We study the quantum hard-rods model and obtain compact analytical expressions for density form factors, and a semi-analytical treatment for dynamic and static structure factors calculations, greatly reducing computational complexity. We identify conditions under which these form factors vanish and analyze real-space correlations, confirming the model's Tomonaga-Luttinger liquid behavior. The results reveal universal features of low energy physics of a gapless quantum fluid and its relation to Luttinger liquid theory, providing precise benchmarks for numerical simulations. This work establishes quantum hard rods as an important testbed for theories of strongly correlated one-dimensional systems.
We study the quantum hard-rods model and obtain compact analytical expressions for density form factors, and a semi-analytical treatment for dynamic and static structure factors calculations, greatly reducing computational complexity. We identify conditions under which these form factors vanish and analyze real-space correlations, confirming the model's Tomonaga-Luttinger liquid behavior. The results reveal universal features of low energy physics of a gapless quantum fluid and its relation to Luttinger liquid theory, providing precise benchmarks for numerical simulations. This work establishes quantum hard rods as an important testbed for theories of strongly correlated one-dimensional systems.
The one-dimensional hard rod model describes impenetrable bosons with finite diameter, extending the Lieb-Liniger model to systems with excluded volume interactions. Here, we investigate the thermodynamics of quantum HRs using Yang-Yang theory, path integral quantum Monte-Carlo calculations, and Luttinger liquid theory. We first discuss the behavior of characteristic thermodynamic quantities, exhibiting deviations to the Lieb-Liniger model for sufficiently high densities, with excellent agreement between analytical and numerical results. We then show that the hard rod model exhibits Tomonaga-Luttinger liquid behavior across a wide range of parameters, at zero and finite temperature, as unveiled by correlation functions. The Tomonaga-Luttinger parameter and thermal length can be extracted by fitting correlation functions to Tomonaga-Luttinger liquid theory, hence demonstrating a robust method for thermometry. This work provides a comprehensive study of strongly correlated hard rod systems at finite temperatures, with applications to quantum wires, spin chains, and ultracold atoms.
The zero-temperature dynamical structure factor $S(q,\ensuremath{\omega})$ 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, $S(q,\ensuremath{\omega})$ reveals a crossover from the Tonks-Girardeau gas to a quasisolid regime, along which the low-energy properties are found in agreement with the nonlinear Luttinger liquid theory. Our quantitative estimate of $S(q,\ensuremath{\omega})$ extends beyond the low-energy limit and confirms a theoretical prediction regarding the behavior of $S(q,\ensuremath{\omega})$ at specific wave vectors ${\mathcal{Q}}_{n}=n2\ensuremath{\pi}/a$, 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 4He 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.
We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for an arbitrary many-body state of the system, with finite temperature states and the ground state being important special cases that we analyze in detail. We demonstrate that the expression obeys fundamental relations such like the f-sum rule and the detailed balance. We also reveal the hidden fermionic structure behind the correlator. In the static limit we show that it can be written in terms of universal functions, which, at zero temperature, coincide with the level spacing distribution function of the Gaussian unitary ensemble. Our Letter provides a full and exact characterization of a dynamic correlation function in a strongly correlated interacting quantum many-body system.
We obtain an exact analytic expression for the dynamical structure factor of one-dimensional quantum gas of hard rods. Our result is valid for an arbitrary many-body state of the system, with finite temperature states and the ground state being important special cases that we analyse in detail. We demonstrate that the expression obeys fundamental relations such like the f-sum rule and the detailed balance. We also reveal the hidden fermionic structure behind the correlator. In the static limit we show that it can be written in terms of universal functions which, at zero temperature, coincide with the level spacing distribution function of the Gaussian Unitary Ensemble. Our work provides a full and exact characterisation of a dynamic correlation function in a strongly correlated interacting quantum many-body system.
We compute the zero-temperature dynamical structure factor of one-dimensional liquid ^{4}He by means of state-of-the-art quantum Monte Carlo and analytic continuation techniques. By increasing the density, the dynamical structure factor reveals a transition from a highly compressible critical liquid to a quasisolid regime. In the low-energy limit, the dynamical structure factor can be described by the quantum hydrodynamic Luttinger-liquid theory, with a Luttinger parameter spanning all possible values by increasing the density. At higher energies, our approach provides quantitative results beyond the Luttinger-liquid theory. In particular, as the density increases, the interplay between dimensionality and interaction makes the dynamical structure factor manifest a pseudo-particle-hole continuum typical of fermionic systems. At the low-energy boundary of such a region and moderate densities, we find consistency, within statistical uncertainties, with predictions of a power-law structure by the recently developed nonlinear Luttinger-liquid theory. In the quasisolid regime, we observe a novel behavior at intermediate momenta, which can be described by new analytical relations that we derive for the hard-rods model.
One-dimensional liquid 4He beyond Luttinger theory
We investigate zero temperature liquid 4He in strictly one dimension by means of state-of-the-art Quantum Monte Carlo and analytic continuation techniques. The system displays the unique feature of spanning all the possible values of the Tomonaga-Luttinger liquid parameter KL by only changing the density. We explore the behavior of the dynamical structure factor S(q,ω) beyond the limits of applicability of Tomonaga-Luttinger liquid theory in the whole range in KL. We observe a crossover from a weakly interacting Bose gas regime at low density (KL≫1) to a quasi-solid regime at high density (KL≪1), which we interpret in terms of novel analytical expressions for the spectrum of hard-rods. During this transition the interplay between dimensionality and interaction makes S(q,ω) manifest a pseudo particle-hole continuum typical of a fermionic system, while the Bogoliubov mode evolves into a remnant of the roton mode. We provide also a perturbative estimation of the drag force experienced by a soft impurity moving along the system.