Thermal pure matrix product state in two dimensions: tracking thermal equilibrium from paramagnet down to the Kitaev spin liquid state

Matthias Gohlke^1*, Atsushi Iwaki², Chisa Hotta²

¹Theory of Quantum Matter, Okinawa Institute of Science and Technology, Onna, Okinawa, Japan
²Department of Basic Science, The University of Tokyo, Tokyo, Japan

* Presenter:Matthias Gohlke, email:matthias.gohlke@oist.jp

Numerical studies of Quantum many body systems at finite temperature are generically difficult, in particular if one is interested in systems with competing interactions. On general grounds, one considers either of two approaches for representing a thermal state: The Gibbs state of the density operator which is a mixture of an exponential numbers of states and purity zero, whereas the thermal pure quantum (TPQ) state is a single pure wave function with purity one. Using random sampling methods, however, one can also construct various thermal mixed quantum states (TMQ) with a purity in-between 0 and 1 [1]. In this talk, we illustrate that matrix product states (MPS) can provide a thermal mixed quantum state representation in equilibrium in two spatial dimensions over the entire temperature range. We start off by illustrating the TPQ-MPS ansatz [2] on the Kitaev honeycomb model as a prominent, non-trivial example hosting a quantum spin liquid ground state. Our method is able to qualitatively capture its characteristic double-peak in the specific heat [3,4]. Further applications to other two-dimensional quantum systems will be discussed.

[1] A. Iwaki and C. Hotta, PRB 106, 094409 (2022).
[2] A. Iwaki, A. Shimizu, and C. Hotta, PRR 3, L022015 (2021).
[3] J. Nasu, M. Udagawa, and Y. Motome, PRB 92, 115122 (2015).
[4] M. Gohlke, A. Iwaki, C. Hotta, SciPost Phys. 15, 206 (2023)

Keywords: Quantum Spin Liquid, Tensor Networks, Matrix Product States, Thermal Quantum State