arXiv:2109.09916 · Journal of Physics A Mathematical and Theoretical

Emptiness formation in polytropic quantum liquids

Hsiu-Chung Yeh, Dimitri M. Gangardt, Alex Kamenev

Published Jan 4, 2022• 4 citations

Abstract

Abstract We study large deviations in interacting quantum liquids with the polytropic equation of state P ( ρ ) ∼ ρ γ , where ρ is density and P is pressure. By solving hydrodynamic equations in imaginary time we evaluate the instanton action and calculate the emptiness formation probability (EFP), the probability that no particle resides in a macroscopic interval of a given size. Analytic solutions are found for a certain infinite sequence of rational polytropic indexes γ and the result can be analytically continued to any value of γ ⩾ 1. Our findings agree with (and significantly expand on) previously known analytical and numerical results for EFP in quantum liquids. We also discuss interesting universal spacetime features of the instanton solution.

DOI: 10.1088/1751-8121/ac47b1

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arXiv:2109.09916 · Journal of Physics A Mathematical and Theoretical

Emptiness formation in polytropic quantum liquids

Hsiu-Chung Yeh, Dimitri M. Gangardt, Alex Kamenev

Published Jan 4, 2022• 4 citations

arXiv HTML PDF

Abstract

DOI: 10.1088/1751-8121/ac47b1

Related papers

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|x|<R

. For a weakly interacting liquid there is parametrically wide regime ${n}^{\ensuremath{-}1}<R<\ensuremath{\xi}$ (here

n

is the average density and $\ensuremath{\xi}$ is the healing length) where EFP exhibits a nontrivial crossover from the Poisson to the Gaussian behavior. We employ the instanton technique [NATO Science Series II: Mathematics, Physics and Chemistry (2004), Vol. 221] to study quantitative details of these regime and compare it with previously reported special cases.

We study a correlation function for the one-dimensional isotropic

{XY}

model (

{XX0}

model), which is called the Emptiness Formation Probability (EFP). It is the probability of the formation of a ferromagnetic string in the anti-ferromagnetic ground state. Using the expression of the EFP as a Toeplitz determinant, we discuss its asymptotic behaviors. We also compare the analytical results with numerical calculations as the density-matrix renormalization group and the quantum Monte-Carlo method.