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.

arXiv comment9 pages, 8 figures, new material presented

References in corpus (44)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Area laws for the entanglement entropy - a review
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Spin Liquid Ground State of the $S=1/2$ Kagome Heisenberg Model
• Time-dependent density-matrix renormalization-group using adaptive effective Hilbert spaces
• Matrix Product Density Operators: Simulation of finite-T and dissipative systems
• An Area Law for One Dimensional Quantum Systems
• Unifying time evolution and optimization with matrix product states
• Functional renormalization group approach to correlated fermion systems
• Ab Initio Quantum Chemistry using the Density Matrix Renormalization Group
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• Entropy scaling and simulability by Matrix Product States
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Tensor product methods and entanglement optimization for ab initio quantum chemistry
• Measuring orbital interaction using quantum information theory
• Computational Complexity of interacting electrons and fundamental limitations of Density Functional Theory
• Controlling the accuracy of the density matrix renormalization group method: The Dynamical Block State Selection approach
• Simulating Strongly Correlated Quantum Systems with Tree Tensor Networks
• Fermionic Projected Entangled Pair States
• Quantum information analysis of electronic states at different molecular structures
• A positive tensor network approach for simulating open quantum many-body systems
• Quantum data compression, quantum information generation, and the density-matrix renormalization group method
• Obtaining highly-excited eigenstates of many-body localized Hamiltonians by the density matrix renormalization group
• Two-site entropy and quantum phase transitions in low-dimensional models
• Density-matrix renormalization-group method in momentum space
• Quantum Hamiltonian Complexity
• Contraction of fermionic operator circuits and the simulation of strongly correlated fermions
• Simulation of interacting fermions with entanglement renormalization
• Fermionic Quantum Critical Point of Spinless Fermions on a Honeycomb Lattice
• Improved energy extrapolation with infinite projected entangled-pair states applied to the 2D Hubbard model
• Unitary circuits for strongly correlated fermions
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Fermionic orbital optimisation in tensor network states
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Fermionic Implementation of Projected Entangled Pair States Algorithm
• Application of the Density Matrix Renormalization Group in momentum space
• Entanglement structure of the Hubbard model in momentum space
• Phase diagram of interacting spinless fermions on the honeycomb lattice
• The density matrix renormalization group algorithm on kilo-processor architectures: implementation and trade-offs
• Entanglement production by independent quantum channels
• Towards overcoming the entanglement barrier when simulating long-time evolution

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• Two-electron wavefunctions are matrix product states with bond dimension Three