Theory of hole propagation in one-dimensional insulators and superconductors

Sorella, Sandro; Parola, Alberto

doi:10.1103/physrevb.57.6444

Cited by 33 publications

(20 citation statements)

References 47 publications

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“…͑39͒ is very similar to old types of wave functions 9 and previous approaches to consider the single hole dynamics. 21 The common feature of this approach with the Kondo problem is that the single-particle ͑or -hole͒ excitation acts like a real space impurity in the frame where the extra particle is taken fixed. The impurity problem is a peculiar characteristic of the Kondo model fixed point and therefore, we expect that the Jastrow-Slater approach should be able to introduce another energy scale, the Kondo one, in the problem of the photoemission spectrum, very similarly to the DMFT scenario.…”

Section: Discussionmentioning

confidence: 99%

Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

Tayo

Sorella

2008

Phys. Rev. B

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We show that it is possible to describe the ground state of the Luttinger model in terms of a Jastrow-Slater wave function. Moreover, our findings reveal that one-particle excitations and their corresponding dynamics can be faithfully represented only when a Jastrow factor of a similar form is applied to a coherent superposition of many Slater determinants. We discuss the possible relevance of this approach for the theoretical description of photoemission spectra in higher dimensionality, where the present wave function can be straightforwardly generalized and can be used as a variational ansatz, which is exact for the one-dimensional ͑1D͒ Luttinger model.

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Section: Discussionmentioning

confidence: 99%

Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

Tayo

Sorella

2008

Phys. Rev. B

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“…A considerable progress was achieved in understanding gapful models [7]. However, it is still largely an open problem in the gapless case, and, with few exceptions (see, e.g., [8,9,10,11]), the threshold exponents µ are not known. For the model (1), the most complete results so far were obtained by combining numerics with the algebraic Bethe ansatz [12,13].…”

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confidence: 99%

“…The constraints are equivalent to five linear equations on the coefficients c n in Eqs. (5) and (11). In order to satisfy these equations, it is sufficient to keep the first five integrals of motion in Eq.…”

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confidence: 99%

Threshold Singularities in the Dynamic Response of Gapless Integrable Models

Cheianov

Pustilnik

2008

Phys. Rev. Lett.

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We develop a method of an asymptotically exact treatment of threshold singularities in dynamic response functions of gapless integrable models. The method utilizes the integrability to recast the original problem in terms of the low-energy properties of a certain deformed Hamiltonian. The deformed Hamiltonian is local, hence it can be analysed using the conventional field theory methods. We apply the technique to spinless fermions on a lattice with nearest-neighbors repulsion, and evaluate the exponent characterizing the threshold singularity in the dynamic structure factor.PACS numbers: 02.30. Ik, 71.10.Pm, 75.10.Pq One-dimensional (1D) interacting systems [1, 2, 3] occupy a special place in quantum physics. Although interactions have much stronger effect in 1D than in higher dimensions, it is often possible to evaluate observable quantities exactly. Besides forming the basis of our understanding of strong correlations, 1D models have long served as a test bed for various approximate methods.Many properties of interacting 1D systems can be understood by considering integrable models [2]. The paradigmatic example is N spinless fermions on a lattice with L cites with periodic boundary conditions,Here n m = ψ † m ψ m and ∆ is the repulsion strength [4]. The experimentally relevant [5] response function for the model (1) is the dynamic structure factor|f is an eigenstate of Eq. (1) with energy ǫ f , and |0 is the ground state with ǫ 0 being the ground state energy.In any 1D system, conservation laws restrict the support of correlation functions in (ω, q) plane. For example, S(q, ω) > 0 only at ω > ω 0 (q), see Fig. 1. On general grounds, S(q, ω) is expected to exhibit a power-law singularity at the threshold [6],Although exact eigenstates of integrable models can be constructed using the Bethe ansatz [2], evaluation of dynamic correlation functions is very difficult. A considerable progress was achieved in understanding gapful models [7]. However, it is still largely an open problem in the gapless case, and, with few exceptions (see, e.g., [8,9,10,11]), the threshold exponents µ are not known. For the model (1), the most complete results so far were obtained by combining numerics with the algebraic Bethe ansatz [12,13]. The main limitation of this technique is very slow convergence towards the thermodynamic limit, which makes it very difficult to evaluate the exponent. In the alternative Luttinger liquid approach [1,3,14], a 1D system is described by two parameters, the sound velocity v = (dω 0 /dq) q→0 , and the Luttinger parameter κ characterizing the interaction strength. At q → 2k F , Luttinger liquid theory yields Eq. (3) with the exponentAt q → 0, however, one finds S ∝ δ(ω − vq). The discrepancy with Eq. (3) is due to the omission in the fixed-point Luttinger liquid Hamiltonian [3,14] of the irrelevant in the RG sense operators [13,14] representing the spectrum nonlinearity. Indeed, for small q, most of the spectral weight of S(q, ω) is confined to a narrow interval of ω of the width δω ∼ ω 1 − ω 0 about ...

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“…The features of the spectra of the 1D compound fit rather well with the concept of spin-charge separation that has emerged from Bethe-Ansatz and bosonization studies of the 1D Hubbard model [6][7][8] and from the exact solution of the t-J model at the supersymmetric point. 9,10 Theoretically, spin-charge separation implies that for long wavelengths, the Hamiltonian of a hole can be decomposed into two commuting parts HϭH h ϩH s , where both the holon part H h and the spinon part H s , are free-fermion Hamiltonians. [9][10][11] As a consequence, the single-hole Green's function takes the form…”

Section: Introductionmentioning

confidence: 99%

“…9,10 Theoretically, spin-charge separation implies that for long wavelengths, the Hamiltonian of a hole can be decomposed into two commuting parts HϭH h ϩH s , where both the holon part H h and the spinon part H s , are free-fermion Hamiltonians. [9][10][11] As a consequence, the single-hole Green's function takes the form…”

Section: Introductionmentioning

confidence: 99%

Single-hole dynamics in thet−Jmodel

Apel

Everts²,

Körner³

2002

Phys. Rev. B

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The quasiparticle weight of a single hole in an antiferromagnetic background is studied in the semiclassical approximation. We start from the t-J model, generalize it to arbitrary spin S by employing an appropriate coherent state representation for the hole, and derive an effective action for the dynamics in the longwavelength low-energy limit. In the same limit, we find an expression for the single-hole Green's function which we evaluate in an 1/S expansion. Our approach has the advantage of being applicable in one and in two dimensions. We find two qualitatively different results in these two cases: while in one dimension our results are compatible with a vanishing quasiparticle weight, this weight is found to be finite in two dimensions, indicating normal quasiparticle behavior of the hole in this last case.

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Theory of hole propagation in one-dimensional insulators and superconductors

Cited by 33 publications

References 47 publications

Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

Exact Jastrow-Slater wave function for the one-dimensional Luttinger model

Threshold Singularities in the Dynamic Response of Gapless Integrable Models

Single-hole dynamics in thet−Jmodel

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