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 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.

Physical Review LettersJun 29, 20260 citations

Dynamic structure factor of quantum hard rods from exact form factors

Stanisław Kiedrzyński, Emilia Witkowska, Miłosz Panfil

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.

arXiv:2509.02314Physical review. B./Physical review. BDec 10, 20251 citation

Dynamical structure factor of one-dimensional hard rods

Mário Motta, E. Vitali, M. Rossi +2 more

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 $^{4}\mathrm{He}$ 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.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 $^{4}\mathrm{He}$ 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.

arXiv:1608.07722Physical Review AOct 13, 201631 citations

Ground-State Properties of a One-Dimensional System of Hard Rods

Ferran Mazzanti, G. E. Astrakharchik, Jordi Boronat +1 more

A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasicondensate.A quantum Monte Carlo simulation of a system of bosonic hard rods in one dimension is presented and discussed. The calculation is exact since the analytical form of the wave function is known and is in excellent agreement with predictions obtained from asymptotic expansions valid at large distances. The analysis of the static structure factor and the pair distribution function indicates that a solidlike and a gaslike phases exist at high and low densities, respectively. The one-body density matrix decays following a power law at large distances and produces a divergence in the low density momentum distribution at k=0 which can be identified as a quasicondensate.

arXiv:0705.4377Physical Review LettersJan 17, 200826 citations

Off-diagonal ground-state properties of a one-dimensional gas of Fermi hard rods

Ferran Mazzanti, G. E. Astrakharchik, Jordi Boronat +1 more

A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HRs) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground-state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Nonanalytical contributions to the one-body density matrix are also discussed and found to be less relevant with increasing density.A variational Monte Carlo calculation of the one-body density matrix and momentum distribution of a system of Fermi hard rods (HRs) is presented and compared with the same quantities for its bosonic counterpart. The calculation is exact within statistical errors since we sample the exact ground-state wave function, whose analytical expression is known. The numerical results are in good agreement with known asymptotic expansions valid for Luttinger liquids. We find that the difference between the absolute value of the bosonic and fermionic density matrices becomes marginally small as the density increases. In this same regime, the corresponding momentum distributions merge into a common profile that is independent of the statistics. Nonanalytical contributions to the one-body density matrix are also discussed and found to be less relevant with increasing density.

arXiv:0712.3593Physical Review AApr 29, 200811 citations

Dynamical Properties of Quantum Many-Body Systems at Zero Temperature

Eduardo R. Gagliano, C. A. Balseiro

We present a method to compute dynamical correlation functions in quantum many-body systems at zero temperature. The ground state of a finite system is evaluated exactly by a modified Lanczos method and from it the real-frequency correlation functions are obtained by a projective technique for the memory-function formalism. We apply the method to the density-density correlation function of a one-dimensional spinless fermion system. Exact results are recovered in the noninteracting limit; in the strong-coupling limit our results are compared with Monte Carlo simulation and analytical approximations.We present a method to compute dynamical correlation functions in quantum many-body systems at zero temperature. The ground state of a finite system is evaluated exactly by a modified Lanczos method and from it the real-frequency correlation functions are obtained by a projective technique for the memory-function formalism. We apply the method to the density-density correlation function of a one-dimensional spinless fermion system. Exact results are recovered in the noninteracting limit; in the strong-coupling limit our results are compared with Monte Carlo simulation and analytical approximations.

Physical Review LettersDec 28, 1987256 citations

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}\mathrm{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.