Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems with matrix-product states

Krumnow C, Veis L, Eisert J, Legeza O (2021)

Publication Type: Journal article

Publication year: 2021

Journal

Physical Review B American Physical Society

Book Volume: 104

Article Number: 075137

Journal Issue: 7

DOI: 10.1103/PhysRevB.104.075137

Abstract

Tensor network methods have progressed from variational techniques based on matrix-product states able to compute properties of one-dimensional condensed-matter lattice models into methods rooted in more elaborate states, such as projected entangled pair states aimed at simulating the physics of two-dimensional models. In this work, we advocate the paradigm that for two-dimensional fermionic models, matrix-product states are still applicable to significantly higher accuracy levels than direct embeddings into one-dimensional systems allow for. To do so, we exploit schemes of fermionic mode transformations and overcome the prejudice that one-dimensional embeddings need to be local. This approach takes the insight seriously that the suitable exploitation of both the manifold of matrix-product states and the unitary manifold of mode transformations can more accurately capture the natural correlation structure. By demonstrating the residual low levels of entanglement in emerging modes, we show that matrix-product states can describe ground states strikingly well. The power of the approach is exemplified by investigating a phase transition of spinless fermions for lattice sizes up to 10×10.

Involved external institutions

Freie Universität Berlin DE Germany (DE) Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ) Hungarian Academy of Sciences / Magyar Tudományos Akadémia (MTA) HU Hungary (HU)

How to cite

APA:

Krumnow, C., Veis, L., Eisert, J., & Legeza, O. (2021). Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems with matrix-product states. Physical Review B, 104(7). https://doi.org/10.1103/PhysRevB.104.075137

MLA:

Krumnow, C., et al. "Effective dimension reduction with mode transformations: Simulating two-dimensional fermionic condensed matter systems with matrix-product states." Physical Review B 104.7 (2021).

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