Surface free energy of the open XXZ spin-1/2 chain

Abstract

We study the boundary free energy of the XXZ spin-$\tf{1}{2}$ chain subject to diagonal boundary fields. We first show that the representation for its finite Trotter number approximant obtained by Bortz, Frahm and Göhmann is related to the partition function of the six-vertex model with reflecting ends. Building on the Tsuchiya determinant representation for the latter quantity we are able to take the infinite Trotter number limit. This yields a representation for the surface free energy which involves the solution of the non-linear integral equation that governs the thermodynamics of the XXZ spin-1/2 chain subject to periodic boundary conditions. We show that this integral representation allows one to extract the low-$T$ asymptotic behavior of the boundary magnetization at finite external magnetic field on the one hand and numerically plot this function on the other hand.

35 pages, 11 figures, V3: some new plots added

References in corpus (7)

• Correlation functions of the open XXZ chain I
• Correlation functions of the open XXZ chain II
• Thermodynamics of impurities in the anisotropic Heisenberg spin-1/2 chain
• Boundary contributions to specific heat and susceptibility in the spin-1/2 XXZ chain
• Boundary susceptibility in the open XXZ-chain
• On the normalization of the partition function of Bethe Ansatz systems
• Low-$T$ asymptotic expansion of the solution to the Yang-Yang equation

Cited by in corpus (40)

• Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble Predictions
• Correlations after quantum quenches in the XXZ spin chain: Failure of the Generalized Gibbs Ensemble
• The Quench Action
• Roadmap on Atomtronics: State of the art and perspective
• Antiperiodic spin-1/2 XXZ quantum chains by separation of variables: Complete spectrum and form factors
• Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble
• A Gaudin-like determinant for overlaps of Néel and XXZ Bethe states
• Exact steady states for quantum quenches in integrable Heisenberg spin chains
• Quench action approach for releasing the Néel state into the spin-1/2 XXZ chain
• Quantum quenches in the sinh-Gordon model: steady state and one point correlation functions
• On Generalized Gibbs Ensembles with an infinite set of conserved charges
• Entanglement spreading in non-equilibrium integrable systems
• Overlaps after quantum quenches in the sine-Gordon model
• Non-perturbative Defect One-Point Functions in Planar $\mathcal{N}=4$ Super-Yang-Mills
• Néel-XXZ state overlaps: odd particle numbers and Lieb-Liniger scaling limit
• Quantum quenches to the attractive one-dimensional Bose gas: exact results
• Exact solution for the quench dynamics of a nested integrable system
• Overlaps of $q$-raised Néel states with XXZ Bethe states and their relation to the Lieb-Liniger Bose gas
• Overlaps between eigenstates of the XXZ spin-1/2 chain and a class of simple product states
• Overlaps of Partial Neel States and Bethe States
• Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains
• Universal terms in the overlap of the ground state of the spin-1/2 XXZ chain with the Néel state
• Overlaps with arbitrary two-site states in the XXZ spin chain
• Overlap distributions for quantum quenches in the anisotropic Heisenberg chain
• On the form factors of local operators in the Bazhanov-Stroganov and chiral Potts models
• Integrable quenches in nested spin chains I: the exact steady states
• Quantum Quench in a Harmonically Trapped One-Dimensional Bose Gas
• Quench action and large deviations: work statistics in the one-dimensional Bose gas
• On factorized overlaps: Algebraic Bethe Ansatz, twists, and Separation of Variables
• Inner products in integrable Richardson-Gaudin models
• On exact overlaps in integrable spin chains
• Open XXZ chain and boundary modes at zero temperature
• Perturbative post-quench overlaps in Quantum Field Theory
• Reflection algebra and functional equations
• Correlation and entanglement spreading in nested spin chains
• Thermodynamic limit of the six-vertex model with reflecting end
• Cylinder partition function of the 6-vertex model from algebraic geometry
• Generalized thermalization for integrable system under quantum quench
• TCSA and the finite volume boundary state
• Boundary logarithmic corrections to the dynamical correlation functions of one-dimensional spin-1/2 chains