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

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 spin-less fermions for lattice sizes up to 10x10.

9 pages, 8 figures, new material presented

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Cited by in corpus (5)

• Two dimensional quantum lattice models via mode optimized hybrid CPU-GPU density matrix renormalization group method
• Disentangling Interacting Systems with Fermionic Gaussian Circuits: Application to Quantum Impurity Models
• Fermionic Magic Resources of Quantum Many-Body Systems
• Lifshitz transition in the phase diagram of two-leg $t$-$J$ ladder systems at low filling
• Two-electron wavefunctions are matrix product states with bond dimension Three