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Updated: May 30, 2026

Excitonic Hamiltonians for Calculating Optical Absorption Spectra and Optoelectronic Properties of Molecular Aggregates and Solids

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A quantum transfer matrix method for one-dimensional disordered electronic systems.

L P Yang¹, Y J Wang, W H Xu

¹Institute of Theoretical Physics, Chinese Academy of Sciences, PO Box 2735, Beijing 100080, People's Republic of China.

Journal of Physics. Condensed Matter : an Institute of Physics Journal

|August 10, 2011

Summary

We introduce a new quantum transfer matrix method to calculate thermodynamic properties of disordered electronic systems. This approach simplifies calculations by expressing the partition function using local transfer matrices.

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Area of Science:

Condensed matter physics
Quantum mechanics
Statistical mechanics

Background:

Disordered electronic systems exhibit complex behavior impacting their thermodynamic properties.
Accurate calculation of thermodynamic properties is crucial for understanding these systems.
Existing methods may face challenges in handling disorder and dimensionality.

Purpose of the Study:

To develop a novel quantum transfer matrix method for studying thermodynamic properties.
To apply this method to one-dimensional (1D) disordered electronic systems.
To demonstrate the method's efficacy using the 1D disordered Anderson model.

Main Methods:

Development of a novel quantum transfer matrix method.
Expressing the partition function as a product of local 2x2 transfer matrices.
Application to the 1D disordered Anderson model.

Main Results:

The partition function is successfully represented as a product of local transfer matrices.
Thermodynamic quantities for the 1D disordered Anderson model were calculated.
The method provides a tractable approach for analyzing disordered systems.

Conclusions:

The novel quantum transfer matrix method is effective for studying thermodynamic properties of 1D disordered electronic systems.
The method offers a simplified computational approach.
This work contributes to the understanding of quantum disordered systems.