We discuss the characterization and stability of the Haldane phase in integer spin chains on the basis of simple, physical arguments. We find that an odd-$S$ Haldane phase is a topologically non-trivial phase which is protected by any one of the following three global symmetries: (i) the dihedral group of $π$-rotations about $x,y$ and $z$ axes; (ii) time-reversal symmetry $S^{x,y,z} \rightarrow - S^{x,y,z}$; (iii) link inversion symmetry (reflection about a bond center), consistently with previous results [Phys. Rev. B \textbf{81}, 064439 (2010)]. On the other hand, an even-$S$ Haldane phase is not topologically protected (i.e., it is indistinct from a trivial, site-factorizable phase). We show some numerical evidence that supports these claims, using concrete examples.
Symmetry protection of critical phases and global anomaly in $1+1$ dimensions
基于Gepner和Witten发现的离散$\mathbb{Z}_2$对称性的整体反常，我们导出了一个在$(1+1)$维SU（2）Wess-Zumino-Witten理论中的选择定则.在SU（2）对称和$\mathbb{Z}_2$对称同时存在的情况下，只有当$k\equiv k' \mod{2}$满足时，才有可能在能级$k$和能级$k'$ Wess-Zumino-Witten理论之间发生重整化群流.这将洛伦兹不变的SU（2）对称临界行为分为两个“受保护的”类别，分别对应于偶数和奇数能级，限制了洛伦兹不变量子自旋链可能的无间隙临界行为。
Topological Protection by Local Support Symmetry and Destructive Interference
Ajou University（亚洲大学）；Korea Advanced Institute of Science and Technology（韩国科学技术院）；Konkuk University（建国大学）；Hongik University（弘益大学）；Princeton University（普林斯顿大学）；Donostia International Physics Center（圣塞巴斯蒂安国际物理中心）；IKERBASQUE, Basque Foundation for Science（伊卡巴斯基奎，巴斯克科学基金会）
The bulk electric polarization works as a nonlocal order parameter that characterizes topological quantum matters. Motivated by a recent paper [H. Watanabe \textit{et al.}, Phys. Rev. B {\bf 103}, 134430 (2021)], we discuss magnetic analogs of the bulk polarization in one-dimensional quantum spin systems, that is, quantized magnetizations on the edges of one-dimensional quantum spin systems.The edge magnetization shares the topological origin with the fractional edge state of the topological odd-spin Haldane phases. Despite this topological origin, the edge magnetization can also appear in top…
Disorder-enhanced topological protection and universal quantum criticality in a spin-3/2 topological superconductor
Texas Center for Superconductivity and Department of Physics, University of Houston（休斯顿大学物理系超导电性中心）；Department of Physics and Astronomy, Rice University（莱斯大学物理与天文学系）；Rice Center for Quantum Materials, Rice University（莱斯大学量子材料中心）
Topological protection is employed in fault-tolerant error correction and in developing quantum algorithms with topological qubits. But, topological protection intrinsic to models being simulated, also robustly protects calculations, even on NISQ hardware. We leverage it by simulating Kitaev-inspired models on IBM quantum computers and accurately determining their phase diagrams. This requires constructing conventional quantum circuits for Majorana braiding to prepare the ground states of Kitaev-inspired models. The entanglement entropy is then measured to calculate the quantum phase boundarie…
Higher-fold chiral fermions that go beyond two-fold Weyl fermions have recently been reported in crystalline systems. Here, we focus on such excitations in several binary, ternary and quaternary alloys/compounds with CoGe, BiSbPt and KMgBO3 as the representative examples that belong to the crystal space group (SG) 198. We found distinct three-fold, four-fold and six-fold chiral fermions in the bulk via Density Functional computations. We provide general symmetry arguments for the protection of these degeneracies with special emphasis on the four-fold fermions. Our surface spectra simulations s…
Topological delocalization and tuning of surface channel separation in Bi2Se2Te Topological Insulator Thin films
三维拓扑绝缘体（TI）的表面态具有抗后向散射的拓扑保护作用。然而，体电子对输运数据的贡献是表面拓扑保护的一个障碍。我们报告的化学势的调谐在大块的Bi 2 Se 2 Te TI薄膜，钉扎它附近的中心的散装带隙，从而抑制散装载流子。这些薄膜的温度依赖性电阻显示出低至50K的活化行为，随后在较低温度下发生金属转变，这是TI表面态稳健性的标志。用二维弱反定域化现象解释了拓扑保护和表面支配输运的表现。在这项工作中，我们进一步探讨了TI中的表面到体耦合的效果，这是由参与运输的有效导电表面通道的数量捕获的。单个导电通道的存在表明强的表面到体耦合，这对纯拓扑输运是有害的。我们证明了在薄膜的相对表面上的拓扑表面态的解耦，从而抑制了体输运。我们的研究结果提供了一个更深入的了解，随着拓扑输运行为和它们各自的可调性的表面到体耦合。
The nature of symmetry-protected topological phases of Heisenberg spin chains in totally symmetric representations of rank N of the SU(N) group is investigated through a Majorana fermion study starting from an integrable point. The latter approach generalizes the one pioneered by Tsvelik [A. M. Tsvelik, Phys. Rev. B 42, 10 499 (1990)] to describe the low-energy properties of the Haldane phase of the spin-1 Heisenberg chain from three massive Majorana fermions. We find for all N the emergence of a non-degenerate gapped phase with edge states whose topological protection depends on the parity of…
Quantum-simulator hardware promises new insights into problems from particle and nuclear physics. A major challenge is to reproduce gauge invariance, as violations of this quintessential property of lattice gauge theories can have dramatic consequences, e.g., the generation of a photon mass in quantum electrodynamics. Here, we introduce an experimentally friendly method to protect gauge invariance in $\mathrm{U}(1)$ lattice gauge theories against coherent errors in a controllable way. Our method employs only single-body energy-penalty terms, thus enabling practical implementations. As we deriv…
