Constructive Fermionic Matrix Product States for Projected Fermi Sea
arXiv:2408.00858 · doi:10.1103/PhysRevResearch.7.013182
Abstract
Projected wave functions offer a means for incorporating local correlation effects in gapless electronic phases of matter like metals. Although such wave functions can be readily specified formally, it is challenging to compute their associated physical observables. Tensor network approaches offer a modern numerical method for this task. In this work, we develop and demonstrate a constructive tensor-network approach for obtaining physical quantities, like fermion two-point functions and density-density correlation functions, for one-dimensional projected Fermi sea states. We benchmark our method against exact analytical results for spin-1/2 electrons subjected to the Gutzwiller projection, and then present results on spinless fermions with nearest-neighbor repulsion. For a state with two pairs of Fermi points, we reveal a correlation-tuning of the characteristic wave vector of the charge density modulation in the system.
arXiv comment17 pages, 10 figures; version 2: Typos corrected and references updated
References in corpus (39)
- The density-matrix renormalization group in the age of matrix product states
- The density-matrix renormalization group
- Entanglement in quantum critical phenomena
- 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
- Entanglement Spectrum as a Generalization of Entanglement Entropy: Identification of Topological Order in Non-Abelian Fractional Quantum Hall Effect States
- Entanglement renormalization
- Tensor networks for complex quantum systems
- Entanglement entropy of fermions in any dimension and the Widom conjecture
- Violation of the entropic area law for Fermions
- Renormalization and tensor product states in spin chains and lattices
- Tensor-entanglement renormalization group approach to 2D quantum systems
- Fermionic Projected Entangled Pair States
- Entanglement in solvable many-particle models
- The half-filled Landau level: the case for Dirac composite fermions
- LDA+Gutzwiller Method for Correlated Electron Systems: Formalism and Its Applications
- Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
- Fermionic Gaussian states: an introduction to numerical approaches
- Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
- LDA+Gutzwiller Method for Correlated Electron Systems
- Tensor network representations of parton wave functions
- Finite and Infinite Matrix Product States for Gutzwiller Projected Mean-Field Wavefunctions
- Efficient tensor network representation for Gutzwiller projected states of paired fermions
- Density matrix renormalization group boosted by Gutzwiller projected wave functions
- Critical entanglement spectrum of one-dimensional symmetry protected topological phases
- Matrix product state algorithms for Gaussian fermionic states
- Gutzwiller Projected wavefunctions in the fermonic theory of S=1 spin chains
- Matrix product states for Hartree-Fock-Bogoliubov wave functions
- Tensor Networks Can Resolve Fermi Surfaces
- Exact analytic results for the Gutzwiller wave function with finite magnetization
- Variational Discrete Action Theory
- A Fast Impurity Solver Based on Gutzwiller variational approach
- U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
- Foundations of the Variational Discrete Action Theory
- Projected d-wave superconducting state: a fermionic projected entangled pair state study
- Precise ground state of multi-orbital Mott systems via the variational discrete action theory
- Efficient construction of tensor-network representations of many-body Gaussian states
- Gutzwiller Variational Method for Intersite Coulomb Interactions: The Spinless Fermion Model in One Dimension
- Stacked tree construction for free-fermion projected entangled pair states