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理论物理通讯：英文版

Quantum Phase Transitions, Entanglement Spectrum, and Schmidt Gap in Bond-Alternative S=1 Antiferromagnetic Chain

刘光华, 张钰, 田光善

Published Jan 1, 2014• 0 citations
OpenAlex

Abstract

0.587，并且 QPT 的秒顺序特性被验证。平、奇怪的契约的二倍地退化的纠纷系列在霍尔丹阶段被观察，由哪个能容易把霍尔丹阶段与汗衫暗淡的阶段区分开来。铁磁性的关联在整个参数区域被发现的近邻居的 antiferromagnetic 关联和 next-nearest-neighbor。在批评的无团的点，尽管指数地腐烂的 antiferromagnetic 关联被观察，它最后来临到经常的价值。因此，远程的关联存在并且关联长度在批评的点变得分叉。

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0.587，并且 QPT 的秒顺序特性被验证。平、奇怪的契约的二倍地退化的纠纷系列在霍尔丹阶段被观察，由哪个能容易把霍尔丹阶段与汗衫暗淡的阶段区分开来。铁磁性的关联在整个参数区域被发现的近邻居的 antiferromagnetic 关联和 next-nearest-neighbor。在批评的无团的点，尽管指数地腐烂的 antiferromagnetic 关联被观察，它最后来临到经常的价值。因此，远程的关联存在并且关联长度在批评的点变得分叉。
Bipartite entanglement, entanglement spectrum, and Schmidt gap in S=1 bond-alternative antiferromagnetic Heisenberg chain are investigated by the infinite time-evolving block decimation (iTEBD) method. The quantum phase transition (QPT) from the singlet-dimer phase to the Haldane phase can be detected by the singular behavior of bipartite entanglement, the sudden change of the entanglement spectrum, and the completely vanishing of the Schmidt gap. The critical point is determined to be around r c ≃ 0.587, and the second-order character of the QPT is verified. Doubly degenerate entanglement spectra of both even and odd bonds are observed in the Haldane phase, by which one can distinguish the Haldane phase from the singlet-dimer phase easily. Nearest-neighbor antiferromagnetic correlations and next-nearest-neighbor ferromagnetic correlations are found in the whole parameter region. At the critical massless point, although exponentially decaying antiferromagnetic correlation is observed, it approaches to a constant value finally. Therefore, long-range correlations exist and the correlation length becomes divergent at the critical point.
A series of symmetry-protected topological(SPT) and trivial spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with alternating next-nearest-neighbour interaction are investigated using two kinds of entanglement spectra defined by different divisions of the whole chain. In the case one of the next-nearest-neighbor interaction vanishes, the model reduces to the ΔΔΔ-chain in which a series of spin-gap phases are found in J. Phys. Soc. Jpn. 77, 044707 (2008). From the degeneracy of the entanglement spectra, these phases are identified as the SPT and trivial phases. It is found that the ground state phases boundaries are insensitive to the strength of the alternation in next-nearest neighbor interaction. These results are consistent with the analysis based on the nonlinear σσσ model and exact solution on the ferromagnetic-nonmagnetic phase boundary.
The topological classification of a series of frustration-induced spin-gap phases in the spin-1/2 ferromagnetic--antiferromagnetic alternating Heisenberg chain with next-nearest-neighbour interaction reported in J. Phys. Soc. Jpn. 82, 064703 (2013) is confirmed using two kinds of entanglement spectra defined by different divisions of the whole chain. For the numerical calculation, the iDMRG method is used. The results are consistent with the valence bond solid picture proposed in the previous paper.