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

Seiringer, Robert; Warzel, Simone

doi:10.1088/1367-2630/18/3/035002

Cited by 28 publications

(31 citation statements)

References 54 publications

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“…Additional results of this type, establishing the absence of particle transport in the disordered isotropic XY chain, can be found in [1]. Similar results for the disordered Tonks-Girardeau gas, which can be viewed as a continuum analogue of the XY chain, can be found in [52].…”

Section: Absence Of Particle and Energy Transportsupporting

confidence: 66%

Localization properties of the disordered XY spin chain

et al. 2017

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We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, propagation bounds of Lieb-Robinson type, decay of correlation functions, absence of particle transport, bounds on the bipartite entanglement, and bounded entanglement growth under the dynamics. We also prove new results on the absence of energy transport and Fock space localization. All these properties are made accessible to mathematical analysis due to the exact mapping of the XY chain to a system of quasi-free fermions given by the Jordan-Wigner transformation. Motivated by these results we discuss conjectured properties of more general disordered quantum spin and other systems as possible directions for future mathematical research.

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Section: Absence Of Particle and Energy Transportsupporting

confidence: 66%

Localization properties of the disordered XY spin chain

et al. 2017

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“…This recent paper [27] succeeds in establishing these properties for the Tonks-Girardeau (TG) gas subject to a random external potential. More precisely, the TG gas is the impenetrable particle (g  ¥) limit of the Lieb-Liniger model conditions.…”

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confidence: 95%

“…A key observation in [27] is that the rigorous derivation of this and other MBL properties of the disordered TG gas can be based on Anderson localization for the effective Hamiltonian H L . The latter is well known to hold for several standard choices of the random potential V, such as alloy-type (continuum Anderson-type) random potentials, Gaussian random potentials, and random potentials generated by Brownian motion on a compact manifold.…”

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confidence: 99%

“…In particular, the authors of [27] develop methods to show that eigencorrelator localization for H L leads to a proof that reduced one-particle density matrices for the many-body eigenstates of L  have exponentially decaying correlations, thus establishing absence of off-diagonal long-range order and, as a consequence, absence of Bose-Einstein condensation for the disordered TG gas. Another consequence of one-particle localization of H L derived in [27] is the vanishing of the superfluid density of L  (following [10] defined via the helicity modulus, i.e. increase of the ground state energy under twisting the boundary condition).…”

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confidence: 99%

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Many-body localization for disordered Bosons

Stolz

2016

New J. Phys.

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Concrete models of interacting quantum systems for which expected manifestations of the manybody 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.

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“…An important progress toward a full non-perturbative proof of MBL has been recently obtained in [13,14] but the proof is based on an assumption called limited level attraction (eigenvalues do not accumulate too strongly near states with almost the same energies) which is still unproven. Other proofs of MBL are devoted to systems which can be mapped in non interacting ones [15,16].In recent cold atoms experiments [17] evidence of MBL has been reported. The disorder is not random (as in the above mentioned theoretical works) but quasirandom, but the theory of MBL can be developed also in that case [18].…”

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confidence: 99%

Interacting spinning fermions with quasi‐random disorder

Mastropietro

2016

Annalen der Physik

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Interacting spinning fermions with strong quasi-random disorder are analyzed via rigorous Renormalization Group (RG) methods combined with KAM techniques. The correlations are written in terms of an expansion whose convergence follows from number-theoretical properties of the frequency and cancellations due to Pauli principle. A striking difference appears between spinless and spinning fermions; in the first case there are no relevant effective interactions while in presence of spin an additional relevant quartic term is present in the RG flow. The large distance exponential decay of the correlations present in the non interacting case, consequence of the single particle localization, is shown to persist in the spinning case only for temperatures greater than a power of the many body interaction, while in the spinless case this happens up to zero temperature. In recent cold atoms experiments [17] evidence of MBL has been reported. The disorder is not random (as in the above mentioned theoretical works) but quasi-random, but the theory of MBL can be developed also in that case [18]. The experiments use two laser beams with incommensurate frequencies, superimposing to a one dimensional lattice a periodic potential with a period that is incommensurate with the underlying lattice, producing a realization of an interacting Aubry-Andre' model [19]; subsequent experiments considered two coupled chains [20].Random or quasi random disorder have similar properties, at least for strong disorder. In particular, a strong incommensurate potential produces localization of the single particles eigenstates [21], [22], as in the random case, while for weak potential there is no localization. There is then a metal-insulator transition as for 3D random disorder (in 1D the eigenstates in the random case are instead always localized). Such properties are due to a close relation with the Kolmogorov-Arnold-Moser (KAM) theorem for the stability of tori of perturbed Hamiltonian systems. The simplest generalization of the Aubry-Andre' model to interacting fermions is the one with the following Hamiltonian

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

Cited by 28 publications

References 54 publications

Localization properties of the disordered XY spin chain

Localization properties of the disordered XY spin chain

Many-body localization for disordered Bosons

Interacting spinning fermions with quasi‐random disorder

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