Reflection positivity and infrared bounds for quantum spin systems

Björnberg, Jakob E.; Ueltschi, Daniel

doi:10.48550/arxiv.2204.12896

Cited by 2 publications

(2 citation statements)

References 40 publications

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“…For models with long-range interactions, there are analogous mathematical theorems for classical systems at finite temperature, and for quantum systems in which the interaction strength depends on the Manhattan distance r i − r j 1 [19]. In a recent work, Björnberg and Ueltschi addressed quantum models with interactions depending on the Euclidean distance r i − r j 2 , although their results require large S and spatial dimension three or higher [56]. Absent a rigorous proof of LRO for the two-dimensional, spin-1/2, dipolar XY model, one can study it using semi-analytic spin wave theory and various numerical methods [18,22,27].…”

Section: Ground State Properties Of the Xy Modelmentioning

confidence: 99%

Continuous symmetry breaking in a two-dimensional Rydberg array

Chen

Bornet

Bintz

et al. 2023

Nature

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Section: Ground State Properties Of the Xy Modelmentioning

confidence: 99%

Continuous symmetry breaking in a two-dimensional Rydberg array

Chen

Bornet

Bintz

et al. 2023

Nature

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“…For models with long-range interactions, there are analogous mathematical theorems for classical systems at finite temperature, and for quantum systems in which the interaction strength depends on the Manhattan distance r i − r j 1 [25]. In a recent work, Björnberg and Ueltschi addressed quantum spin-S models with interactions depending on the Euclidean distance r i − r j 2 , although their results require large S and spatial dimension three or higher [55]. Absent a rigorous proof of LRO for the two-dimensional, spin-1/2, dipolar XY model, one can study it using semi-analytic spin wave theory and various numerical methods [24,28,31].…”

Section: Ground State Properties Of the Xy Modelmentioning

confidence: 99%

Continuous Symmetry Breaking in a Two-dimensional Rydberg Array

Chen¹,

Bornet²,

Bintz³

et al. 2022

Preprint

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Spontaneous symmetry breaking underlies much of our classification of phases of matter and their associated transitions [1][2][3]. It provides an example of the power of many-body interactions, enabling a collection of individual degrees of freedom to align its behavior across large spatial and temporal scales. Crucially, the nature of the underlying symmetry being broken determines many of the qualitative properties of the phase; this is illustrated by the case of discrete versus continuous symmetry breaking. Indeed, in contrast to the discrete case, the breaking of a continuous symmetry is governed by Goldstone's theorem, which predicts the existence of gapless modes that mediate power-law correlations [4,5]. In this work, we realize a two-dimensional dipolar XY model -which exhibits a continuous spin-rotational symmetry -utilizing a Rydberg quantum simulator. We demonstrate the adiabatic preparation of correlated low-temperature states of both the XY ferromagnet and the XY antiferromagnet. In the ferromagnetic case, we characterize the presence of long-range XY order, a feature prohibited in absence of the long-range dipolar interaction. Complementing recent works utilizing the Rydberg-blockade mechanism to realize Ising-type interactions (with a discrete spin rotation symmetry) [6-9], our work opens the door to exploring the many-body physics of XY interactions in a programmable quantum simulator.

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Reflection positivity and infrared bounds for quantum spin systems

Cited by 2 publications

References 40 publications

Continuous symmetry breaking in a two-dimensional Rydberg array

Continuous symmetry breaking in a two-dimensional Rydberg array

Continuous Symmetry Breaking in a Two-dimensional Rydberg Array

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