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

Perk, Jacques H. H.; Au-Yang, Helen

doi:10.1007/s10955-009-9758-5

Cited by 71 publications

(64 citation statements)

References 87 publications

(183 reference statements)

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“…In passing, we mention that a different approach based on the solution of differential equations has been proposed in Ref. [69] for computing similar correlation functions.…”

Section: Computation Of the Correlation Functionsmentioning

confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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Fluctuation-dissipation relations, i.e., the relation between two-time correlation and linear response functions, were successfully used to search for signs of equilibration and to identify effective temperatures in the non-equilibrium behavior of a number of macroscopic classical and quantum systems in contact with thermal baths. Among the most relevant cases in which the effective temperatures thus defined were shown to have a thermodynamic meaning one finds the stationary dynamics of driven super-cooled liquids and vortex glasses, and the relaxation of glasses. Whether and under which conditions an effective thermal behavior can be found in quantum isolated many-body systems after a global quench is a question of current interest. We propose to study the possible emergence of thermal behavior long after the quench by studying fluctuation-dissipation relations in which (possibly time-or frequency-dependent) parameters replace the equilibrium temperature. If thermalization within the Gibbs ensemble eventually occurs these parameters should be constant and equal for all pairs of observables in "partial" or "mutual" equilibrium. We analyze these relations in the paradigmatic quantum system, i.e., the quantum Ising chain, in the stationary regime after a quench of the transverse field. The lack of thermalization to a Gibbs ensemble becomes apparent within this approach. Contents

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“…In passing, we mention that a different approach based on the solution of differential equations has been proposed in Ref. [69] for computing similar correlation functions.…”

Section: Computation Of the Correlation Functionsmentioning

confidence: 99%

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

2012

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“…In the literature are already present several detailed analysis of the Fredholm determinant (56). For instance, one could set up an expansion similar to [52][53][54] for the time-dependent correlation functions of the critical Ising chain or to [49] for the full-counting statistics by solving a Riemann-Hilbert problem. On the other hand, in the celebrated paper [41], Jimbo, Miwa, Mori and Sato discovered that the Fredholm determinant (56) is equal to the τ function, τ 0 , of the Painlevé V equation (28) with x = i2χ, parameters θ 0 = θ t = θ * = 0, and satisfying the boundary conditions…”

Section: The XX Spin Chainmentioning

confidence: 99%

“…We represent the difference ∆ 0 between the logarithm of the EFP for |h| < 1 (region Σ 0 ) and the terms in the interpolation conjectured in (53) except the one that contains the Painlevé V τ function, see(54). Thus ∆ 0 should be asymptotically equal to log τ (−x/γ) where x = 2L log |h|.…”

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confidence: 99%

Emptiness formation probability and Painlevé V equation in the XY spin chain

Ares¹,

Viti²

2020

J. Stat. Mech.

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“…This spin model exhibits a nonzero transverse magnetization at the zero transverse field due to its multiple sites spin coupling and shows a rich ground-state phase diagram [63][64][65][66]. The Hamiltonian reads…”

Section: The Modelmentioning

confidence: 99%

Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model

2014

Phys. Rev. E

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We study the Riemannian metric and the Euler characteristic number of the Bloch band in a onedimensional spin model with multi-site spins exchange interactions. The Euler number of the Bloch band originates from the Gauss-Bonnet theorem on the topological characterization of the closed Bloch states manifold in the first Brillouin zone. We study this approach analytically in a transverse field XY spin chain with three-site spin coupled interactions. We define a class of cyclic quantum distance on the Bloch band and on the ground state, respectively, as a local characterization for quantum phase transitions. Specifically, we give a general formula for the Euler number by means of the Berry curvature in the case of two-band models, which reveals its essential relation to the first Chern number of the band insulators. Finally, we show that the ferromagnetic-paramagnetic phases transition in zero-temperature can be distinguished by the Euler number of the Bloch band.

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

Cited by 71 publications

References 87 publications

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Dynamic correlations, fluctuation-dissipation relations, and effective temperatures after a quantum quench of the transverse field Ising chain

Emptiness formation probability and Painlevé V equation in the XY spin chain

Quantum distance and the Euler number index of the Bloch band in a one-dimensional spin model

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