# Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium

@article{Nardis2016ExactCI, title={Exact correlations in the Lieb-Liniger model and detailed balance out-of-equilibrium}, author={Jacopo de Nardis and Miłosz Panfil}, journal={arXiv: Quantum Gases}, year={2016} }

We study the density-density correlation function of the 1D Lieb-Liniger model and obtain an exact expression for the small momentum limit of the static correlator in the thermodynamic limit. We achieve this by summing exactly over the relevant form factors of the density operator in the small momentum limit. The result is valid for any eigenstate, including thermal and non-thermal states. We also show that the small momentum limit of the dynamic structure factors obeys a generalized detailed…

## 37 Citations

### Low-density limit of dynamical correlations in the Lieb–Liniger model

- Mathematics, Physics
- 2020

We derive explicit expressions for dynamical correlations of the field and density operators in the Lieb–Liniger model, within an arbitrary eigenstate with a small particle density D . They are valid…

### Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

- Physics
- 2017

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in…

### Ground-State Static Correlation Functions of the Lieb–Liniger Model

- Physics
- 2018

In this chapter, I characterize a strongly-correlated, ultracold one-dimensional Bose gas on a ring through its equilibrium, static correlation functions. The gas is described by the Lieb–Liniger…

### Drude Weight for the Lieb-Liniger Bose Gas

- Physics, Mathematics
- 2017

Based on the method of hydrodynamic projections we derive a concise formula for the Drude weight of the repulsive Lieb-Liniger $\delta$-Bose gas. Our formula contains only quantities which are…

### Particle-hole pairs and density–density correlations in the Lieb–Liniger model

- Physics
- 2017

We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb–Liniger model. We focus on the density operator and we show…

### Conjectures about the structure of strong- and weak-coupling expansions of a few ground-state observables in the Lieb-Liniger and Yang-Gaudin models

- Mathematics, PhysicsSciPost Physics
- 2019

In this paper, we apply experimental number theory to two integrable
quantum models in one dimension, the Lieb-Liniger Bose gas and the
Yang-Gaudin Fermi gas with contact interactions. We identify…

### Large-time and long-distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas

- PhysicsPhysical Review B
- 2022

We study thermal correlation functions of the one-dimensional impenetrable lattice anyons. These correlation functions can be presented as a difference of two Fredholm determinants. To describe large…

### Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via coupled Heisenberg equations

- PhysicsSciPost Physics
- 2022

The Kitaev model on the honeycomb lattice, while being integrable via the spin-fermion mapping, has generally resisted an analytical treatment of the far-from-equilibrium dynamics due to the…

### Out-of-equilibrium dynamics of the Kitaev model on the Bethe lattice via a set of Heisenberg equations

- Physics
- 2021

The Kitaev model on the honeycomb lattice, while being integrable via the spinfermion mapping, has generally resisted an analytical treatment of the far-fromequilibrium dynamics due to the extensive…

### Real-time evolution in the Hubbard model with infinite repulsion

- PhysicsSciPost Physics
- 2022

We consider the real-time evolution of the Hubbard model in the limit of infinite coupling. In this limit the Hamiltonian of the system is mapped into a number-conserving quadratic form of spinless…

## References

SHOWING 1-10 OF 56 REFERENCES

### Finite-temperature correlations in the Lieb-Liniger one-dimensional Bose gas

- Physics
- 2014

We address the problem of calculating finite-temperature response functions of an experimentally relevant low-dimensional, strongly correlated system: the integrable one-dimensional Bose gas with a…

### Dynamical density-density correlations in the one-dimensional Bose gas

- Physics
- 2006

The zero-temperature dynamical structure factor of the one-dimensional Bose gas with delta-function interaction (Lieb-Liniger model) is computed as a function of momentum and frequency using a hybrid…

### Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution

- Physics
- 2017

We study the ground-state properties and excitation spectrum of the Lieb-Liniger model, i.e. the one-dimensional Bose gas with repulsive contact interactions. We solve the Bethe-Ansatz equations in…

### Relaxation dynamics of the Lieb-Liniger gas following an interaction quench: a coordinate Bethe-ansatz analysis

- Physics
- 2015

We investigate the relaxation dynamics of the integrable Lieb-Liniger model of contact-interacting bosons in one dimension following a sudden quench of the collisional interaction strength. The…

### Polarizability and dynamic structure factor of the one-dimensional Bose gas near the Tonks-Girardeau limit at finite temperatures

- Physics
- 2006

Correlation functions related to the dynamic density response of the one-dimensional Bose gas in the model of Lieb and Liniger are calculated. An exact Bose-Fermi mapping is used to work in a…

### Split Fermi seas in one-dimensional Bose fluids

- Physics
- 2014

For the one-dimensional repulsive Bose gas (Lieb-Liniger model), we study a special class of highly excited states obtained by giving a finite momentum to subgroups of particles. These states, which…

### Local correlations in the 1D Bose gas from a scaling limit of the XXZ chain

- Mathematics
- 2011

We consider the K-body local correlations in the (repulsive) 1D Bose gas for general K, both at finite size and in the thermodynamic limit. Concerning the latter we develop a multiple integral…

### Solution for an interaction quench in the Lieb-Liniger Bose gas

- Physics
- 2014

We study a quench protocol where the ground state of a free many-particle bosonic theory in one dimension is let unitarily evolve in time under the integrable Lieb-Liniger Hamiltonian of…

### Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons

- Physics
- 2014

We apply the logic of the quench action to give an exact analytical expression for the time evolution of the one-body density matrix after an interaction quench in the Lieb–Liniger model from the…

### Correlation functions for one-dimensional bosons at low temperature

- Physics
- 2011

We consider the low-temperature limit of the long-distance asymptotic behavior of the finite-temperature density–density correlation function in the one-dimensional Bose gas derived recently in the…