Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

Honecker, A.; Richter, Johannes; Schnack, Juergen; Wietek, Alexander

doi:10.5488/cmp.23.43712

Cited by 5 publications

(1 citation statement)

References 68 publications

(141 reference statements)

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“…These schemes, sometimes also called typicality or (microcanonical) thermal pure quantum states [13][14][15][16], have been used very successfully in particular in the field of correlated electron systems, see e.g. [16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35] but also in quantum chemistry [36,37].…”

Section: Introductionmentioning

confidence: 99%

Accuracy of the typicality approach using Chebyshev polynomials

Schlüter,

Gayk,

Schmidt

et al. 2021

Preprint

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Trace estimators allow to approximate thermodynamic equilibrium observables with astonishing accuracy. A prominent representative is the finite-temperature Lanczos method (FTLM) which relies on a Krylov space expansion of the exponential describing the Boltzmann weights. Here we report investigations of an alternative approach which employs Chebyshev polynomials. This method turns out to be also very accurate in general, but shows systematic inaccuracies e.g. produced by the smoothing kernel at low temperatures. Applications to archetypical quantum spin systems are discussed as examples.

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Section: Introductionmentioning

confidence: 99%

Accuracy of the typicality approach using Chebyshev polynomials

Schlüter,

Gayk,

Schmidt

et al. 2021

Preprint

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Quantum Phase Transition at Nonzero Doping in a Random t−J Model

et al. 2021

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Supersymmetry on the lattice: Geometry, topology, and flat bands

Roychowdhury,

Attig,

Trebst

et al. 2024

Phys. Rev. Research

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In quantum mechanics, supersymmetry (SUSY) posits an equivalence between two elementary degrees of freedom, bosons, and fermions defined by local rules. Here we apply it to find connections between bosonic and fermionic lattice models in the realm of condensed-matter physics and uncover a novel fivefold way topology it demands in these systems. At the single-particle level, our connections pair a bosonic and fermionic lattice model, either describing the hopping of number-conserving particles or local couplings between fermion parity-conserving particles. The pair are isospectral except for zero modes, such as flat bands, quadratic band touchings, and nexus points, whose existence is undergirded by the Witten index of the SUSY theory. We develop a unifying framework to formulate these SUSY connections in terms of general lattice graph correspondences. Notably, in this framework, the supercharge operator that generates SUSY is Hermitian and can itself be interpreted as a hopping Hamiltonian on a bipartite lattice, a feature that enables the discovery of materials or model lattices hosting the SUSY partners. To illustrate the power of SUSY, we present 16 use cases of SUSY, that span topics including frustrated magnets, Kitaev spin liquids, and topological superconductors, the majority of which turn out to provide insights into the discovery and design of flat bands and topological materials. Published by the American Physical Society 2024

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Loop-gas description of the localized-magnon states on the kagome lattice with open boundary conditions

Cited by 5 publications

References 68 publications

Accuracy of the typicality approach using Chebyshev polynomials

Accuracy of the typicality approach using Chebyshev polynomials

Quantum Phase Transition at Nonzero Doping in a Random t−J Model

Supersymmetry on the lattice: Geometry, topology, and flat bands

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