The Algebraic Bethe Ansatz and Tensor Networks

Abstract

We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a conserved number of down-spins. The tensor network formulation suggestes possible extensions of the Algebraic Bethe Ansatz to two dimensions.

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Cited by in corpus (33)

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• Matrix product solutions of boundary driven quantum chains
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Fast-forwarding quantum evolution
• Tensor network representations of parton wave functions
• Algebraic Bethe Circuits
• Preparing Bethe Ansatz Eigenstates on a Quantum Computer
• Efficient tensor network representation for Gutzwiller projected states of paired fermions
• Obtaining highly excited eigenstates of the localized XX chain via DMRG-X
• Kitaev honeycomb tensor networks: exact unitary circuits and applications
• The Bethe Ansatz as a Quantum Circuit
• The nested Algebraic Bethe Ansatz for the supersymmetric t-J and Tensor Networks
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Integrable spin chains and the Clifford group
• Non-Hermitian boost deformation
• Quantum Error-Detection at Low Energies
• Matrix product operator representations for the local conserved quantities of the Heisenberg chain
• Bethe Ansatz, Quantum Circuits, and the F-basis
• On integrable matrix product operators with bond dimension $D=4$
• Entanglement at the interplay between single- and many-bodyness
• Permutation of Tensor-Train Cores for Computing Moments on Stochastic Differential Equations
• Fractal decompositions and tensor network representations of Bethe wavefunctions
• Efficient Eigenstate Preparation in an Integrable Model with Hilbert Space Fragmentation
• Maximal Entanglement: Applications in Quantum Information and Particle Physics
• Integrability and scattering of the boson field theory on a lattice
• Les Houches Lecture Notes on Tensor Networks
• Double-bracket quantum algorithms for high-fidelity ground state preparation
• Matrix Product Wave Function of the Ground State and Elementary Excitation in the Spin-1/2 Chain
• Periodic revivals from supersymmetry in a fermionic kinetically constrained model