Computational studies of frustration and disorder

von

Biswas, Sounak

TaschenbuchKartoniert, Paperback

114 Seiten

Englisch

Peter Lang Gmbh, Internationaler Verlag Der Wissenschaftenerschienen am22.12.2022

Transverse field Ising antiferromagnets on frustrated lattices (and closely related quantumdimer, quantum link models and anisotropic spin models) have served as paradigmatic examplesof the interplay between quantum fluctuations, thermal fluctuations, and the entropiceffects associated with a large degeneracy of configurations with low exchange energy. They have been used to study a host of interesting phenomena associated with this interplay.Although ground state methods such as diffusion Monte Carlo and exact diagonalizationhave been used to study the quantum phases of of such model Hamiltonians and relatedquantum dimer and link models, efficient cluster algorithms for completely unbiasedMonte Carlo studies of the T ¿ 0 quantum statistical mechanics of these systemshave been largely unavailable in spite of the important role played by such models in thetheory of frustrated quantum systems. Continuous-time cluster algorithms have been formulatedfor transverse field Ising models previously. However, these methods typicallyconstruct clusters based on a "link-decomposition" of the Hamiltonian into terms living onthe links of the spatial lattice. While these cluster algorithms work well for ferromagneticsystems, they are rather inadequate for frustrated systems, since clusters formed by thempercolate and freeze. Studies of models with frustration have mostly relied on growingone-dimensional clusters in the imaginary time direction.The bulk of this book addresses this problem and describes our attempts to alleviate it. Ourapproach uses a plaquette decomposition of the Hamiltonian within the Stochastic SeriesExpansion (SSE) framework of Sandvik to construct clusters based on a plaquette percolation process. Flipping these clusters does not change the weight of a configuration. In the case of frustrated bosonic systems with a conserved charge (and equivalent XXZ spin models), merely working with an appropriate plaquette decomposition of the Hamiltonian suffices to dramatically improve the efficiency of directed loop updates within the SSE framework. As we will see, this does not suffice for SSE simulations of frustrated transverse field Ising models. The key ingredient needed in such systems which have no conserved charge is the notion of premarked motifs that are imprinted on each spatial plaquette at the start of the cluster construction process.mehr

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KlappentextTransverse field Ising antiferromagnets on frustrated lattices (and closely related quantumdimer, quantum link models and anisotropic spin models) have served as paradigmatic examplesof the interplay between quantum fluctuations, thermal fluctuations, and the entropiceffects associated with a large degeneracy of configurations with low exchange energy. They have been used to study a host of interesting phenomena associated with this interplay.Although ground state methods such as diffusion Monte Carlo and exact diagonalizationhave been used to study the quantum phases of of such model Hamiltonians and relatedquantum dimer and link models, efficient cluster algorithms for completely unbiasedMonte Carlo studies of the T ¿ 0 quantum statistical mechanics of these systemshave been largely unavailable in spite of the important role played by such models in thetheory of frustrated quantum systems. Continuous-time cluster algorithms have been formulatedfor transverse field Ising models previously. However, these methods typicallyconstruct clusters based on a "link-decomposition" of the Hamiltonian into terms living onthe links of the spatial lattice. While these cluster algorithms work well for ferromagneticsystems, they are rather inadequate for frustrated systems, since clusters formed by thempercolate and freeze. Studies of models with frustration have mostly relied on growingone-dimensional clusters in the imaginary time direction.The bulk of this book addresses this problem and describes our attempts to alleviate it. Ourapproach uses a plaquette decomposition of the Hamiltonian within the Stochastic SeriesExpansion (SSE) framework of Sandvik to construct clusters based on a plaquette percolation process. Flipping these clusters does not change the weight of a configuration. In the case of frustrated bosonic systems with a conserved charge (and equivalent XXZ spin models), merely working with an appropriate plaquette decomposition of the Hamiltonian suffices to dramatically improve the efficiency of directed loop updates within the SSE framework. As we will see, this does not suffice for SSE simulations of frustrated transverse field Ising models. The key ingredient needed in such systems which have no conserved charge is the notion of premarked motifs that are imprinted on each spatial plaquette at the start of the cluster construction process.

Details

ISBN/GTIN978-5-10-200095-0

ProduktartTaschenbuch

EinbandartKartoniert, Paperback

Verlag

Peter Lang Gmbh, Internationaler Verlag Der Wissenschaften

Erscheinungsjahr2022

Erscheinungsdatum22.12.2022

Seiten114 Seiten

SpracheEnglisch

MasseBreite 152 mm, Höhe 229 mm, Dicke 6 mm

Gewicht178 g