Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains

Fuji, Yohei; Pollmann, Frank; Oshikawa, Masaki

doi:10.1103/physrevlett.114.177204

Cited by 47 publications

(73 citation statements)

References 40 publications

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“…Tensor-network [22] and spatial gauge field [23] arguments have been presented to justify this general rule. The rule is also consistent with numerous studies of SPT phases protected by specific spatial symmetries [39,41,[101][102][103][104][105][106][107][108], especially Ref. [41], which considered all 3D space-groups.…”

Section: Appendix A: the Twisted Generalized Cohomology Hypothesissupporting

confidence: 90%

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

Xiong

Alexandradinata

2018

Phys. Rev. B

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It is demonstrated that fermionic/bosonic symmetry-protected topological (SPT) phases across different dimensions and symmetry classes can be organized using geometric constructions that increase dimensions and symmetry-reduction maps that change symmetry groups. Specifically, it is shown that the interacting classifications of SPT phases with and without glide symmetry fit into a short exact sequence, so that the classification with glide is constrained to be a direct sum of cyclic groups of order 2 or 4. Applied to fermionic SPT phases in the Wigner-Dyson class AII, this implies that the complete interacting classification in the presence of glide is Z4⊕Z2⊕Z2 in 3 dimensions. In particular, the hourglass-fermion phase recently realized in the band insulator KHgSb must be robust to interactions. Generalizations to spatiotemporal glide symmetries are discussed. arXiv:1709.06998v3 [cond-mat.str-el]

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Section: Appendix A: the Twisted Generalized Cohomology Hypothesissupporting

confidence: 90%

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

Xiong

Alexandradinata

2018

Phys. Rev. B

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“…Our results clarify that fragile topological phases can exist in a much more general setting than systems of noninteracting electrons. Their necessary ingredients appear to be spatial symmetries which are rich enough to protect distinct product states [1,22,26,29,30], together with particles carrying a charge which is unbounded and single-signed. Provided oppositely charged particles are physically prohibited, fragile topological phases showcase protected ground-state entanglement much like their conventional counterparts.…”

Section: Discussionmentioning

confidence: 99%

Fragile topological phases in interacting systems

Else

Watanabe

2019

Phys. Rev. B

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Topological phases of matter are defined by their nontrivial patterns of ground-state quantum entanglement, which is irremovable so long as the excitation gap and the protecting symmetries, if any, are maintained. Recent studies on noninteracting electrons in crystals have unveiled a peculiar variety of topological phases, which harbors nontrivial entanglement that can be dissolved simply by the the addition of entanglement-free, but charged, degrees of freedom. Such topological phases have a weaker sense of robustness than their conventional counterparts, and are therefore dubbed "fragile topological phases." In this work, we show that fragile topology is a general concept prevailing beyond systems of noninteracting electrons. Fragile topological phases can generally occur when a system has a U(1) charge conservation symmetry, such that only particles with one sign of the charge are physically allowed (e.g. electrons but not positrons). We demonstrate that fragile topological phases exist in interacting systems of both fermions and of bosons. arXiv:1809.02128v2 [cond-mat.str-el]

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“…In particular, the identification of the symmetries of the VBS phases is a non-trivial matter. 28,29 The boundaries between the phases as well as the ensuing g.s. degeneracies can be established via DMRG simulations (see Appendix D): in Fig.…”

Section: Z J I Z W F F I L J W D a R K D O N X V J S = " > A A A C mentioning

confidence: 99%

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

et al. 2019

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We show that the coupling of homogeneous Heisenberg spin-1/2 ladders in different phases leads to the formation of interfacial zero energy Majorana bound states. Unlike Majorana bound states at the interfaces of topological quantum wires, these states are void of topological protection and generally susceptible to local perturbations of the host spin system. However, a key message of our work is that in practice they show a high degree of resilience over wide parameter ranges which may make them interesting candidates for applications. Introduction:The Majorana fermion has become one of the most important fundamental quasi particles of condensed matter physics. Besides its key role as a building block in correlated quantum matter, much of this interest is motivated by perspectives in quantum information. 1-3 Majorana qubits have unique properties which make them ideal candidates for applications in, e.g., stabilizer code quantum computation. 4 Current experimental attempts to isolate and manipulate Majorana bound states (MBSs) focus on interfaces between distinct phases of symmetry protected topological (SPT) quantum matter. These material platforms have the appealing property that MBSs are protected against local perturbations by principles of topology. In practice, however, topological protection may play a lesser role than one might hope, and various obtrusive aspects of realistic quantum materials appear to challenge the isolation and manipulation of MBSs. Specifically, in topological quantum wires based on the hybrid semiconductor-superconductor platform 5 or on coupled ferromagnetic atoms, 6 all relevant scales are confined to narrow windows in energy. In this regard, proposals to realize MBSs in topological insulator nanowires 7 may offer superior solutions. However, these realizations require a high level of tuning of external parameters, notably of magnetic fields, and may be met with their own difficulties.In this Letter, we suggest an alternative hardware platform for the isolation of zero-energy MBSs. Our proposal does not engage topology. Specifically, local perturbations of the microscopic Hamiltonian may induce nonlocal correlations between the emergent Majorana quantum particles. However, we argue below that in practice this problem is less drastic than one might fear, and that the current architecture may grant a high level of effective protection. The numerical evidence provided below certainly points in this direction.The material platform we suggest is based on spin ladder materials. Their phases can be classified by combining standard Landau-Ginzburg symmetry breaking with the presence of SPT order. 8,9 We show here that combining ladders in different phases provides a systematic means to generating interface MBSs. The formal bridge between the physics of spin ladders and that of Majorana fermions is provided by a two-step mapping, first representing the spin degrees of freedom by bosons, followed by refermionization of the latter into an effective Majorana theory. 10 We will discuss how nume...

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Distinct Trivial Phases Protected by a Point-Group Symmetry in Quantum Spin Chains

Cited by 47 publications

References 40 publications

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

Organizing symmetry-protected topological phases by layering and symmetry reduction: A minimalist perspective

Fragile topological phases in interacting systems

Nontopological Majorana Zero Modes in Inhomogeneous Spin Ladders

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