High temperature series expansion of thermodynamic functions in a Heisenberg spin chain with a site dependent coupling

The high-temperature series expansion for quantum spin models is a well-established tool to compute thermodynamic quantities and equal-time spin correlations, in particular for frustrated interactions. We extend the scope of this expansion to the dynamic Matsubara spin-spin correlator and develop an algorithm that yields exact expansion coefficients in the form of rational numbers. We focus on Heisenberg models with a single coupling constant J and spin lengths S=1/2,1. The expansion coefficients up to 12th order in J/T are precomputed on all possible $\sim 10^6$ graphs embeddable in arbitrary lattices and are provided in a repository. This enables calculation of static momentum-resolved susceptibilities for arbitrary site-pairs or wavevectors. We test our results for the antiferromagnetic S=1/2 chain and triangular lattice model. An important application that we discuss in a companion letter is the calculation of real-frequency dynamic structure factors. This is achieved by identifying the high-frequency expansion coefficients of the Matsubara correlator with frequency moments of the spectral function.The high-temperature series expansion for quantum spin models is a well-established tool to compute thermodynamic quantities and equal-time spin correlations, in particular for frustrated interactions. We extend the scope of this expansion to the dynamic Matsubara spin-spin correlator and develop an algorithm that yields exact expansion coefficients in the form of rational numbers. We focus on Heisenberg models with a single coupling constant J and spin lengths S=1/2,1. The expansion coefficients up to 12th order in J/T are precomputed on all possible $\sim 10^6$ graphs embeddable in arbitrary lattices and are provided in a repository. This enables calculation of static momentum-resolved susceptibilities for arbitrary site-pairs or wavevectors. We test our results for the antiferromagnetic S=1/2 chain and triangular lattice model. An important application that we discuss in a companion letter is the calculation of real-frequency dynamic structure factors. This is achieved by identifying the high-frequency expansion coefficients of the Matsubara correlator with frequency moments of the spectral function.

arXiv:2505.23699Physical review. B./Physical review. BOct 1, 20253 citations

High Temperature Expansion for the SU(n) Heisenberg Model in One Dimension

Noboru Fukushima, Yoshio Kuramoto

Thermodynamic properties of the SU( $n$ ) Heisenberg model in one dimension is studied by means of high-temperature expansion for arbitrary $n$ . The specific heat up to $O[(βJ)^{23}]$ and the correlation function up to $O[(βJ)^{18}]$ are derived with $βJ$ being the antiferromagnetic exchange in units of temperature. It is found for $n>2$ that the specific heat shows a shoulder in the high-temperature side of a peak. The origin of this structure is clarified by deriving the temperature dependence of the correlation function. With decreasing temperature, the short-range correlation with two-site periodicity develops first, and then another correlation with $n$ -site periodicity at lower temperature. This behavior is in contrast to that of the inverse square interaction model, where the specific heat shows a single peak according to the exact solution. Our algorithm has an advantage that neither computational time nor memory depends on the multiplicity $n$ per site; the series coefficients are obtained as explicit functions of $n$ .Thermodynamic properties of the SU($n$) Heisenberg model in one dimension is studied by means of high-temperature expansion for arbitrary $n$. The specific heat up to $O[(βJ)^{23}]$ and the correlation function up to $O[(βJ)^{18}]$ are derived with $βJ$ being the antiferromagnetic exchange in units of temperature. It is found for $n>2$ that the specific heat shows a shoulder in the high-temperature side of a peak. The origin of this structure is clarified by deriving the temperature dependence of the correlation function. With decreasing temperature, the short-range correlation with two-site periodicity develops first, and then another correlation with $n$-site periodicity at lower temperature. This behavior is in contrast to that of the inverse square interaction model, where the specific heat shows a single peak according to the exact solution. Our algorithm has an advantage that neither computational time nor memory depends on the multiplicity $n$ per site; the series coefficients are obtained as explicit functions of $n$.

arXiv:cond-mat/0110550Journal of the Physical Society of JapanMay 15, 200210 citations

Thermodynamics of the spin-S antiferromagnetic Heisenberg chain

Pedro D Sacramento

The European Physical Journal BSep 1, 19946 citations

Thermodynamics of quantum spin chains

Alessandro Cuccoli, V. Tognetti, Ruggero Vaia +1 more

Springer eBooksApr 7, 20080 citations

Finite and high-temperature series expansion via many-body perturbation theory: application to Heisenberg spin-1/2 XXZ chain

Mohamed Amine Tag, Abid Boudiar, Mohamed El-Hadi Mansour +3 more

Abstract We present a new algorithm to evaluate the grand potential at high and finite temperatures using many-body perturbation theory. This algorithm enables us to calculate the contribution of any Hugenholtz or Feynman vacuum diagrams and formulate the results as a sum of divided differences. Additionally, the proposed method is applicable to any interaction in any dimension, allowing us to calculate thermodynamic quantities efficiently at any given temperature, particularly at high temperatures.Furthermore, we apply this algorithm to the Heisenberg spin-1/2 XXZ chain. We obtain all coefficients of the high-temperature expansion of the free energy and susceptibility per site of this model up to the sixth order.Abstract We present a new algorithm to evaluate the grand potential at high and finite temperatures using many-body perturbation theory. This algorithm enables us to calculate the contribution of any Hugenholtz or Feynman vacuum diagrams and formulate the results as a sum of divided differences. Additionally, the proposed method is applicable to any interaction in any dimension, allowing us to calculate thermodynamic quantities efficiently at any given temperature, particularly at high temperatures.Furthermore, we apply this algorithm to the Heisenberg spin-1/2 XXZ chain. We obtain all coefficients of the high-temperature expansion of the free energy and susceptibility per site of this model up to the sixth order.

Physica ScriptaMay 10, 20245 citations

\sim 10^6

graphs embeddable in arbitrary lattices and are provided in a repository. This enables calculation of static momentum-resolved susceptibilities for arbitrary site-pairs or wavevectors. We test our results for the antiferromagnetic S=1/2 chain and triangular lattice model. An important application that we discuss in a companion letter is the calculation of real-frequency dynamic structure factors. This is achieved by identifying the high-frequency expansion coefficients of the Matsubara correlator with frequency moments of the spectral function.

Thermodynamic properties of the SU(

n

) Heisenberg model in one dimension is studied by means of high-temperature expansion for arbitrary

n

. The specific heat up to

O[(βJ)^{23}]

and the correlation function up to

O[(βJ)^{18}]

are derived with

βJ

being the antiferromagnetic exchange in units of temperature. It is found for

n>2

that the specific heat shows a shoulder in the high-temperature side of a peak. The origin of this structure is clarified by deriving the temperature dependence of the correlation function. With decreasing temperature, the short-range correlation with two-site periodicity develops first, and then another correlation with

n

-site periodicity at lower temperature. This behavior is in contrast to that of the inverse square interaction model, where the specific heat shows a single peak according to the exact solution. Our algorithm has an advantage that neither computational time nor memory depends on the multiplicity

n

per site; the series coefficients are obtained as explicit functions of

n