchange by the exact diagonalization method of finite cluster of spins. The relationship between the global phase diagram and the ground-state entanglement is investigated. It is shown that the block-block entanglement of different block size and geometry manifests richer information of the system. We find that the extremal point of the two-site block-block entanglement on the rung locates a transition point exactly due to SU (4) symmetry at this point. The scaling behavior of the block-block entanglement is discussed. Our results suggest that the block-block entanglement can be used as a convenient marker of quantum phase transition in some complex spin systems.

Topological identification of a spin-12two-leg ladder with four-spin ring exchange

“…The staggered dimer and scalar-chirality phases around the self-dual point are Z 2 symmetry-breaking phase with twofold degeneracy in the thermodynamic limit. 20 In a N = 16 system, there is a finite-size gap in the S z = 0 sector of H cyc for most values of and we can obtain the Berry phase. However, results around the self-dual point in Fig.…”

“…This adiabatic connection is consistent with the fact that the ground state is well approximated by the product of local rung singlets and is identified by entanglement concurrence of two spins on a rung. 20 …”

“…20 Motivated by the vectorchirality order parameter, we consider the adiabatic modification from H cyc ͉ =0.8 in the dominant vector-chirality phase to a decoupled model as follows:…”

“…11 Especially, the two-leg ladder model with the multiplespin exchange interactions has been studied extensively. [12][13][14][15][16][17][18][19] To clarify its rich phases, not only correlation functions corresponding to phases but also entanglement concurrence, 20 entanglement entropy, 21,22 and string order 14,23 are useful to characterize the phases. As such a novel order parameter, which is beyond the Ginzburg-Landau symmetry-breaking description, there is an order parameter based on the topological invariants corresponding to the topological order.…”

Semiclassical approach to competing orders in a two-leg spin ladder with ring exchange

“…16). The model (1) is interesting in its own right and has been studied extensively over the years and its phase diagram [26][27][28][29][30] , ground-state-and dynamical properties 14,[31][32][33] , quantum phase transitions [34][35][36] , and entanglement properties [37][38][39] have been explored by both analytical and numerical approaches.…”