Transfer matrix approach to quantum systems subject to certain Lindblad evolution

The fundamental link between entanglement dynamics and non-equilibrium statistics in isolated quantum systems has been established in theory and confirmed via experiment. However, the understanding of several consequential phenomena, such as the Many-Body Localization (MBL), has been obstructed by the lack of a systematic approach to obtain many-body entanglement dynamics. This paper introduces the Quantum Correlation Transfer Function (QCTF) approach to entanglement dynamics...

The application of methods of time-dependent density functional theory (TDDFT) to systems of qubits provided the interesting possibility of simulating an assigned Hamiltonian evolution by means of an auxiliary Hamiltonian having different two-qubit interactions and hence a possibly simpler wave function evolution. In this note we extend these methods to some instances of Lindblad evolution of a spin chain.

With their constantly increasing peak performance and memory capacity, modern supercomputers offer new perspectives on numerical studies of open many-body quantum systems. These systems are often modeled by using Markovian quantum master equations describing the evolution of the system density operators. In this paper we address master equations of the Lindblad form, which are a popular theoretical tool in quantum optics, cavity quantum electrodynamics, and optomechanics. By ...

We consider a quantum quench in the spin-1/2 Heisenberg XXZ chain. At late times after the quench it is believed that the expectation values of local operators approach time-independent values, that are described by a generalized Gibbs ensemble. Employing a quantum transfer matrix approach we show how to determine short-range correlation functions in such generalized Gibbs ensembles for a class of initial states.

Explicit solution for the 2-point correlation function in a non-equilibrium steady state of a nearly isotropic boundary-driven open XY spin 1/2 chain in the Lindblad formulation is provided. A non-equilibrium quantum phase transition from exponentially decaying correlations to long-range order is discussed analytically. In the regime of long-range order a new phenomenon of correlation resonances is reported, where the correlation response of the system is unusually high for c...

In this work we study the heat transport in an XXZ spin-1/2 Heisenberg chain with homogeneous magnetic field, incoherently driven out of equilibrium by reservoirs at the boundaries. We focus on the effect of bulk dephasing (energy-dissipative) processes in different parameter regimes of the system. The non-equilibrium steady state of the chain is obtained by simulating its evolution under the corresponding Lindblad master equation, using the time evolving block decimation met...

Understanding the intricate properties of one-dimensional quantum systems coupled to multiple reservoirs poses a challenge to both analytical approaches and simulation techniques. Fortunately, density matrix renormalization group-based tools, which have been widely used in the study of closed systems, have also been recently extended to the treatment of open systems. We present an implementation of such method based on state-of-the-art matrix product state (MPS) and tensor ne...

We study quantum transport properties of an open Heisenberg XXZ spin 1/2 chain driven by a pair of Lindblad jump operators satisfying a global `microcanonical' constraint, i.e. conserving the total magnetization. We will show that this system has an additional discrete symmetry which is particular to the Liouvillean description of the problem. Such symmetry reduces the dynamics even more than what would be expected in the standard Hilbert space formalism and establishes exist...

We formulate and discuss explicit computation of dynamic correlation functions in open quadradic fermionic systems which are driven and dissipated by the Lindblad jump processes that are linear in canonical fermionic operators. Dynamic correlators are interpreted in terms of local quantum quench where the pre-quench state is the non-equilibrium steady state, i.e. a fixed point of the Liouvillian. As an example we study the XY spin 1/2 chain and the Kitaev Majorana chains with...

We perform a systematic symmetry classification of many-body Lindblad superoperators describing general (interacting) open quantum systems coupled to a Markovian environment. Our classification is based on the behavior of the many-body Lindbladian under antiunitary symmetries and unitary involutions. We find that Hermiticity preservation reduces the number of symmetry classes, while trace preservation and complete positivity do not, and that the set of admissible classes depe...