To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate the ground-state phase diagram of the transverse-field Ising model with algebraically decaying long-range Ising interactions on quasi-one-dimensional infinite-cylinder triangular lattices. Technically, we apply various approaches including low- and high-field series expansions. For the classical long-range Ising model, we investigate cylinders with an arbitrary even circumference. We show the occurrence of gapped stripe-ordered phases emerging out of the infinitely degenerate nearest-neighbor Ising ground-state space on the two-dimensional triangular lattice. Further, while cylinders with circumferences 6, 10, 14, etc., are always in the same stripe phase for any decay exponent of the long-range Ising interaction, the family of cylinders with circumferences 4, 8, 12, etc., displays a phase transition between two different types of stripe structures. For the full long-range transverse-field Ising model, we concentrate on cylinders with circumference four and six. The ground-state phase diagram consists of several quantum phases in both cases including an $x$ -polarized phase, stripe-ordered phases, and clock-ordered phases which emerge from an order-by-disorder scenario already present in the nearest-neighbor model. In addition, the generic presence of a potential intermediate gapless phase with algebraic correlations and associated Kosterlitz-Thouless transitions is discussed for both cylinders.To gain a better understanding of the interplay between frustrated long-range interactions and zero-temperature quantum fluctuations, we investigate the ground-state phase diagram of the transverse-field Ising model with algebraically decaying long-range Ising interactions on quasi-one-dimensional infinite-cylinder triangular lattices. Technically, we apply various approaches including low- and high-field series expansions. For the classical long-range Ising model, we investigate cylinders with an arbitrary even circumference. We show the occurrence of gapped stripe-ordered phases emerging out of the infinitely degenerate nearest-neighbor Ising ground-state space on the two-dimensional triangular lattice. Further, while cylinders with circumferences 6, 10, 14, etc., are always in the same stripe phase for any decay exponent of the long-range Ising interaction, the family of cylinders with circumferences 4, 8, 12, etc., displays a phase transition between two different types of stripe structures. For the full long-range transverse-field Ising model, we concentrate on cylinders with circumference four and six. The ground-state phase diagram consists of several quantum phases in both cases including an $x$-polarized phase, stripe-ordered phases, and clock-ordered phases which emerge from an order-by-disorder scenario already present in the nearest-neighbor model. In addition, the generic presence of a potential intermediate gapless phase with algebraic correlations and associated Kosterlitz-Thouless transitions is discussed for both cylinders.

arXiv:1907.10693Physical review. B./Physical review. BOct 7, 201932 citations

Correlations in the Ising-model

M. Helm

Physics Letters ADec 1, 19700 citations

The long-range interactions in the linear Ising model

R. Z. Bariev, M.P. Zhelifonov

Physics Letters ANov 1, 19725 citations

Phases at complex temperature : spiral correlation functions and regions of Fisher zeros for Ising models

Felicitas Beichert

In this thesis we analyse the Fisher zeros for various Ising models. We show that there is long-range spiral order on the contours of zeros for classical one-dimensional Ising chains and that there is an imaginary “latent heat” associated with crossing those contours. Then we can see how areas of Fisher zeros fill in as we turn the Ising chain into Ising ladders of different widths, which seems to contradict the standard analysis presented in the literature and can be attributed to a different approach to the thermodynamic limit. Finally, we report results on frustrated two-dimensional classical Ising lattices, in particular the triangular and the kagomé lattice, and the quantum Ising problem.In this thesis we analyse the Fisher zeros for various Ising models. We show that there is long-range spiral order on the contours of zeros for classical one-dimensional Ising chains and that there is an imaginary “latent heat” associated with crossing those contours. Then we can see how areas of Fisher zeros fill in as we turn the Ising chain into Ising ladders of different widths, which seems to contradict the standard analysis presented in the literature and can be attributed to a different approach to the thermodynamic limit. Finally, we report results on frustrated two-dimensional classical Ising lattices, in particular the triangular and the kagomé lattice, and the quantum Ising problem.

Jan 1, 20130 citations

Spreading of correlations and entanglement in the long-range transverse Ising chain

Schneider, J. T., Julien Despres, S. J. Thomson +2 more

Whether long-range interactions allow for a form of causality in nonrelativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by nonuniversal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or superballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.Whether long-range interactions allow for a form of causality in nonrelativistic quantum models remains an open question with far-reaching implications for the propagation of information and thermalization processes. Here, we study the out-of-equilibrium dynamics of the one-dimensional transverse Ising model with algebraic long-range exchange coupling. Using a state of the art tensor-network approach, complemented by analytic calculations and considering various observables, we show that a weak form of causality emerges, characterized by nonuniversal dynamical exponents. While the local spin and spin correlation causal edges are sub-ballistic, the causal region has a rich internal structure, which, depending on the observable, displays ballistic or superballistic features. In contrast, the causal region of entanglement entropy is featureless and its edge is always ballistic, irrespective of the interaction range. Our results shed light on the propagation of information in long-range interacting lattice models and pave the way to future experiments, which are discussed.

Mar 5, 202129 citations

x

-polarized phase, stripe-ordered phases, and clock-ordered phases which emerge from an order-by-disorder scenario already present in the nearest-neighbor model. In addition, the generic presence of a potential intermediate gapless phase with algebraic correlations and associated Kosterlitz-Thouless transitions is discussed for both cylinders.