Exact spectral function of the Tonks-Girardeau gas at finite temperature
arXiv:2208.13132 · doi:10.1103/PhysRevA.106.053306
Abstract
We report on the derivation of determinant representations for the Green's functions and spectral function of the trapped Tonks-Girardeau gas on the lattice and in the continuum. Our results are valid for any type of statistics of the constituent particles, at zero and finite temperature and arbitrary confining potentials, including nonequilibrium scenarios induced by sudden changes of the external potential. In addition, they are also extremely efficient and easy to implement numerically with the main computational effort being represented by the calculation of partial overlaps of the dynamically evolved single particle wavefunctions. In the lattice case we show that the spectral function of a system with a strong harmonic potential presents only two singular lines compared with three singular lines in the case of a homogeneous system.
20 pages, 2 figures, RevTeX 4.2, Eq. 91 corrected
References in corpus (47)
- Thermalization and its mechanism for generic isolated quantum systems
- Observation of the Pairing Gap in a Strongly Interacting Fermi Gas
- Using photoemission spectroscopy to probe a strongly interacting Fermi gas
- Exact coherent states of a harmonically confined Tonks-Girardeau gas
- Generalized hydrodynamics in strongly interacting 1D Bose gases
- Bragg spectroscopy of a strongly interacting Fermi gas
- The 1D interacting anyon gas: low-energy properties and Haldane exclusion statistics
- Fermionization in an expanding 1D gas of hard-core bosons
- Emergence of quasi-condensates of hard-core bosons at finite momentum
- Anyon-fermion mapping and applications to ultracold gases in tight waveguides
- Universal properties of hard-core bosons confined on one-dimensional lattices
- Probing nearest-neighbor correlations of ultracold fermions in an optical lattice
- Fermionization and bosonization of expanding 1D anyonic fluids
- Thermalisation of a trapped one-dimensional Bose gas via diffusion
- Relaxation in the XX quantum chain
- Universal correlations of trapped one-dimensional impenetrable bosons
- Momentum distribution dynamics of a Tonks-Girardeau gas: Bragg reflections of a quantum many-body wavepacket
- The effect of atom losses on the distribution of rapidities in the one-dimensional Bose gas
- Fermi-Bose transformation for the time-dependent Lieb-Liniger gas
- Ground-state properties of hard core bosons in one-dimensional harmonic traps
- Conformal field theory on top of a breathing one-dimensional gas of hard core bosons
- Correlation Functions of One-Dimensional Lieb-Liniger Anyons
- Sudden Expansion of a One-Dimensional Bose Gas from Power-Law Traps
- Analytical expression for a post-quench time evolution of the one-body density matrix of one-dimensional hard-core bosons
- Ground-state properties of hard-core anyons in one-dimensional optical lattices
- Finite-temperature properties of hard-core bosons confined on one-dimensional optical lattices
- One-particle density matrix and momentum distribution function of one-dimensional anyon gases
- Entanglement properties and moment distributions of a system of hard-core anyons on a ring
- Bosonic continuum theory of one-dimensional lattice anyons
- One-Dimensional Impenetrable Anyons in Thermal Equilibrium. I. Anyonic Generalization of Lenard's Formula
- One-Dimensional Impenetrable Anyons in Thermal Equilibrium. II. Determinant Representation for the Dynamic Correlation Functions
- Strongly interacting trapped one-dimensional quantum gases: an exact solution
- Exact entanglement growth of a one-dimensional hard-core quantum gas during a free expansion
- Probing quasi-particle states in strongly interacting atomic gases by momentum-resolved Raman photoemission spectroscopy
- Correlation functions of one-dimensional strongly interacting two-component gases
- Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
- Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
- Off-diagonal correlations of lattice impenetrable bosons in one dimension
- Effective free-fermionic form factors and the XY spin chain
- Integrability breaking in the one dimensional Bose gas: Atomic losses and energy loss
- Systematic strong coupling expansion for out-of-equilibrium dynamics in the Lieb-Liniger model
- Correlation functions and momentum distribution of one-dimensional hard-core anyons in optical lattices
- On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
- Non-equilibrium dynamics of the anyonic Tonks-Girardeau gas at finite temperature
- Exact Dynamical Correlations of Hard-Core Anyons in One-Dimensional Lattices
- Exact dynamical correlations of nonlocal operators in quadratic open Fermion systems: a characteristic function approach
- The relevant excitations for the one-body function in the Lieb-Liniger model
Cited by in corpus (4)
- Finite temperature single-particle Green's function in the Lieb-Liniger model
- Exact spectral function and nonequilibrium dynamics of the strongly interacting Hubbard model
- Nonequilibrium dynamics in one-dimensional strongly interacting two-component gases
- Space-time first-order correlations of an open Bose-Hubbard model with incoherent pump and loss