Quantum phase transition for the XY chain with Dzyaloshinsky–Moriya interaction

Ye, Biao‐Liang; Luo, Yan; Jiang, Shuyuan; Zhang, Dan; Xu, Jianqin; Wang, Xiaohao; Yang, Chui‐Ping

doi:10.1142/s021974991850051x

Cited by 1 publication

(2 citation statements)

References 30 publications

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“…Here we also obtain the exact energy spectrum for this model using Eqs. (17)(18)(19)(20)(21)(22)(23)(24)(25)(26)(27)(28)(29)(30) and analyze what ground and first excited states are composed of by examining odd/even sector and the number of fermions occupation. If we restrict ourselves to the region −2 < g < 2, we find that the ground state comes from the even sector (b = 1/2) with no fermions and the first excited state is constructed from the odd sector (b = 0) with one-fermion occupation.…”

Section: Ghz-cluster Modelmentioning

confidence: 99%

“…Therefore, quantum entanglement may be an alternative way to detect a quantum phase transition [15,25], other than the thermodynamic quantities. Besides interest from quantum information and quantum phase transitions [26][27][28][29][30][31], quantum entanglement is not only a powerful theoretical concept but also has been measured in several recent experiments [32][33][34][35]. In particular, (cluster) spin models can be implemented in experiments and simulated in quantum information processors [36][37][38][39][40][41][42][43][44].…”

Section: Introductionmentioning

confidence: 99%

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Geometric entanglement and quantum phase transition in generalized cluster-XY models

Deger

Wei

2019

Quantum Inf Process

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In this work, we investigate quantum phase transition (QPT) in a generic family of spin chains using the ground-state energy, the energy gap, and the geometric measure of entanglement (GE). In many of prior works, GE per site was used. Here, we also consider GE per block with each block size being two. This can be regarded as a coarse grain of GE per site. We introduce a useful parameterization for the family of spin chains that includes the XY models with n-site interaction, the GHZ-cluster model and a cluster-antiferromagnetic model, the last of which exhibits QPT between a symmetry-protected topological phase and a symmetry-breaking antiferromagnetic phase. As the models are exactly solvable, their ground-state wavefunctions can be obtained and thus their GE can be studied. It turns out that the overlap of the ground states with translationally invariant product states can be exactly calculated and hence the GE can be obtained via further parameter optimization. The QPTs exhibited in these models are detected by the energy gap and singular behavior of geometric entanglement. In particular, the XzY model exhibits transitions from the nontrivial SPT phase to a trivial paramagnetic phase. Moreover, the halfway XY model exhibits a first-order transition across the Barouch-McCoy circle, on which it was only a crossover in the standard XY model.

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