Thermodynamics of the spin-$1/2$ Heisenberg-Ising chain at high temperatures: a rigorous approach

Göhmann, Frank; Goomanee, Salvish; Kozłowski, Karol K.; Suzuki, Junji

doi:10.48550/arxiv.1811.12020

Cited by 3 publications

(5 citation statements)

References 22 publications

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“…(ii) For the special case of the XXZ chain a rigorous proof was recently provided for high enough finite temperatures [25]. Since the proof uses basically only the locality of the interaction of the model, it is expected to be generalizable at least to all fundamental integrable models.…”

Section: Partition Function and Free Energy Per Lattice Sitementioning

confidence: 99%

“…[15]) and by considering the XX chain (this is recommended as an exercise, for some information see [20]). In addition we would like to recommend the work [25], where the case of high but finite temperature was treated with full mathematical rigour.…”

Section: Commentsmentioning

confidence: 99%

“…This means that we may choose the M − n roots x j from a set of N/2 inequivalent values, giving N/2 M −n different solutions. In [25] the high-T limit was worked out on more rigorous grounds, starting from the nonlinear integral equations for the excited states.…”

Section: Commentsmentioning

confidence: 99%

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Statistical mechanics of integrable quantum spin systems

Göhmann

2019

Preprint

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Section: Partition Function and Free Energy Per Lattice Sitementioning

confidence: 99%

Section: Commentsmentioning

confidence: 99%

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Statistical mechanics of integrable quantum spin systems

Göhmann

2019

Preprint

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“…The most systematic approach to the thermodynamics of the XXZ spin chain is based on the Thermodynamic Bethe Ansatz (TBA) method, which first version was invented in 1969 by C. N. Yang and C. P. Yang [13], who used it to study the one-dimensional gas of delta-interacting bosons. Application of the TBA for calculation of the thermodynamic quantities in the XXZ spin chain was started in 1971 by Takahashi [14] and Gaudin [15], and later continued by many other authors [10,[16][17][18][19]. Thermodynamics of the more general XYZ spin-chain model was studied by means of the TBA in [16,20,21].…”

Section: Introductionmentioning

confidence: 99%

Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point

Rutkevich¹

2020

Phys. Rev. E

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The scaling limit of the Heisenberg XXZ spin chain at zero magnetic field is studied in the gapped antiferromagnetic phase. For a spin-chain ring having Nx sites, the universal Casimir scaling function, which characterises the leading finite-size correction term in the large-Nx expansion of the ground state energy, is calculated by numerical solution of the nonlinear integral equation of the convolution type. It is shown that the same scaling function describes the temperature dependence of the free energy of the infinite XXZ chain at low enough temperatures in the gapped scaling regime. I. INTRODUCTIONIntegrable models of statistical mechanics and field theory [1, 2] provide us with a very important source of information about the thermodynamic and dynamical properties of the magnetically ordered systems. Of particular importance is any progress in solutions of such models in the scaling region near the continuous phase transition points, since, due to the universality of critical fluctuations, it does not only yield the exact and detailed information about the model itself but also about the whole universality class it represents.In this paper we address the universal finite-size and thermodynamic properties of the anisotropic spin-1/2 XXZ chain in the massive antiferromagnetic phase in the critical region close to the quantum phase transition at the isotropic point. The Hamiltonian of the model has the form H = J 2 arXiv:1904.11324v3 [cond-mat.stat-mech]

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“…In practice, the complexity of the Bethe ansatz wave functions means that such calculations are extremely difficult and new mathematical methods need to be devised. Initial attempts focused on the case of systems equivalent with free fermions [5][6][7][8][15][16][17][18][19][20][21][22][23][24][25][26][27] but very recently results were obtained for the Lieb-Liniger [28][29][30][31][32][33][34][35][36][37][38] and the XXZ spin-chain [39][40][41][42][43][44][45][46][47][48][49][50][51] models away from the free fermion point. Analytical derivations of the low-energy asymptotics of correlation functions are important because they can be compared with the predictions of TLL but they can also provide insight and identify systems not described by TLL theory.…”

Section: Introductionmentioning

confidence: 99%

Correlation functions of one-dimensional strongly interacting two-component gases

Pâţu¹

2019

Phys. Rev. A

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We address the problem of calculating the correlation functions of one-dimensional two-component gases with strong repulsive contact interactions. The model considered in this paper describes particles with fractional statistics and in appropriate limits reduces to the Gaudin-Yang model or the spinor Bose gas. In the case of impenetrable particles we derive a Fredholm determinant representation for the temperature-, time-, and space-dependent correlation functions which is very easy to implement numerically and constitute the starting point for the analytical investigation of the asymptotics. Making use of this determinant representation and the solution of an associated Riemann-Hilbert problem we derive the low-energy asymptotics of the correlators in the spin-incoherent regime characterized by near ground-state charge degrees of freedom but a highly thermally disordered spin sector. The asymptotics present features reminiscent of spin-charge separation with the spin part exponentially decaying in space separation and oscillating with a period proportional to the statistics parameter while the charge part presents scaling with anomalous exponents which cannot be described by any unitary conformal field theory. The momentum distribution and the Fourier transform of the dynamical Green's function are asymmetrical for arbitrary statistics, a direct consequence of the broken space-reversal symmetry. Due to the exponential decay the momentum distribution n(k) at zero temperature does not present algebraic singularities but the tails obey the universal decay lim k→±∞ n(k) ∼ C/k 4 with the amplitude C given by Tan's contact. As a function of the statistics parameter the contact is a monotonic function reaching its minimum for the fermionic system and the maximum for the bosonic system.

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Thermodynamics of the spin-$1/2$ Heisenberg-Ising chain at high temperatures: a rigorous approach

Cited by 3 publications

References 22 publications

Statistical mechanics of integrable quantum spin systems

Statistical mechanics of integrable quantum spin systems

Scaling in the massive antiferromagnetic XXZ spin-1/2 chain near the isotropic point

Correlation functions of one-dimensional strongly interacting two-component gases

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