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arXiv · 2201.06588

Exactly Solvable 1D Quantum Models with Gamma Matrices

Yash Chugh·Kusum Dhochak·Uma Divakaran·Prithvi Narayan·Amit Kumar Pal
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Abstract

In this paper, we write exactly solvable generalizations of 1-dimensional quantum XY and Ising-like models by using $2^d$-dimensional Gamma ($\Gamma$) matrices as the degrees of freedom on each site. We show that these models result in quadratic Fermionic Hamiltonians with Jordan-Wigner like transformations. We illustrate the techniques using a specific case of 4-dimensional $\Gamma$ matrices and explore the quantum phase transitions present in the model.

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Yash Chugh, Kusum Dhochak, Uma Divakaran, Prithvi Narayan, Amit Kumar Pal. 2022-01-17. Exactly Solvable 1D Quantum Models with Gamma Matrices. https://doi.org/10.1103/physreve.106.024114

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