On the logarithmic bipartite fidelity of the open XXZ spin chain at $\Delta =-1/2$

Abstract

The open XXZ spin chain with the anisotropy $\Delta =-\frac{1}{2}$ and a one-parameter family of diagonal boundary fields is studied at finite length. A determinant formula for an overlap involving the spin chain's ground-state vectors for different lengths is found. The overlap allows one to obtain an exact finite-size formula for the ground state's logarithmic bipartite fidelity. The leading terms of its asymptotic series for large chain lengths are evaluated. Their expressions confirm the predictions of conformal field theory for the fidelity.

arXiv commentRevised version, 31 pages, 2 figures

References in corpus (30)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Scaling of Entanglement close to a Quantum Phase Transitions
• Entanglement entropy and conformal field theory
• Entanglement in a simple quantum phase transition
• Boundary S-Matrix and Boundary State in Two-Dimensional Integrable Quantum Field Theory
• Boundary K-Matrices for the Six Vertex and the n(2n-1) A_{n-1} Vertex Models
• Spin chains and combinatorics
• The quantum symmetric XXZ chain at Delta=-1/2, alternating sign matrices and plane partitions
• The Importance of being Odd
• Magic in the spectra of the XXZ quantum chain with boundaries at Delta=0 and Delta=-1/2
• Spin chains and combinatorics: twisted boundary conditions
• One-boundary Temperley-Lieb algebras in the XXZ and loop models
• Universal behavior of a bipartite fidelity at quantum criticality
• Asymptotics of symmetric polynomials with applications to statistical mechanics and representation theory
• The XXZ spin chain at $\Delta =-1/2$: Bethe roots, symmetric functions and determinants
• Sum rules for the ground states of the O(1) loop model on a cylinder and the XXZ spin chain
• Logarithmic corrections to the free energy from sharp corners with angle $2\pi$
• Open spin chains with dynamic lattice supersymmetry
• Punctured plane partitions and the q-deformed Knizhnik--Zamolodchikov and Hirota equations
• Finite size emptiness formation probability of the XXZ spin chain at $\Delta =-1/2$
• Correlation Functions and the Boundary qKZ Equation in a Fractured XXZ Chain
• Open boundary Quantum Knizhnik-Zamolodchikov equation and the weighted enumeration of Plane Partitions with symmetries
• Finite-size corrections for universal boundary entropy in bond percolation
• Finite-size left-passage probability in percolation
• On the transfer matrix of the supersymmetric eight-vertex model. II. Open boundary conditions
• Boundary emptiness formation probabilities in the six-vertex model at $\Delta =-\frac{1}{2}$
• Bipartite fidelity of critical dense polymers
• Refined Razumov-Stroganov conjectures for open boundaries
• The open XXZ chain at $\Delta =-1/2$ and the boundary quantum Knizhnik-Zamolodchikov equations

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