Abstract
We compare the efficiency of different matrix product state (MPS) based methods for the calculation of two-time correlation functions in open quantum systems. The methods are the purification approach[1] and two approaches[2,3] based on the Monte-Carlo wave function (MCWF) sampling of stochastic quantum trajectories using MPS techniques. We consider a XXZ spin chain either exposed to dephasing noise or to a dissipative local spin flip. We find that the preference for one of the approaches in terms of numerical efficiency depends strongly on the specific form of dissipation.
Highlights
To conclude we have presented a comparison of three different matrix product state (MPS) based methods for the calculation of two-time functions in open quantum systems
This comprises the purification approach and two different approaches based on the stochastic unraveling of the Lindblad dynamics
First we compared the two stochastic approaches in the situation of an XXZ spin chain subjected to a dephasing noise starting initially in the classical Neel state
Summary
The investigation of open quantum many-body systems has been a very active field of research over the past decades. In this work we present a comprehensive study on the application of matrix product state (MPS) algorithms to the determination of two-time correlation functions in open systems. L =1 describing a chain of L spins, where Jx and Jz are exchange couplings according to different spin directions and Slα is the spin operator in direction α at site l In equilibrium this model is well understood and exhibits in the ground state, three phases for different ratios of the interaction strengths [40, 41]: For −1 ≤ Jz/Jx ≤ 1 a gapless Tomonaga-Luttinger liquid is formed, whereas Jz/Jx < −1 and Jz/Jx > 1 present gapped phases showing ferromagnetic and antiferromagnetic nature, respectively. Similar ’lossy’ defects have been studied in a variety of models previously and interesting transport effects and meta-stable states have been identified [45,46,47,48,49,50,51,52,53,54,55]
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