Exponential asymptotic spin correlations in anisotropic spin-1/2<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mtext>XY</mml:mtext></mml:math>chains at finite temperatures

Krones, Jörn; Stolze, Joachim

doi:10.1103/physrevb.84.052406

Cited by 5 publications

(5 citation statements)

References 26 publications

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“…In this section, we explain how combining this general theory with simple Wick-theorem calculations, one can reproduce the known exponential decay of σ + x (t)σ − 0 (0) , and its generalisation to arbitrary parameter range and GGE. This, in particular, corrects a conjecture made in [30] (which was not completely verified as the authors only tested the gapless regime |h| < 2). We verify our predictions by numerical calculations, and further explore the twist fields themselves, showing agreement with the BFT.…”

Section: Transverse Correlators From Ballistic Fluctuationssupporting

confidence: 84%

“…In this section we show and discuss how the analytic predictions for the transverse correlation function obtained in the previous sections compare with numerical results. There are a number of studies in the literature that considered the time evolution of correlation functions in spin chain [30,34,35], however the numerical results we present are new. In Fig.…”

Section: Comparison With Numerical Resultsmentioning

confidence: 88%

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The hydrodynamic theory of dynamical correlation functions in the XX chain

Del Vecchio,

Doyon

2021

Preprint

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By the hydrodynamic linear response theory, dynamical correlation functions decay as power laws along certain velocities, determined by the flux Jacobian. Such correlations are obtained by hydrodynamic projections, and physically, they are due to propagating "sound waves" or generalisation thereof, transporting conserved quantities between the observables. However, some observables do not emit sound waves, such as order parameters associated to symmetry breaking. In these cases correlation functions decay exponentially everywhere, a behaviour not captured by the hydrodynamic linear response theory. Focussing on spin-spin correlation functions in the XX quantum chain, we first review how hydrodynamic linear response works, emphasising that the necessary fluid cell averaging washes out oscillatory effects. We then show how, beyond linear response, Euler hydrodynamics can still predict the exponential decay of correlation functions of order parameters. This is done by accounting for the large-scale fluctuations of domain walls, via the recently developed ballistic fluctuation theory. We use the framework of generalised hydrodynamics, which is particularly simple in this model due to its free fermion description. In particular, this reproduces, by elementary calculations, the exponential decay in the celebrated formulae by A.R. Its, A.G. Izergin, V.E. Korepin, N.A. Slavnov (1993) and by X. Jie (1998), which were originally obtained by intricate Fredholm determinant analysis; and gives a new formula in a parameter domain where no result was obtained before. We confirm the results by numerical simulations.

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Section: Transverse Correlators From Ballistic Fluctuationssupporting

confidence: 84%

Section: Comparison With Numerical Resultsmentioning

confidence: 88%

The hydrodynamic theory of dynamical correlation functions in the XX chain

Del Vecchio,

Doyon

2021

Preprint

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“…In the limit of infinite chain the formulas are reduced to (34), (35) and (36) and allow to re-derive the asymptotics of correlation function σ x 0 σ x d at d → ∞ in a simple way. It is interesting to derive analytically the long-time and long-distance asymptotic behavior of the σ x spin correlations at finite temperature observed recently in [38] by numeric analysis.…”

Section: Discussionmentioning

confidence: 99%

“…Another way to calculate the two-point correlation function is to use integral representation for the L-particle contribution (38) in terms of energies in transverse direction on the Ising lattice:…”

Section: Shifting the Contours Of The Integrations Bymentioning

confidence: 99%

Form factors of the finite quantumXY-chain

Iorgov¹

2011

J. Phys. A: Math. Theor.

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Explicit factorized formulas for the matrix elements (form-factors) of the spin operators σ x and σ y between the eigenvectors of the Hamiltonian of the finite quantum periodic XY-chain in a transverse field were derived. The derivation is based on the relations between three models: the model of quantum XY-chain, Ising model on 2D lattice and N = 2 Baxter-Bazhanov-Stroganov τ (2) -model. Due to these relations we transfer the formulas for the form-factors of the latter model recently obtained by the use of separation of variables method to the model of quantum XYchain. Hopefully, the formulas for the form-factors will help in analysis of multipoint dynamic correlation functions at a finite temperature. As an example, we re-derive the asymptotics of two-point correlation function in the disordered phase without the use of the Toeplitz determinants and the Wiener-Hopf factorization method.

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“…Therefore, no easy analysis of these observables is possible in fermionic terms. An explicit evaluation requires either analytical mappings which enable an evaluation in the scaling region 35 or extensive numerics in terms of Pfaffians whose dimensions grow linearly with the spatial range of the correlation 29 . The problem of an infinite number of operators is avoided in the string operator basis (25).…”

Section: Spectral Weightmentioning

confidence: 99%

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

Fauseweh

Uhrig

2013

Phys. Rev. B

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The one-dimensional transverse field Ising model is solved by continuous unitary transformations in the high-field limit. A high accuracy is reached due to the closure of the relevant algebra of operators which we call string operators. The closure is related to the possibility to map the model by Jordan-Wigner transformation to non-interacting fermions. But it is proven without referring to this mapping. The effective model derived by the continuous unitary transformations is used to compute the contributions of one, two, and three elementary excitations to the diagonal dynamic structure factors. The three-particle contributions have so far not been addressed analytically, except close to the quantum critical point.

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Exponential asymptotic spin correlations in anisotropic spin-1/2XYchains at finite temperatures

Cited by 5 publications

References 26 publications

The hydrodynamic theory of dynamical correlation functions in the XX chain

The hydrodynamic theory of dynamical correlation functions in the XX chain

Form factors of the finite quantumXY-chain

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

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