Numerical Contraction of the Tensor Network generated by the Algebraic Bethe Ansatz

Abstract

The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations. Whereas the spectrum is usually obtained directly, the eigenstates are available only in terms of complex mathematical expressions. This makes it very hard in general to extract properties from the states, like, for example, correlation functions. In our work, we apply the tools of Tensor Network States to describe the eigenstates approximately as Matrix Product States. From the Matrix Product State expression, we then obtain observables like correlation functions directly.

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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