The zero-temperature dynamical structure factor $S(q,\omega)$ of one-dimensional hard rods is computed using state-of-the-art quantum Monte Carlo and analytic continuation techniques, complemented by a Bethe Ansatz analysis. As the density increases, $S(q,\omega)$ reveals a crossover from the Tonks-Girardeau gas to a quasi-solid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\omega)$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\omega)$ at specific wavevectors $\mathcal{Q}_n=n 2 \pi/a$, where $a$ is the core radius, resulting from the interplay of the particle-hole boundaries of suitably rescaled ideal Fermi gases. We observe significant similarities between hard rods and one-dimensional $^4$He at high density, suggesting that the hard-rods model may provide an accurate description of dense one-dimensional liquids of quantum particles interacting through a strongly repulsive, finite-range potential.

Dynamical structure factor of one-dimensional hard rods / M. Motta, E. Vitali, M. Rossi, D.E. Galli, G. Bertaina. - In: PHYSICAL REVIEW A. - ISSN 2469-9926. - 94:4(2016 Oct). [10.1103/PhysRevA.94.043627]

Dynamical structure factor of one-dimensional hard rods

D.E. Galli
Penultimo
;
G. Bertaina
Ultimo
2016

Abstract

The zero-temperature dynamical structure factor $S(q,\omega)$ of one-dimensional hard rods is computed using state-of-the-art quantum Monte Carlo and analytic continuation techniques, complemented by a Bethe Ansatz analysis. As the density increases, $S(q,\omega)$ reveals a crossover from the Tonks-Girardeau gas to a quasi-solid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\omega)$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\omega)$ at specific wavevectors $\mathcal{Q}_n=n 2 \pi/a$, where $a$ is the core radius, resulting from the interplay of the particle-hole boundaries of suitably rescaled ideal Fermi gases. We observe significant similarities between hard rods and one-dimensional $^4$He at high density, suggesting that the hard-rods model may provide an accurate description of dense one-dimensional liquids of quantum particles interacting through a strongly repulsive, finite-range potential.
one-dimensional systems; quantum Monte Carlo; analytic continuation; Bethe ansatz; hard-core interaction
Settore FIS/03 - Fisica della Materia
Settore FIS/02 - Fisica Teorica, Modelli e Metodi Matematici
ott-2016
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/2434/443847
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