Split Fermi seas in one-dimensional Bose fluids

Fokkema, Thessa; Eliëns, I. S.; Caux, Jean-Sébastien

doi:10.1103/physreva.89.033637

Cited by 29 publications

(42 citation statements)

References 41 publications

(44 reference statements)

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“…This suggests that one should be able to derive the relation between critical exponents and the finite-size spectrum for states of zero entropy density using H-or any combination of the conserved quantities for that matter-and the corresponding energy function, also when this is not in line with the statistical ensemble. This has indeed been verified numerically in studies of dynamical correlations in out-ofequilibrium zero entropy states in the Lieb-Liniger and XXZ models [29,30].…”

Section: Introductionmentioning

confidence: 69%

General finite-size effects for zero-entropy states in one-dimensional quantum integrable models

Eliëns¹,

Caux²

2016

J. Phys. A: Math. Theor.

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Abstract. We present a general derivation of the spectrum of excitations for gapless states of zero entropy density in Bethe ansatz solvable models. Our formalism is valid for an arbitrary choice of bare energy function which is relevant to situations where the Hamiltonian for time evolution differs from the Hamiltonian in a (generalized) Gibbs ensemble, i.e. out of equilibrium. The energy of particle and hole excitations, as measured with the time-evolution Hamiltonian, is shown to include additional contributions stemming from the shifts of the Fermi points that may now have finite energy. The finite-size effects are also derived and the connection with conformal field theory discussed. The critical exponents can still be obtained from the finite-size spectrum, however the velocity occurring here differs from the one in the constant Casimir term. The derivation highlights the importance of the phase shifts at the Fermi points for the critical exponents of asymptotes of correlations. We generalize certain results known for the ground state and discuss the relation to the dressed charge (matrix). Finally, we discuss the finite-size corrections in the presence of an additional particle or hole which are important for dynamical correlation functions.

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Section: Introductionmentioning

confidence: 69%

General finite-size effects for zero-entropy states in one-dimensional quantum integrable models

Eliëns¹,

Caux²

2016

J. Phys. A: Math. Theor.

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“…The ground state is an archetypical, and the most important, critical state. Other interesting example of a critical state is the split Fermi sea state introduced in [56]. The filling function for the finite temperature state [57] is…”

Section: The Lieb-liniger Modelmentioning

confidence: 99%

Particle-hole pairs and density–density correlations in the Lieb–Liniger model

Nardis¹,

Panfil²

2018

J. Stat. Mech.

100

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We review the recently introduced thermodynamic form factors for pairs of particle-hole excitations on finite-entropy states in the Lieb-Liniger model. We focus on the density operator and we show how the form factors can be used for analytic computations of dynamical correlation functions. We derive a new representation for the form factors and we discuss some aspects of their structure. We rigorously show that in the small momentum limit (or equivalently, on hydrodynamic scales) a single particle-hole excitation fully saturates the spectral sum and we also discuss the contribution from two particle-hole pairs. Finally we show that thermodynamic form factors can be also used to study the ground state correlations and to derive the edge exponents.arXiv:1712.06581v5 [cond-mat.quant-gas] 30 May 2018

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“…In constructing a multi-component Tomonaga-Luttinger liquid [35][36][37] we follow Ref. [20] and introduce a species of chiral fermions ψ ia for each of the Fermi points k ia . In the continuum limit, c j → Ψ(x), we expand the Jordan-Wigner fermion in terms of the chiral fermions as…”

Section: Dynamical Structure Factormentioning

confidence: 99%

Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state

2016

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Pumping a finite energy density into a quantum system typically leads to 'melted' states characterized by exponentially-decaying correlations, as is the case for finite-temperature equilibrium situations. An important exception to this rule are states which, while being at high energy, maintain a low entropy. Such states can interestingly still display features of quantum criticality, especially in one dimension. Here, we consider high-energy states in anisotropic Heisenberg quantum spin chains obtained by splitting the ground state's magnon Fermi sea into separate pieces. Using methods based on integrability, we provide a detailed study of static and dynamical spin-spin correlations. These carry distinctive signatures of the Fermi sea splittings, which would be observable in eventual experimental realizations. Going further, we employ a multi-component Tomonaga-Luttinger model in order to predict the asymptotics of static correlations. For this effective field theory, we fix all universal exponents from energetics, and all non-universal correlation prefactors using finite-size scaling of matrix elements. The correlations obtained directly from integrability and those emerging from the Luttinger field theory description are shown to be in extremely good correspondence, as expected, for the large distance asymptotics, but surprisingly also for the short distance behavior. Finally, we discuss the description of dynamical correlations from a mobile impurity model, and clarify the relation of the effective field theory parameters to the Bethe Ansatz solution. SciPost Physics SubmissionA Simplification for symmetric seas 23 B Moses states and generalized TBA 24 C Perturbative expressions for effective-field-theory parameters 24References 25

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Split Fermi seas in one-dimensional Bose fluids

Cited by 29 publications

References 41 publications

General finite-size effects for zero-entropy states in one-dimensional quantum integrable models

General finite-size effects for zero-entropy states in one-dimensional quantum integrable models

Particle-hole pairs and density–density correlations in the Lieb–Liniger model

Correlations of zero-entropy critical states in the XXZ model: integrability and Luttinger theory far from the ground state

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