Efficient conversion from fermionic Gaussian states to matrix product states
arXiv:2408.01155 · doi:10.1088/2058-9565/addae0
Abstract
Fermionic Gaussian states are eigenstates of quadratic Hamiltonians and are widely used in quantum many-body problems. We propose a highly efficient algorithm that converts fermionic Gaussian states to matrix product states. It can be formulated for finite-size systems without translation invariance, but becomes particularly appealing when applied to infinite systems with translation invariance. If the ground states of a topologically ordered system on infinite cylinders are expressed as matrix product states, then the fixed points of the transfer matrix can be harnessed to filter out the anyon eigenbasis, also known as minimally entangled states. This allows for efficient computation of universal properties, such as the entanglement spectrum and modular matrices. The potential of our method is demonstrated by numerical calculations in two chiral spin liquids that have the same topological orders as the bosonic Laughlin and Moore-Read states, respectively. The anyon eigenbasis for the first one has been worked out before and serves as a useful benchmark. The anyon eigenbasis of the second one is, however, not transparent, and its successful construction provides a nontrivial corroboration of our method.
14 pages, 7 figures
References in corpus (57)
- The density-matrix renormalization group in the age of matrix product states
- 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
- Calculation of reduced density matrices from correlation functions
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Renormalization and tensor product states in spin chains and lattices
- Quasi-particle Statistics and Braiding from Ground State Entanglement
- Fermionic Projected Entangled Pair States
- Differentiable Programming Tensor Networks
- Variational optimization with infinite projected entangled-pair states
- Topological characterization of fractional quantum Hall ground states from microscopic Hamiltonians
- Characterizing topological order by studying the ground states of an infinite cylinder
- Algorithms for finite Projected Entangled Pair States
- Gradient methods for variational optimization of projected entangled-pair states
- Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
- Tensor network trial states for chiral topological phases in two dimensions and a no-go theorem in any dimension
- Non-Abelian Statistics in a Quantum Antiferromagnet
- Momentum polarization: an entanglement measure of topological spin and chiral central charge
- Projected entangled-pair states can describe chiral topological states
- Topological Entanglement Entropy of Z2 Spin liquids and Lattice Laughlin states
- Fermionic magnons, non-Abelian spinons, and spin quantum Hall effect from an exactly solvable Kitaev Hamiltonian with SU(2) symmetry
- Non-Abelian chiral spin liquid in a quantum antiferromagnet revealed by an iPEPS study
- Parent Hamiltonian for the non-Abelian chiral spin liquid
- Compression of Correlation Matrices and an Efficient Method for Forming Matrix Product States of Fermionic Gaussian States
- Generalized Hartree-Fock Theory for Interacting Fermions in Lattices: Numerical Methods
- Symmetries and boundary theories for chiral Projected Entangled Pair States
- Tensor network representations of parton wave functions
- Variational Monte Carlo method for fermionic models combined with tensor networks and applications to the hole-doped two-dimensional Hubbard model
- Lattice spin models for non-Abelian Chiral Spin Liquids
- Abelian SU Chiral Spin Liquids on the Square Lattice
- 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
- Finding the ground state of a lattice gauge theory with fermionic tensor networks: a demonstration
- Matrix product state algorithms for Gaussian fermionic states
- Non-Abelian Chiral Spin Liquid on the Kagome Lattice
- Matrix product states for Hartree-Fock-Bogoliubov wave functions
- Tensor Networks Can Resolve Fermi Surfaces
- Coexistence of non-Abelian chiral spin liquid and magnetic order in a spin-1 antiferromagnet
- Finite Projected Entangled Pair States for the Hubbard model
- Possible chiral spin liquid state in the kagome Heisenberg model
- Matrix-Product based Projected Wave Functions Ansatz for Quantum Many-Body Ground States
- Twisting the Dirac cones of the SU(4) spin-orbital liquid on the honeycomb lattice
- U(1)-symmetric Gaussian fermionic projected entangled paired states and their Gutzwiller projection
- Resonating valence bond realization of spin-1 non-Abelian chiral spin liquid on the torus
- Projected d-wave superconducting state: a fermionic projected entangled pair state study
- Fermionic Gaussian PEPS in : Rotations and Relativistic Limits
- Fermionic tensor networks for higher order topological insulators from charge pumping
- Efficient construction of tensor-network representations of many-body Gaussian states
- Non-Abelian chiral spin liquid on spin-1 kagome lattice: truncation of an exact Hamiltonian and numerical optimization
- Global quantum phase diagram and non-Abelian chiral spin liquid in a spin-3/2 square lattice antiferromagnet
- Finite-Entanglement Scaling of 2D Metals
- Constructive Fermionic Matrix Product States for Projected Fermi Sea
- Stacked tree construction for free-fermion projected entangled pair states