Thermodynamics and Tomonaga-Luttinger liquid behavior of the quantum 1D hard rod model
arXiv:2505.20376 · doi:10.1103/8gzf-v52y
Abstract
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.
References in corpus (51)
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- Many-Body Physics with Individually-Controlled Rydberg Atoms
- One dimensional Bosons: From Condensed Matter Systems to Ultracold Gases
- Transport in Out-of-Equilibrium XXZ Chains: Exact Profiles of Charges and Currents
- Realizing quantum Ising models in tunable two-dimensional arrays of single Rydberg atoms
- The ALPS project release 2.0: Open source software for strongly correlated systems
- Emergent hydrodynamics in integrable quantum systems out of equilibrium
- Bosonizing one-dimensional cold atomic gases
- Worm Algorithm for Continuous-space Path Integral Monte Carlo Simulations
- Strongly correlated gases of Rydberg-dressed atoms: quantum and classical dynamics
- Supersolid symmetry breaking from compressional oscillations in a dipolar quantum gas
- Pinning quantum phase transition for a Luttinger liquid of strongly interacting bosons
- Experimental investigations of the dipolar interactions between single Rydberg atoms
- Beyond Tonks-Girardeau: strongly correlated regime in quasi-one-dimensional Bose gases
- Mott transition in one dimension
- The quasi-periodic Bose-Hubbard model and localization in one-dimensional cold atomic gases
- Collective many-body interaction in Rydberg dressed atoms
- Critical Behavior and Fractality in Shallow One-Dimensional Quasiperiodic Potentials
- Interactions Between Rydberg-Dressed Atoms
- Drude Weight for the Lieb-Liniger Bose Gas
- Excitation spectrum of a supersolid
- Emergence of quasi-condensates of hard-core bosons at finite momentum
- Bosons in one-dimensional incommensurate superlattices
- Lieb-Liniger Bosons in a Shallow Quasiperiodic Potential: Bose Glass Phase and Fractal Mott Lobes
- Colloidal Hard Spheres: Triumphs, Challenges and Mysteries
- Interacting fermions in self-similar potentials
- Mott Transition for Strongly-Interacting 1D Bosons in a Shallow Periodic Potential
- Resonant Rydberg Dressing of Alkaline-Earth Atoms via Electromagnetically Induced Transparency
- Tan's Contact for Trapped Lieb-Liniger Bosons at Finite Temperature
- Dynamical structure factor of one-dimensional hard rods
- Rydberg dressing of a one-dimensional Bose-Einstein condensate
- Thermodynamic behavior of a one-dimensional Bose gas at low temperature
- Incorporating exact two-body propagators for zero-range interactions into -body Monte Carlo simulations
- Unraveling the Excitation Spectrum of Many-Body Systems from Quantum Quenches
- Local quench spectroscopy of many-body quantum systems
- Ground-State Properties of a One-Dimensional System of Hard Rods
- Luttinger liquid behavior of one-dimensional 3He
- Spectroscopy of elementary excitations from quench dynamics in a dipolar XY Rydberg simulator
- Beyond-Luttinger-Liquid thermodynamics of a one-dimensional contact repulsive Bose gas
- Two-body interactions and decay of three-level Rydberg-dressed atoms
- Quench dynamics of quantum spin models with flat bands of excitations
- Analytic thermodynamic properties of the Lieb-Liniger gas
- Mott transition for a Lieb-Liniger gas in a shallow quasiperiodic potential: Delocalization induced by disorder
- Quench Spectroscopy of a Disordered Quantum System
- Finding the phase diagram of strongly-correlated disordered bosons using quantum quenches
- Gaussian-state Ansatz for the non-equilibrium dynamics of quantum spin lattices
- Ion-induced interactions in a Tomonaga-Luttinger liquid
- One Dimensional 1H, 2H and 3H
- Quantum hard disks on a lattice
- Diffusive hydrodynamics of hard rods from microscopics