Correlated fragile topology: A parton approach

Latimer, Katherine; Wang, Chong

doi:10.1103/physrevb.103.045128

Cited by 11 publications

(10 citation statements)

References 22 publications

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“…Finally, combining Eqs. (32)(33)(34)(35) and λ 1 A x+y = 0, a relation among the cohomology generators in H * (p4m, Z 2 ) (see Appendix E), we establish that Eq. ( 27) indeed holds, as expected.…”

mentioning

confidence: 58%

“…One can check that none of the 3 basic no-go theorems is triggered, so this distribution of DOF also corresponds to the trivial group element, and there should be no associated LSM constraint. Indeed, this configuration is where the DOF are on a honeycomb lattice, and it is known that sym-SRE ground states are allowed in this case [30][31][32][33], consistent with the absence of any LSM constraint. Second, imagine putting DOF with nontrivial PR on the type-a IWP.…”

Section: Gs = P6mmentioning

confidence: 77%

“…[54] are assumed to be realizable by product states. It is known that some SRE states in a honeycomb lattice spin-1/2 system cannot be realized by product states, so we do not make this assumption [30][31][32][33]. This DSL should also be emergible in a triangular or kagome lattice spin-1 system.…”

Section: B Dslmentioning

confidence: 99%

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Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Ye,

Guo,

et al. 2021

Preprint

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Lieb-Schultz-Mattis (LSM) theorems provide powerful constraints on the emergibility problem, i.e. whether a quantum phase or phase transition can emerge in a many-body system with local interactions. We derive the topological partition functions that characterize the LSM constraints in spin systems with Gs × Gint symmetry, where Gs is an arbitrary space group in one or two spatial dimensions, and Gint is any internal symmetry whose projective representations are classified by Z k 2 with k an integer. We then apply these results to study the emergibility of a class of exotic quantum critical states, including the well-known deconfined quantum critical point (DQCP), U (1) Dirac spin liquid (DSL), and the recently proposed non-Lagrangian Stiefel liquid. These states can emerge as a consequence of the competition between a magnetic state and a non-magnetic state. We identify all possible realizations of these states on systems with SO(3) × Z T 2 internal symmetry and either p6m or p4m lattice symmetry. Many interesting examples are discovered, including a DQCP adjacent to a ferromagnet, stable DSLs on square and honeycomb lattices, and a class of quantum critical spinquadrupolar liquids of which the most relevant spinful fluctuations carry spin-2. In particular, there is a realization of spin-quadrupolar DSL that is beyond the usual parton construction. We further use our formalism to analyze the stability of these states under symmetry-breaking perturbations, such as spin-orbit coupling. As a concrete example, we find that a DSL can be stable in a recently proposed candidate material, NaYbO2.

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confidence: 58%

Section: Gs = P6mmentioning

confidence: 77%

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Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Ye,

Guo,

et al. 2021

Preprint

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“…Fragile topology was first realized in a noninteracting model given by Po et al [6], and much work has been done in understanding these systems in the noninteracting regime. In interacting systems, however, there have * joshi.ashish.42a@st.kyoto-u.ac.jp been relatively fewer studies [12,17,18]. On the other hand, STIs have been extensively studied with interactions and are predicted to show unconventional correlated topological states [19][20][21].…”

Section: Introductionmentioning

confidence: 99%

“…[17] shows that the noninteracting classification of rotation-protected 2D topological crystalline insulators (which, in the absence of symmetry-protected edge states, will always be in either the atomic or fragile phase) reduces when interactions are introduced. FTIs, which cannot exist in the noninteracting regime and thus require electron correlations as a necessary ingredient, have also been realized [12,18]. Thus, it is still an open question whether electron correlations in FTIs can lead to nontrivial physics or not.…”

Section: Introductionmentioning

confidence: 99%

Mott transition and magnetism in a fragile topological insulator

Joshi,

Peters

2021

Preprint

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We study the effects of electronic correlations on fragile topology using dynamical mean-field theory. Fragile topological insulators (FTIs) offer obstruction to the formation of exponentially localized Wannier functions, but they can be trivialized by adding certain trivial degrees of freedom. For the same reason, FTIs do not host symmetry-protected flow of edge states between bulk bands in cylindrical boundary conditions but are expected to have a spectral flow between the fragile bands and other bands under certain twisted boundary conditions. We here analyze commonly observed effects of strong correlations, such as the Mott-insulator transition and magnetism, on a known model hosting fragile topology. We show that in the nonmagnetic case, fragile topology, along with the twisted boundary states, is stable with interactions below a critical interaction strength. Above this interaction strength, a transition to the Mott insulating phase occurs, and the twisted boundary states disappear. Furthermore, by applying a homogeneous magnetic field, the fragile topology is destroyed. However, we show that a magnetic field can induce a topological phase transition which converts a fragile topological insulator to a Chern insulator. Finally, we study ferromagnetic solutions of the fragile topological model.

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Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

Herzog-Arbeitman,

Bernevig

2024

Reference Module in Materials Science and Materials Engineering

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Correlated fragile topology: A parton approach

Cited by 11 publications

References 22 publications

Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Topological characterization of Lieb-Schultz-Mattis constraints and applications to symmetry-enriched quantum criticality

Mott transition and magnetism in a fragile topological insulator

Topological Gapped Phases of Matter: Band Theory to Fractional Chern Insulators

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