Low-energy and dynamical properties of a single hole in the<i>t</i>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mrow><mml:msub><mml:mrow><mml:mi mathvariant="italic">J</mml:mi></mml:mrow><mml:mrow><mml:mi mathvariant="italic">z</mml:mi></mml:mrow></mml:msub></mml:mrow></mml:math>model

Zhong, Q. F.; Sorella, Sandro

doi:10.1103/physrevb.51.16135

Cited by 14 publications

(11 citation statements)

References 32 publications

(87 reference statements)

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“…In a first step, we introduce additional complete sets of single fermion states in the numerator of Eq. (2.5), such that G(i, j, τ, σ) becomes 6) where the sum l runs over all possible intermediate one particle states in the fermionic Hilbert space {| f l }.…”

Section: The Model and The Algorithmmentioning

confidence: 99%

Single-hole dynamics in thet−Jmodel on a square lattice

2000

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We present quantum Monte Carlo (QMC) simulations for a single hole in a t-J model from J = 0.4t to J = 4t on square lattices with up to 24 × 24 sites. The lower edge of the spectrum is directly extracted from the imaginary time Green's function. In agreement with earlier calculations, we find flat bands around (0, ±π), (±π, 0) and the minimum of the dispersion at (±π/2, ±π/2). For small J both self-consistent Born approximation and series expansions give a bandwidth for the lower edge of the spectrum in agreement with the simulations, whereas for J/t > 1, only series expansions agree quantitatively with our QMC results. This band corresponds to a coherent quasiparticle. This is shown by a finite size scaling of the quasiparticle weight Z( k) that leads to a finite result in the thermodynamic limit for the considered values of J/t. The spectral function A( k, ω) is obtained from the imaginary time Green's function via the maximum entropy method. Resonances above the lowest edge of the spectrum are identified, whose J-dependence is quantitatively described by string excitations up to J/t = 2.

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Section: The Model and The Algorithmmentioning

confidence: 99%

Single-hole dynamics in thet−Jmodel on a square lattice

2000

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“…In classical physics this would correspond to a Galileo transformation from the laboratory frame to the reference frame locally at rest with respect to the hole. This transformation can be easily generalized to quantum mechanics [18] and the derivation can be performed in arbitrary dimension. As a first step we notice that the t − J Hamiltonian (1.3) is translationally invariant and then any one hole state with definite momentum k and spin ↑ can be written as:…”

Section: The Effective Hole Hamiltonianmentioning

confidence: 99%

Theory of hole propagation in one-dimensional insulators and superconductors

Sorella

Parola

1998

Phys. Rev. B

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The dynamical properties of hole motion in an antiferromagnetic background are determined in one-dimensional models in zero magnetic field, where spin isotropy holds, as well as in an external magnetic field. The latter case is also relevant, via particle-hole transformation, to the problem of hole propagation in one-dimensional "superconductors." The singularities in the spectral function are investigated by means of bosonization techniques and perturbation theories. Results are then compared with Bethe ansatz solutions and Lanczos diagonalizations. The formalism also leads to interesting connections to the single impurity; problem in Luttinger liquids. A rich structure is found in the spectral function whenever spin isotropy is broken, suggesting the presence of exotic momentum dependence in photoemission spectra of (quasi) one dimensional materials

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“…The deviation occurs because the finite difference is substituted for the differential in the LSD method. 17) Now, let us turn to the anisotropic case. We show S xx (q, ω) for the IS XXZ model with ∆ = 2, 5, and 10 in Figs.…”

Section: Excitation Spectra and Dynamical Structure Factorsmentioning

confidence: 99%

“…In order to extract the behavior of S µµ (q, ω) in the thermodynamic limit from finitesize data, we use the Lanczos spectra decoding (LSD) method. 17) The procedure gives the DSF as follows:…”

Section: §1 Introductionmentioning

confidence: 99%

Dynamical Structure Factors of the Spin-1/2XXZChain with Inverse-Square Exchange and Ising Anisotropy

Saiga

Kuramoto

1998

J. Phys. Soc. Jpn.

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The dynamical properties of the S = 1/2 antiferromagnetic XXZ chain are studied by the exact diagonalization and the recursion method of finite systems up to 24 sites. Two types of the exchange interaction are considered: one is the nearest-neighbor type, and the other is the inverse-square one. As the Ising anisotropy becomes larger, there appears a noticeable difference in the transverse component S xx (q, ω) between the two types of the exchange. For the nearest-neighbor type, the peak frequency of S xx (q, ω) for each q approaches the center of the continuum spectrum. On the contrary, the peak frequency for the inverse-square type moves to the upper edge of the continuum, and separates from the continuum for the anisotropy larger than the threshold value. Whether the interaction between domain walls (solitons) is absent or repulsive in the Ising limit leads to this difference in the behavior of S xx (q, ω). In the longitudinal component S zz (q, ω), on the other hand, the feature of the dynamics is scarcely different between the two types. The energy gap and the static properties are also discussed.KEYWORDS: dynamical structure factor, XXZ chain, inverse-square exchange, nearest-neighbor exchange, Ising anisotropy, Haldane-Shastry model, exact diagonalization, recursion method §1. IntroductionThe physics concerning one-dimensional (1D) quantum systems has been a long-standing problem. Discovery of many quasi-1D quantum magnets has spurred on the studies of the systems. Among those, there are S = 1/2 systems in which a finite energy gap opens in the magnetic excitation spectrum. These systems have various origins of an excitation gap. For example, in CuGeO 3 , the first inorganic compound in which a spinPeierls transition was observed, 1) a gap appears below the critical temperature because of the lattice dimerization and the frustration. The other case with a gap is the XXZ chain with Ising anisotropy. CsCoCl 3 is known to be a typical 1D Ising-like antiferromagnet.2) One of the experimental means to measure the spin gap is the inelastic neutron scattering.3, 4) The neutron scattering brings us not only the information of the spin gap but also the whole excitation spectrum. 5,6) In this context, the dynamical structure factor (DSF) is a physical quantity to investigate carefully, because it is closely related with the experimental data detected by the neutron scattering.Besides connection with experiment, the study of dynamics is indispensable in order to understand the nature of elementary excitations in the system. To this end, it is desirable to find the exact expression of the DSF. Haldane and Zirnbauer 7) achieved this great work in the Haldane-Shastry (HS) model, 8,9) which is an isotropic spin model with exchange interaction proportional to the inverse square of the distance. Their result has the biggest merit that the picture of the elementary excitation is made simple. Recently, an integral representa- * E-mail: saiga@cmpt01.phys.tohoku.ac.jp tion of the exact DSF has been clarified for the nearestn...

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Low-energy and dynamical properties of a single hole in thet-Jzmodel

Cited by 14 publications

References 32 publications

Single-hole dynamics in thet−Jmodel on a square lattice

Single-hole dynamics in thet−Jmodel on a square lattice

Theory of hole propagation in one-dimensional insulators and superconductors

Dynamical Structure Factors of the Spin-1/2XXZChain with Inverse-Square Exchange and Ising Anisotropy

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