Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1512.05282 · New Journal of Physics

Decay of correlations and absence of superfluidity in the disordered Tonks–Girardeau gas

Robert Seiringer, Simone Warzel

Published Feb 26, 2016• 25 citations
arXivHTMLPDF

Abstract

We consider the Tonks–Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose–Einstein condensation and no superfluidity, even at zero temperature.

DOI
10.1088/1367-2630/18/3/035002

Related papers

Many-body localization for disordered Bosons

Günter Stolz

Concrete models of interacting quantum systems for which expected manifestations of the many-body localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys. 18 035002 ) succeeds in deriving such properties for a disordered Tonks–Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose–Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks–Girardeau gas.

New Journal of Physics•Mar 24, 2016•6 citations

Anderson localization of a Tonks-Girardeau gas in potentials with controlled disorder

Juraj Radić, Vladimir Bačić, Dario Jukić +2 more

We theoretically demonstrate features of Anderson localization in a Tonks-Girardeau gas confined in one-dimensional potentials with controlled disorder. That is, we investigate the evolution of the single-particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.

arXiv:1005.4726•Physical Review A•Jun 28, 2010•26 citations

Tonks-Girardeau gas in an optical lattice: Effects of a local potential

Hao Fu, Alberto G. Rojo

The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.

arXiv:cond-mat/0602163•Physical Review A•Jul 21, 2006•6 citations

Superfluidity in a gas of strongly interacting bosons

G. M. Kavoulakis, Y. C. Yu, Magnus Ögren +1 more

We consider small systems of bosonic atoms rotating in a toroidal trap. Using the method of exact numerical diagonalization of the many-body Hamiltonian, we examine the transition from the Bose-Einstein condensed state to the Tonks-Girardeau state. The system supports persistent currents in a wide range between the two limits, even in the absence of Bose-Einstein condensation.

arXiv:cond-mat/0510315•Europhysics Letters (EPL)•Sep 19, 2006•7 citations

Local correlations in the super-Tonks-Girardeau gas

Márton Kormos, Giuseppe Mussardo, Andrea Trombettoni

We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature ${T}_{\mathrm{D}}$. We also find that, for temperatures larger than ${T}_{\mathrm{D}}$, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.

arXiv:1008.4383•Physical Review A•Jan 24, 2011•50 citations

On the nature of Bose–Einstein condensation enhanced by localization

Thomas Jaeck, Joseph V. Pulé, Valentin Anatol'evich Zagrebnov

In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose–Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic-energy states. In these cases Bose–Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic-energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic-energy without any of them being macroscopically occupied.

arXiv:1006.3924•Journal of Mathematical Physics•Oct 1, 2010•8 citations
We consider the Tonks–Girardeau gas subject to a random external potential. If the disorder is such that the underlying one-particle Hamiltonian displays localization (which is known to be generically the case), we show that there is exponential decay of correlations in the many-body eigenstates. Moreover, there is no Bose–Einstein condensation and no superfluidity, even at zero temperature.
Concrete models of interacting quantum systems for which expected manifestations of the many-body localized phase can be rigorously verified are in short supply. Recent work by Seiringer and Warzel (2016 New J. Phys. 18 035002 ) succeeds in deriving such properties for a disordered Tonks–Girardeau gas. This provides a first example of a Boson gas in the strong Bose glass phase, characterized by the absence of Bose–Einstein condensation as well as the absence of superfluidity at zero temperature. The derivation exploits new mathematical tools to overcome problems arising from the non-locality of Fermionic wave functions associated with the states of a Tonks–Girardeau gas.
We theoretically demonstrate features of Anderson localization in a Tonks-Girardeau gas confined in one-dimensional potentials with controlled disorder. That is, we investigate the evolution of the single-particle density and correlations of a Tonks-Girardeau wave packet in such disordered potentials. The wave packet is initially trapped, the trap is suddenly turned off, and after some time the system evolves into a localized steady state due to Anderson localization. The density tails of the steady state decay exponentially, while the coherence in these tails increases. The latter phenomenon corresponds to the same effect found in incoherent optical solitons.
The physics of a Tonks-Girardeau gas confined in an optical lattice in the presence of a local potential is studied. In order to evaluate the single-particle density matrix (SPDM) of the many-body ground state, the Wigner-Jordan transformation is used. The eigenvector with the largest eigenvalue of the SPDM corresponds to the ``Bose-Einstein condensate''(BEC) state. We find that the BEC-state density at the position of the local potential decreases, as expected, in the case of a repulsive potential. For an attractive potential, it decreases or increases depending on the strength of the potential. The superfluidity of this system is investigated both numerically and perturbatively. An experimental method for detecting the effect of an impurity in a Tonks-Girardeau gas is discussed.
We study the local correlations in the super Tonks-Girardeau gas, a highly excited, strongly correlated state obtained in quasi-one-dimensional Bose gases by tuning the scattering length to large negative values using a confinement-induced resonance. Exploiting a connection with a relativistic field theory, we obtain results for the two-body and three-body local correlators at zero and finite temperature. At zero temperature, our result for the three-body correlator agrees with the extension of the results of Cheianov et al. [Phys. Rev. A 73, 051604(R) (2006)], obtained for the ground state of the repulsive Lieb-Liniger gas, to the super-Tonks-Girardeau state. At finite temperature, we obtain that the three-body correlator has a weak dependence on temperature up to the degeneracy temperature TD{T}_{\mathrm{D}}TD​. We also find that, for temperatures larger than TD{T}_{\mathrm{D}}TD​, the values of the three-body correlator for the super-Tonks-Girardeau gas and the corresponding repulsive Lieb-Liniger gas are rather similar, even for relatively small couplings.
In a previous paper we established that for the perfect Bose gas and the mean-field Bose gas with an external random or weak potential, whenever there is generalized Bose–Einstein condensation in the eigenstates of the single particle Hamiltonian, there is also generalized condensation in the kinetic-energy states. In these cases Bose–Einstein condensation is produced or enhanced by the external potential. In the present paper we establish a criterion for the absence of condensation in single kinetic-energy states and prove that this criterion is satisfied for a class of random potentials and weak potentials. This means that the condensate is spread over an infinite number of states with low kinetic-energy without any of them being macroscopically occupied.