Topological phases protected by shifted sublattice symmetry in dissipative quantum systems

Kawasaki, Makio; Mochizuki, Kimihiro; Obuse, Hideaki

doi:10.1103/physrevb.106.035408

Cited by 17 publications

(7 citation statements)

References 55 publications

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“…In this subsection, we will provide an explanation for the distinctive phase transitions observed in the previous subsection, which differs from the effective NH theory H eff . In a sense, these transitions can be understood from the perspective of dynamical signatures in transient dynamics, which have been demonstrated to play an essential role in the topology of open systems [29,60]. To be specifically, the local evolution of observables, can be attributed to the locality arising from the edge master mode.…”

Section: Dynamical Signaturesmentioning

confidence: 99%

“…Notably, when all the jumping terms are neglected, the system is dynamically equivalent to a NH SSH model [1], with a pair of asymmetric hopping terms in the unit cell [28]. By analyzing its shape matrix, which has emerged as a powerful tool for studying topological extensions [16,29], we consider two scenarios: the jump-present case and jump-absent case. Intriguingly, the topology appears to be entirely encoded within the shape matrix.…”

Section: Introductionmentioning

confidence: 99%

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Topological extension including quantum jump

Niu,

Wang

2024

J. Phys. A: Math. Theor.

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Non-Hermitian systems and the Lindblad form master equation have always been regarded as reliable tools in dissipative modeling. Intriguingly, existing literature often obtains an equivalent non-Hermitian Hamiltonian by neglecting the quantum jumping terms in the master equation. However, there lacks investigation into the effects of discarded terms as well as the unified connection between these two approaches. In this study, we study the Su-Schrieffer-Heeger model with collective loss and gain from a topological perspective. When the system undergoes no quantum jump events, the corresponding shape matrix exhibits the same topological properties in contrast to the traditional non-Hermitian theory. Conversely, the occurrence of quantum jumps can result in a shift in the positions of the phase transition. Our study provides a qualitative analysis of the impact of quantum jumping terms and reveals their unique role in quantum systems.

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Section: Dynamical Signaturesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Topological extension including quantum jump

Niu,

Wang

2024

J. Phys. A: Math. Theor.

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“…Note that a chiral symmetry which is a combination of sublattice symmetry and a shift of the energy spectrum (i.e. a shift proportional to the identity matrix) has recently been discussed in the context of non-Hermitian systems [59].…”

Section: B Symmetries Of the Rice-mele Modelmentioning

confidence: 99%

Nonsymmorphic chiral symmetry and solitons in the Rice-Mele model

Allen

Gibbons

et al. 2022

Phys. Rev. B

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The Rice-Mele model has two topological and spatially-inversion symmetric phases, namely the Su-Schrieffer-Heeger (SSH) phase with alternating hopping only, and the charge-density-wave (CDW) phase with alternating energies only. The chiral symmetry of the SSH phase is robust in position space, so that it is preserved in the presence of the ends of a finite system and of textures in the alternating hopping. However, the chiral symmetry of the CDW wave phase is nonsymmorphic, resulting in a breaking of the bulk topology by an end or a texture in the alternating energies. We consider the presence of solitons (textures in position space separating two degenerate ground states) in finite systems with open boundary conditions. We identify the parameter range under which an atomically-sharp soliton in the CDW phase supports a localized state which lies within the band gap, and we calculate the expectation value py of the nonsymmorphic chiral operator for this state, and the soliton electric charge. As the spatial extent of the soliton increases beyond the atomic limit, the energy level approaches zero exponentially quickly or inversely proportionally to the width, depending on microscopic details of the soliton texture. In both cases, the difference of py from one is inversely proportional to the soliton width, while the charge is independent of the width. We investigate the robustness of the soliton level in the presence of disorder and sample-to-sample parameter variations, comparing with a single soliton level in the SSH phase with an odd number of sites.

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“…While Kawabata et al discovered that only 38 of 43 symmetry classes are topologically inequivalent [26], which is known as 38-fold way. The 38-fold way provides a paradigm to explore the topology of a NH system, which has been applied in many NH systems, such as the NH Sachdev-Ye-Kitaev Model [27], and symmetry classes of the open quantum system [28,29].…”

Section: Introductionmentioning

confidence: 99%