Abstract
We consider the XY spin chain with arbitrary time-dependent magnetic field and anisotropy. We argue that a certain subclass of Gaussian states, called Coherent Ensemble (CE) following [1], provides a natural and unified framework for out-of-equilibrium physics in this model. We show that all correlation functions in the CE can be computed using form factor expansion and expressed in terms of Fredholm determinants. In particular, we present exact out-of-equilibrium expressions in the thermodynamic limit for the previously unknown order parameter 1-point function, dynamical 2-point function and equal-time 3-point function.
Highlights
While the quantities that are local in the underlying fermions can be computed efficiently with Pfaffian representations arising from Wick’s theorem [47, 49], there are no known exact representations for expectation values in general Gaussian states in the thermodynamic limit for the quantities that are non-local in the underlying fermions (such as static (2n + 1)-point functions of the order parameter, or any dynamical correlation of the order parameter)
The purpose of this section is to show that essentially all correlation functions and expectation values in the Coherent Ensemble (CE) can be expressed as Fredholm determinants and Pfaffians in the thermodynamic limit
In this work we have addressed the problem of computing out-of-equilibrium observables in the XY spin chain subject to arbitrary time variations of the magnetic field h(t) and anisotropy γ(t)
Summary
Quantum integrable models are special models of many-body quantum physics with both a rich phenomenology and an exact Bethe-ansatz solution. They constitute the point of departure and testbed of any field theory or exact method applying to the interacting case Despite their free fermion formulation, the problem of obtaining analytic expressions for general in- and out-of-equilibrium correlations in the thermodynamic limit is still unsolved for some of these models. At these values of parameters, the form factors of the order parameter are exactly Cauchy determinants, which enables one to use the techniques developed for U(1) symmetric models and obtain Fredholm determinant expressions in the thermodynamic limit We note that these coherent states appeared more or less explicitly in different papers in the literature [67, 68, 74, 77, 98].
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