Equilibrium dynamics of the XX chain

Abstract

The equilibrium dynamics of the spin-1/2 XX chain is re-examined within a recently developed formalism based on the quantum transfer matrix and a thermal form factor expansion. The transversal correlation function is evaluated in real time and space. The high-accuracy calculation reproduces several exact results in limiting cases as well as the well-known asymptotic formulas obtained by the matrix Riemann-Hilbert approach. Furthermore, comparisons to numerical data based on a direct evaluation of the Pfaffian as well as to asymptotic formulas obtained within non-linear Luttinger liquid theory are presented.

22pages, RevTex, title changed, some references and comments are added

References in corpus (12)

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• Exact edge singularities and dynamical correlations in spin-1/2 chains
• Spectral function of spinless fermions on a one-dimensional lattice
• Hidden Grassmann structure in the XXZ model
• Dynamical structure factor at small q for the XXZ spin-1/2 chain
• Hidden Grassmann Structure in the XXZ Model III: Introducing Matsubara direction
• Factorization of the finite temperature correlation functions of the XXZ chain in a magnetic field
• Dynamical correlation functions of the XXZ model at finite temperature
• Long-distance and large-time asymptotic behaviour of dynamic correlation functions in the massless regime of the XXZ spin-1/2 chain
• On singularities of dynamic response functions in the massless regime of the XXZ spin-1/2 chain

Cited by in corpus (16)

• Current operators in integrable models: A review
• Finite temperature and quench dynamics in the Transverse Field Ising Model from form factor expansions
• Exact real-time longitudinal correlation functions of the massive XXZ chain
• A systematic $1/c$-expansion of form factor sums for dynamical correlations in the Lieb-Liniger model
• Out-of-equilibrium dynamics of the XY spin chain from form factor expansion
• Large time and long distance asymptotics of the thermal correlators of the impenetrable anyonic lattice gas
• The hydrodynamic theory of dynamical correlation functions in the XX chain
• Effective free-fermionic form factors and the XY spin chain
• A thermal form factor series for the longitudinal two-point function of the Heisenberg-Ising chain in the antiferromagnetic massive regime
• High-temperature analysis of the transverse dynamical two-point correlation function of the XX quantum-spin chain
• On the Dynamics of Free-Fermionic Tau-Functions at Finite Temperature
• Late-time large-distance asymptotics of the transverse correlation functions of the XX chain in the space-like regime
• Analytical results for the low-temperature Drude weight of the XXZ spin chain
• Enhancement of synthetic magnetic field induced nonreciprocity via bound states in continuum in dissipatively coupled systems
• Exact spectral function of the Tonks-Girardeau gas at finite temperature
• Low-temperature asymptotic of the transverse dynamical structure factor for a magnetically polarized XX chain