Theoretical Solid State Physics

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Tensor network method for free-fermion systems

Tensor network methods have proven to be useful in studying strongly-correlated quantum systems [1]. Their success is due to the fact that low-energy states are typically not highly entangled. In this project, we revisit a very simple many-body system, the spinless fermion model on a square lattice. The metallic states of such a system violate the area law, making their description by tensor network methods challenging [2, 3]. We will explore to what extent tensor network ansatzes can be used to characterize metallic states, two-point correlation functions and the topology of the Fermi surface.

[1] B. Bruognolo. Tensor network techniques for strongly correlated systems: Simulating the quantum many-body wavefunction in zero, one, and two dimensions. Ph.D. thesis, LMU Munich (2017).
[2] W. Li, L. Ding, R. Yu, T. Roscilde and S. Haas. Scaling behavior of entanglement in two- and three-dimensional free-fermion systems. Phys. Rev. B 74, 073103 (2006).
[3] J. Haegeman, B. Swingle, M. Walter, J. Cotler, G. Evenbly, and V. B. Scholz. Rigorous Free-Fermion Entanglement Renormalization from Wavelet Theory. Phys. Rev. X 8, 011003 (2018).