The Inhomogeneous Gaussian Free Field, with application to ground state  correlations of trapped 1d Bose gases

Brun, Yannis; Dubail, Jérôme

doi:10.21468/scipostphys.4.6.037

Cited by 60 publications

(154 citation statements)

References 96 publications

(183 reference statements)

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“…Notice however that, as discussed in detail in Refs. [22,23,52], promoting the model to inhomogeneous v(x) and K(x) leads to possible ambiguities. Different choices are in principle allowed: for example, substituting 1/K(∂ xφ ) 2 in the homogeneous Hamiltonian (5) by [∂ x ( 1/K(x)φ)] 2 instead of 1/K(x)(∂ xφ ) 2 would lead to another inhomogeneous Hamiltonian which would look equally valid.…”

Section: A Definition and Hamiltonianmentioning

confidence: 99%

“…In Refs. [23,52] it is properly argued that, in lagrangian formalism, the correct action reads (the field h(x, τ ) in these references is 2 × φ(x, τ ) here)…”

Section: A Definition and Hamiltonianmentioning

confidence: 99%

“…We refer to Ref. [23] for a more detailed discussion of ground state correlations in the inhomogeneous Luttinger liquid.…”

Section: A Definition and Hamiltonianmentioning

confidence: 99%

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Entanglement entropies of inhomogeneous Luttinger liquids

Bastianello

Dubail

Stéphan

2020

J. Phys. A: Math. Theor.

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We develop a general framework to compute the scaling of entanglement entropy in inhomogeneous one-dimensional quantum systems belonging to the Luttinger liquid universality class. While much insight has been gained in homogeneous systems by making use of conformal field theory techniques, our focus is on systems for which the Luttinger parameter K depends on position, and conformal invariance is broken. An important point of our analysis is that contributions stemming from the UV cutoff have to be treated very carefully, since they now depend on position. We show that such terms can be removed either by considering regularized entropies specifically designed to do so, or by tabulating numerically the cutoff, and reconstructing its contribution to the entropy through the local density approximation. We check our method numerically in the spin-1/2 XXZ spin chain in a spatially varying magnetic field, and find excellent agreement. arXiv:1910.09967v1 [cond-mat.stat-mech]

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Section: A Definition and Hamiltonianmentioning

confidence: 99%

“…In Refs. [23,52] it is properly argued that, in lagrangian formalism, the correct action reads (the field h(x, τ ) in these references is 2 × φ(x, τ ) here)…”

Section: A Definition and Hamiltonianmentioning

confidence: 99%

See 1 more Smart Citation

Entanglement entropies of inhomogeneous Luttinger liquids

Bastianello

Dubail

Stéphan

2020

J. Phys. A: Math. Theor.

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“…The thermodynamic Bethe Ansatz (TBA) description of homogeneous ground state is well known, see e.g. [25], and has been used to predict density profiles [26] and more complicated correlation functions [27,28] in the ground state.…”

Section: Lieb Liniger Model In a Harmonic Trapmentioning

confidence: 99%

Free fermions at the edge of interacting systems

Stéphan

2019

SciPost Phys.

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We study the edge behavior of inhomogeneous one-dimensional quantum systems, such as Lieb-Liniger models in traps or spin chains in spatially varying fields. For free systems these fall into several universality classes, the most generic one being governed by the Tracy-Widom distribution. We investigate in this paper the effect of interactions. Using semiclassical arguments, we show that since the density vanishes to leading order, the strong interactions in the bulk are renormalized to zero at the edge, which simply explains the survival of Tracy-Widom scaling in general. For integrable systems, it is possible to push this argument further, and determine exactly the remaining length scale which controls the variance of the edge distribution. This analytical prediction is checked numerically, with excellent agreement. We also study numerically the edge scaling at fronts generated by quantum quenches, which provide new universality classes awaiting theoretical explanation.

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“…It must be stressed that while the presence of an inhomogeneous velocity does not spoil conformal invariance [72,73], an inhomogeneous K(x) does: therefore it is of utmost importance to have other efficient methods to access entanglement entropies which do not rely on CFT. The parameters v and K are model-dependent and must be properly fixed by an independent analysis of the microscopic system at hand: for example, v and K can be extracted in integrable models by means of Bethe Ansatz techniques [29,30,74], or numerically in generic systems. As anticipated, for the sake of simplicity we focus on finite systems with OBC, but we expect that the same techniques can be applied to different boundary conditions as well.…”

Section: Introductionmentioning

confidence: 99%

Rényi entanglement entropies for the compactified massless boson with open boundary conditions

Bastianello

2019

J. High Energ. Phys.

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We investigate the Rényi entanglement entropies for the one-dimensional massless free boson compactified on a circle, which describes the low energy sector of several interacting many-body 1d systems (Luttinger Liquid). We focus on systems on a finite segment with open boundary conditions and possible inhomogeneities in the couplings. We provide expressions for the Rényi entropies of integer indices in terms of Fredholm determinant-like expressions. Within the homogeneous case, we reduce the problem to the solution of linear integral equations and the computation of Riemann Theta functions. We mainly focus on a single interval in the middle of the system, but results for generic bipartitions are given as well.arXiv:1909.00806v2 [cond-mat.stat-mech]

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The Inhomogeneous Gaussian Free Field, with application to ground state correlations of trapped 1d Bose gases

Cited by 60 publications

References 96 publications

Entanglement entropies of inhomogeneous Luttinger liquids

Entanglement entropies of inhomogeneous Luttinger liquids

Free fermions at the edge of interacting systems

Rényi entanglement entropies for the compactified massless boson with open boundary conditions

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