Realizing discontinuous wave functions with renormalized short-range potentials

Cheon, Taksu; Shigehara, Takaomi

doi:10.1016/s0375-9601(98)00188-1

Cited by 178 publications

(182 citation statements)

References 16 publications

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“…Rather, F (λ|λ ′ ) represents the phase shifts in the fermionic dual which is the Cheon-Shigehara model [32,33] for Lieb-Liniger and spinless lattice fermions for XXZ.…”

Section: The Shift Functionmentioning

confidence: 99%

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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“…Rather, F (λ|λ ′ ) represents the phase shifts in the fermionic dual which is the Cheon-Shigehara model [32,33] for Lieb-Liniger and spinless lattice fermions for XXZ.…”

Section: The Shift Functionmentioning

confidence: 99%

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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“…This is not sufficient and more singular coupling need other means. Our main aim here is to explore a natural alternative with approximating interactions scaled in a nonlinear way as a generalization of the procedure proposed in [CS98a,CS98b] Consider first the Hamiltonian H β on the graph Γ consisting on n halflines coupled at a single vertex by the conditions (7). Consider further the same graph with additional vertices of degree two at each arm, all at the same distance a > 0 from the common junction.…”

mentioning

confidence: 99%

“…To see what the choice of the effective coupling constants b, c should be, let us first modify to our problem the argument of [CS98a]. As we have said, in the nontrivial sector all the functions are the same, so we may drop the arm index.…”

mentioning

confidence: 99%

An approximation to couplings on graphs

Cheon

Exner

2004

J. Phys. A: Math. Gen.

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“…In other words, it does not lead to a unique function depending on (a, b, c, d, ω) which reproduces the whole boundary conditions given in (1) and (2). So, we cannot write a Hamiltonian H = H 0 + Ξ(x), since one does not know a single form for the potential Ξ(x) (actually, a different procedure is to represent a generalized point interaction by making compositions of triple delta functions and then taking certain limits [21], which, however, also cannot be put in the form of an usual potential).…”

Section: The Scattering Amplitudes Characterization Of a General mentioning

confidence: 99%

“…A way to construct generalized point interactions has been recently proposed in a series of papers [5,21]. The idea is to consider different usual delta functions, all separated by a distance y 0 , with appropriate values for their strengths.…”

Section: Remarks and Conclusionmentioning

confidence: 99%

Green functions for generalized point interactions in one dimension: A scattering approach

2002

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Recently, general point interactions in one dimension has been used to model a large number of different phenomena in quantum mechanics. Such potentials, however, requires some sort of regularization to lead to meaningful results. The usual ways to do so rely on technicalities which may hide important physical aspects of the problem. In this work we present a new method to calculate the exact Green functions for general point interactions in 1D. Our approach differs from previous ones because it is based only on physical quantities, namely, the scattering coefficients, R and T , to construct G. Renormalization or particular mathematical prescriptions are not invoked. The simple formulation of the method makes it easy to extend to more general contexts, such as for lattices of N general point interactions; on a line; on a half-line; under periodic boundary conditions; and confined in a box.

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Realizing discontinuous wave functions with renormalized short-range potentials

Cited by 178 publications

References 16 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

An approximation to couplings on graphs

Green functions for generalized point interactions in one dimension: A scattering approach

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