Transfer matrix approach to quantum systems subject to certain Lindblad evolution

The Lindblad master equation for an arbitrary quadratic system of n fermions is solved explicitly in terms of diagonalization of a 4n x 4n matrix, provided that all Lindblad bath operators are linear in the fermionic variables. The method is applied to the explicit construction of non-equilibrium steady states and the calculation of asymptotic relaxation rates in the far from equilibrium problem of heat and spin transport in a nearest neighbor Heisenberg XY spin 1/2 chain in ...

By employing the Lindblad equation, we derive the evolution of the two-point correlator for a free-fermion chain of length $L$ subject to bulk dephasing and boundary losses. We use the Bethe ansatz to diagonalize the Liouvillian ${\mathcal L}^{\scriptscriptstyle(2)}$ governing the dynamics of the correlator. The majority of its energy levels are complex. Precisely, $L(L-1)/2$ complex energies do not depend on dephasing, apart for a trivial shift. The remaining complex levels ...

We study a 1-dimensional XX chain under nonequilibrium driving and local dephasing described by the Lindblad master equation. The analytical solution for the nonequilibrium steady state found for particular parameters in [J.Stat.Mech., L05002 (2010)] is extended to arbitrary coupling constants, driving and homogeneous magnetic field. All one, two and three-point correlation functions are explicitly evaluated. It is shown that the nonequilibrium stationary state is not gaussia...

In recent work Hartmann et al [Phys. Rev. Lett. 102, 057202 (2009)] demonstrated that the classical simulation of the dynamics of open 1D quantum systems with matrix product algorithms can often be dramatically improved by performing time evolution in the Heisenberg picture. For a closed system this was exemplified by an exact matrix product operator solution of the time-evolved creation operator of a quadratic fermi chain with a matrix dimension of just two. In this work we ...

We consider the evolution of two-time correlations in the quantum XXZ spin-chain in contact with an environment causing dephasing. Extending quasi-exact time-dependent matrix product state techniques to consider the dynamics of two-time correlations within dissipative systems, we uncover the full quantum behavior for these correlations along all spin directions. Together with insights from adiabatic elimination and kinetic Monte Carlo, we identify three dynamical regimes. For...

In this paper we apply the nested algebraic Bethe ansatz to compute the eigenvalues and the Bethe equations of the transfer matrix of the new integrable Lindbladian found in [1]. We show that it can be written as an integrable spin chain consisting of two interacting XXZ spin chains. We numerically compute the Liouville gap and its dependence on the parameters in the system such as scaling with the system length and interaction strength.

Many-body quantum systems are subjected to the Curse of Dimensionality: The dimension of the Hilbert space $\mathcal{H}$, where these systems live in, grows exponentially with systems' 'size' (number of their components, "bodies"). It means that, in order to specify a state of a quantum system, we need a description whose length grows exponentially with the system size. However, with some systems it is possible to escape the curse by using low-rank tensor approximations known...

We propose a dissipative method for the preparation of many-body steady entangled states in spin and fermionic chains. The scheme is accomplished by means of an engineered set of Lindbladians acting over the eigenmodes of the system, whose spectrum is assumed to be resolvable. We apply this idea to prepare a particular entangled state of a spin chain described by the XY model, emphasizing its generality and experimental feasibility. Our results show that our proposal is capab...

By considering the one-particle and two-particle scattering data of the spin-1/2 Heisenberg chain at T=0 we derive a continuum limit relating the spin chain to the 1D Bose gas. Applying this limit to the quantum transfer matrix approach of the Heisenberg chain we obtain expressions for the correlation functions of the Bose gas at arbitrary temperatures.

The description of the dynamics of closed quantum systems, governed by the Schroedinger equation at first sight seems incompatible with the Lindblad equation describing open ones. By analyzing closed dynamics of a spin-1/2 chain we reconstruct exponential decays characteristic for the latter model. We identify all necessary ingredients to efficiently model this behavior, such as an infinitely large environment and the coupling to the system weak in comparison to the internal ...