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Abstract:

We develop a Monte Carlo sampling algorithm to numerically evaluate the Lehmann representation for the finite temperature single-particle Green's function in the repulsive Lieb-Liniger model. This allows us to determine the spectral function in the full range of temperatures and interactions, as well as in generalized Gibbs ensembles. We test our results against known results for dynamics at infinite interaction strength and static correlators, and find excellent agreement.

Abstract:

We consider a class of spinless-fermion Lindblad equations that exhibit decoupled BBGKY hierarchies. In the cases where particle number is conserved, their late time behaviour is characterized by diffusive dynamics, leading to an infinite temperature steady state. Some of these models are Yang-Baxter integrable, others are not. The simple structure of the BBGKY hierarchy makes it possible to map the dynamics of Heisenberg-picture operators on few-body imaginary-time Schrödinger equations with non-Hermitian Hamiltonians. We use this formulation to obtain exact hydrodynamic projections of operators quadratic in fermions, and to determine linear response functions in Lindbladian non-equilibrium dynamics.