High temperature expansion of emptiness formation probability for isotropic Heisenberg chain

Abstract

Recently, Göhmann, Klümper and Seel have derived novel integral formulas for the correlation functions of the spin-1/2 Heisenberg chain at finite temperature. We have found that the high temperature expansion (HTE) technique can be effectively applied to evaluate these integral formulas. Actually, as for the emptiness formation probability $P(n)$ of the isotropic Heisenberg chain, we have found a general formula of the HTE for $P(n)$ with arbitrary $n\in {\mathbb{Z}}_{\ge 2}$ up to $O((J/T{)}^4)$. If we fix a magnetic field to a certain value, we can calculate the HTE to much higher order. For example, the order up to $O((J/T{)}^{42})$ has been achieved in the case of $P(3)$ when $h=0$. We have compared these HTE results with the data by Quantum Monte Carlo simulations. They exhibit excellent agreements.

arXiv comment4 pages, 5 eps figures

References in corpus (13)

• Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field
• Thermodynamics of the Anisotropic Spin-1/2 Heisenberg Chain and Related Quantum Chains
• Unified Approach to Thermodynamic Bethe Ansatz and Finite Size Corrections for Lattice Models and Field Theories
• Integral representations for correlation functions of the XXZ chain at finite temperature
• Spin-spin correlation functions of the XXZ-1/2 Heisenberg chain in a magnetic field
• The ALPS project: open source software for strongly correlated systems
• Quantum Spin Chains and Riemann Zeta Function with Odd Arguments
• Correlation Function of the Spin-1/2 XXX Antiferromagnet
• Integral representation of the density matrix of the XXZ chain at finite temperatures
• Emptiness Formation Probability and Quantum Knizhnik-Zamolodchikov Equation
• Quantum Correlations and Number Theory
• Third Neighbor Correlators of Spin-1/2 Heisenberg Antiferromagnet
• First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators

Cited by in corpus (15)

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• Thermal form factors of the XXZ chain and the large-distance asymptotics of its temperature dependent correlation functions
• Short-distance thermal correlations in the massive XXZ chain
• Factorization of multiple integrals representing the density matrix of a finite segment of the Heisenberg spin chain
• Short-distance thermal correlations in the XXZ chain
• Exact thermodynamic limit of short-range correlation functions of the antiferromagnetic $XXZ$-chain at finite temperatures
• Finite temperature density matrix and two-point correlations in the antiferromagnetic XXZ chain
• XX and Ising limits in integral formulae for finite temperature correlation functions of the XXZ chain
• Thermodynamics of the one-dimensional half-filled Hubbard model in the spin-disordered regime
• Fractional exclusion statistics and thermodynamics of the Hubbard chain in the spin-incoherent Luttinger liquid regime
• Emptiness and Depletion Formation Probability in spin models with inverse square interaction
• A note on the high temperature expansion of the density matrix for the isotropic Heisenberg chain
• Universal Low Temperature Asymptotics of the Correlation Functions of the Heisenberg Chain