Critical behavior of one-particle spectral weights in the transverse Ising model

Abstract

We investigate the critical behavior of the spectral weight of a single quasiparticle, one of the key observables in experiment, for the particular case of the transverse Ising model. Series expansions are calculated for the linear chain and the square and simple cubic lattices. For the chain model, a conjectured exact result is discovered. For the square and simple cubic lattices, series analyses are used to estimate the critical exponents. The results agree with the general predictions of Sachdev ͓Quantum Phase Transitions ͑Cambridge University Press, Cambridge, England, 1999͔͒.

Multiparticle spectral properties in the transverse field Ising model by continuous unitary transformations

“…The relative error (not shown in the graphs) remains fairly constant over the whole Brillouin zone. Consequently our results differ from the exact ones found by Hamer et al 32 by only about 1% even close to the critical point at J = 1.9Γ.…”

“…In Ref. 32 Hamer et al derived an analytic expression for the one-particle contribution for the longitudinal structure factors. To our knowledge no data is available in the literature for higher quasi-particle contributions Q α β 0 2.5 ± 0.3 1.0 ± 0.2 π/2 3.0 ± 0.2 2.7 ± 0.2 π 3.0 ± 0.2 2.8 ± 0.1 Table II.…”

New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain

“…We believe that this point of view has been put to rest by the results in this paper. Secondly, during a brief visit in 2005 at the University of New South Wales one of us got to discuss an early version of [68,69] with his colleagues. It led us to calculate the small and large-B expansions for the structure function j σ x 0 σ x j of the Ising chain in a transverse field at zero temperature.…”

Multipartite Entanglement Detection via Structure Factors

“…One-particle spectral functions are investigated for various materials in [9,10,11]. Also, much theoretical work on determining the structure factor and the related spectral weights of particular spin chain models has been done, numerically and analytically [12,13,14,15,16]. Moreover, the structure factor plays an important role in the physics of atoms in optical lattices since it is related to the visibility of the interference pattern [17].…”