Entanglement driven phase transitions in spin–orbital models

Abstract

To demonstrate the role played by the von Neumann entropy (vNE) spectra in quantum phase transitions we investigate the one-dimensional anisotropic SU(2) XXZ ⊗ spin-orbital model with negative exchange parameter. In the case of classical Ising orbital interactions we discover an unexpected novel phase with Majumdar-Ghosh-like spin-singlet dimer correlations triggered by spin-orbital entanglement (SOE) and having k 2 π = orbital correlations, while all the other phases are disentangled. For anisotropic XXZ orbital interactions both SOE and spin-dimer correlations extend to the antiferro-spin/alternating-orbital phase. This quantum phase provides a unique example of two coupled order parameters which change the character of the phase transition from first-order to continuous. Hereby we have established the vNE spectral function as a valuable tool to identify the change of ground state degeneracies and of the SOE of elementary excitations in quantum phase transitions. OPEN ACCESS RECEIVED

Quantum entanglement in the one-dimensional spin-orbitalSU(2)⊗XXZmodel

“…The orbital order changes from phase II (AF/FO) to phase III (AF/AO), as shown in Ref. [50], but the Néel order persists in both of them and manifests itself in the two-spin correlation, S z i S z i+r . For translational invariant and orthonormal linear combinations of the symmetry-broken Néel (AF) states, 18) which is equivalently revealed by the structure factors S zz (k) and T zz (k) defined by Eqs.…”

“…This choice of the exchange coupling restricts somewhat joint spin-orbital fluctuations being large near the SU(4) symmetric point, (x, y) = (0.25, 0.25), in the 1D spin-orbital model with positive, i.e., AF coupling constant [56], but opens other interesting possibilities for entangled states, as we have shown recently [50]. Both total spin magnetization S z and orbital polarization T z are conserved, and time reversal symmetry leads to the total momentum either k = 0 or k = π.…”

“…Here we focus on the model with negative exchange interaction. This choice of the exchange coupling restricts somewhat joint spin-orbital fluctuations being particularly large near the SU(4) symmetric point in the 1D spin-orbital model with positive coupling constant [56], but opens novel possibilities for entangled states, as we show below [50]. An interesting phase with entangled ground state, consisting of alternating spin singlets along the spin-orbital ring, is found for Ising orbital interactions when the dimerization in the spin channel induces the change from FO to alternating orbital (AO) correlations.…”

“…When ∆ = 0, there is no dynamics in the orbital sector, and the orbital structure factor is dominated by a single mode which follows from the Z 2 symmetry [50]. This changes when 0 < ∆ ≤ 1 and the quantum fluctuations in the orbital sector contribute.…”

“…Though much attention was devoted to the ground state in the past [47], it has been noticed only recently that the entanglement entropy of low-energy excitations may provide even more valuable insights [43,48,49] which are of crucial importance to understand the origin of quantum phase transitions in spin-orbital systems [50]. The well known area law of the bipartite entanglement entropy restricts the Hilbert space accessible to a ground state of gapped systems [51,52], while the area law is violated by a leading logarithmic correction in critical systems, whose prefactor is determined by the number of chiral modes and precisely given by Widom conjecture [53].…”