Interaction distance in the extended XXZ model

Patrick, Kristian; Caudrelier, Vincent; Papić, Zlatko; Pachos, Jiannis K.

doi:10.1103/physrevb.100.235128

Cited by 9 publications

(7 citation statements)

References 62 publications

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“…However, W is dependent on the choice of the operator used for Wick's decomposition and therefore needs an upper bound to be physically useful. We demonstrate the efficacy of Wick's theorem by bounding it with the more general diagnostic of Gaussianity -the so-called interaction distance, D F [17][18][19]. Comparing the behaviour of both D F and W, we demonstrate that quantum correlations of the XYZ model exponentially approach those of a free-fermion model as a function of system size, provided the size of the system is larger than the correlation length.…”

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confidence: 88%

Emergence of gaussianity in the thermodynamic limit of interacting fermions

et al. 2021

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Systems of interacting fermions can give rise to ground states whose correlations become effectively free-fermion-like in the thermodynamic limit, as shown by Baxter for a class of integrable models that include the one-dimensional XYZ spin-1 2 chain. Here, we quantitatively analyse this behaviour by establishing the relation between system size and correlation length required for the fermionic Gaussianity to emerge. Importantly, we demonstrate that this behaviour can be observed through the applicability of Wick's theorem and thus it is experimentally accessible. To establish the relevance of our results to possible experimental realisations of XYZ-related models, we demonstrate that the emergent Gaussianity is insensitive to weak variations in the range of interactions, coupling inhomogeneities and local random potentials.

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confidence: 88%

Emergence of gaussianity in the thermodynamic limit of interacting fermions

et al. 2021

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“…For a free system an equivalent expression to (14) does not exist as Wick's theorem given by ( 10) directly provides the two-mode expectation value in terms of single-mode densities. For the ground state of an interacting system the expectation values of single and two-mode density operators are in general unrelated.…”

Section: A Expectation Values and Entanglement Spectra Of Interacting...mentioning

confidence: 99%

Quantifying fermionic interactions from the violation of Wick's theorem

Pachos¹,

Vlachou²

2022

Preprint

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In contrast to interacting systems the ground state of free systems has a highly ordered pattern of quantum correlations, as witnessed by Wick's decomposition. Here, we quantify the effect of interactions by measuring the violation they cause on Wick's decomposition. In particular, we express this violation in terms of the low entanglement spectrum of fermionic systems. Moreover, we establish a relation between the Wick's theorem violation and the interaction distance, the smallest distance between the reduced density matrix of the system and that of the optimal free model closest to the interacting one. Our work provides the means to quantify the effect of interactions in physical systems though measurable quantum correlations.

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“…Refs. [38][39][40][41][42][43][44][45]). Some of these models have a relevance for the description of dipolar fermionic gases or of fermionic Rydberg-dressed states [46].…”

Section: Introductionmentioning

confidence: 99%

Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions

Gotta,

Mazza,

Simon

et al. 2021

Preprint

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We compute the phase diagram of a one-dimensional model of spinless fermions with pair-hopping and nearest-neighbor interaction, first introduced by Ruhman and Altman, using the density-matrix renormalization group combined with various analytical approaches. Although the main phases are a Luttinger liquid of fermions and a Luttinger liquid of pairs, we also find remarkable phases in which only a fraction of the fermions are paired. In such case, two situations arise: either fermions and pairs coexist spatially in a two-fluid mixture, or they are spatially segregated leading to phase separation. These results are supported by several analytical models that describe in an accurate way various relevant cuts of the phase diagram. Last, we identify relevant microscopic observables that capture the presence of these two fluids: while originally introduced in a phenomenological way, they support a wider application of two-fluid models for describing pairing phenomena.

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Interaction distance in the extended XXZ model

Cited by 9 publications

References 62 publications

Emergence of gaussianity in the thermodynamic limit of interacting fermions

Emergence of gaussianity in the thermodynamic limit of interacting fermions

Quantifying fermionic interactions from the violation of Wick's theorem

Two-fluid coexistence and phase separation in a one dimensional model with pair hopping and density interactions

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