Gravitational response of topological quantum states of matter

Jiang, Guodong; Chen, YingKang; Iyer‐Biswas, Srividya; Biswas, Rudro R.

doi:10.1103/physrevb.107.195403

Cited by 4 publications

(2 citation statements)

References 39 publications

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“…Intriguing phenomena have been reported when CIs were proposed in singular lattices with arbitrary n-fold rotational symmetry [25][26][27][28][29], such as defect-core states, fractional charge and multiple branches of edge excitations. These singular lattices can be constructed by 'cutting and gluing' unit sectors with a disk geometry.…”

Section: Introductionmentioning

confidence: 90%

“…Besides, as a topological response of singular CIs, fractional charge emerges around the singularities. For example, the charge fractionalization in unit of e/4 has been reported in the curved-Haldane and curved-Kagomé models [25,27,29,30]. How to construct and characterize the topological properties of curved-QCIs and whether charge fractionalization emerges in curved-QCIs, remain open.…”

Section: Introductionmentioning

confidence: 99%

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C_n -symmetric quasi-periodic Chern insulators

Han,

Zhou,

2024

New J. Phys.

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Chern insulators have been recently extended to quasicrystal systems, namely the quasi-periodic Chern insulators (QCIs). Here we study the topological properties and topological response of QCIs on two-dimensional singular surfaces. Such singular QCIs with arbitrary n−fold rotational symmetry (i.e. Cn-symmetric QCIs) can be constructed by “cutting and gluing” unit sectors on the Dürer’s pentagonal tiling. Chiral edge states and real-space Chern number can well characterize the topological properties of Cn-symmetric QCIs. Intriguingly, we numerically identify the emergence of charge fractionalization in unit of e/10 around the singular center in Cn-symmetric QCIs though their bulk densities are inhomogeneous. In addition, we explore the phase transitions of these Cn-symmetric QCIs.

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Section: Introductionmentioning

confidence: 90%

Section: Introductionmentioning

confidence: 99%

C_n -symmetric quasi-periodic Chern insulators

Han,

Zhou,

2024

New J. Phys.

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Interacting topological quantum chemistry in 2D with many-body real space invariants

Herzog-Arbeitman,

Bernevig,

Song

2024

Nat Commun

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The topological phases of non-interacting fermions have been classified by their symmetries, culminating in a modern electronic band theory where wavefunction topology can be obtained from momentum space. Recently, Real Space Invariants (RSIs) have provided a spatially local description of the global momentum space indices. The present work generalizes this real space classification to interacting 2D states. We construct many-body local RSIs as the quantum numbers of a set of symmetry operators on open boundaries, but which are independent of the choice of boundary. Using the U(1) particle number, they yield many-body fragile topological indices, which we use to identify which single-particle fragile states are many-body topological or trivial at weak coupling. To this end, we construct an exactly solvable Hamiltonian with single-particle fragile topology that is adiabatically connected to a trivial state through strong coupling. We then define global many-body RSIs on periodic boundary conditions. They reduce to Chern numbers in the band theory limit, but also identify strongly correlated stable topological phases with no single-particle counterpart. Finally, we show that the many-body local RSIs appear as quantized coefficients of Wen-Zee terms in the topological quantum field theory describing the phase.

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“Quantum Geometric Nesting” and Solvable Model Flat-Band Systems

Han,

Herzog-Arbeitman,

Bernevig

et al. 2024

Phys. Rev. X

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We introduce the concept of “quantum geometric nesting” (QGN) to characterize the idealized ordering tendencies of certain flat-band systems implicit in the geometric structure of the flat-band subspace. Perfect QGN implies the existence of an infinite class of local interactions that can be explicitly constructed and give rise to solvable ground states with various forms of possible fermion bilinear order, including flavor ferromagnetism, density waves, and superconductivity. For the ideal Hamiltonians constructed in this way, we show that certain aspects of the low-energy spectrum can also be exactly computed including, in the superconducting case, the phase stiffness. Examples of perfect QGN include flat bands with certain symmetries (e.g., chiral or time reversal) and non-symmetry-related cases exemplified with an engineered model for pair-density wave. Extending this approach, we obtain exact superconducting ground states with nontrivial pairing symmetry. Published by the American Physical Society 2024

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Gravitational response of topological quantum states of matter

Cited by 4 publications

References 39 publications

C_n -symmetric quasi-periodic Chern insulators

C_n -symmetric quasi-periodic Chern insulators

Interacting topological quantum chemistry in 2D with many-body real space invariants

“Quantum Geometric Nesting” and Solvable Model Flat-Band Systems

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Gravitational response of topological quantum states of matter

Cited by 4 publications

References 39 publications

Cn -symmetric quasi-periodic Chern insulators

Cn -symmetric quasi-periodic Chern insulators

Interacting topological quantum chemistry in 2D with many-body real space invariants

“Quantum Geometric Nesting” and Solvable Model Flat-Band Systems

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Product

Resources

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C_n -symmetric quasi-periodic Chern insulators

C_n -symmetric quasi-periodic Chern insulators