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Approaching the long-time dynamics of non-Markovian open quantum systems presents a challenging task if the bath is strongly coupled. Recent proposals address this problem through a representation of the so-called process tensor in terms of…
We study the second-order quantum phase-transition of massive real scalar field theory with a quartic interaction ($\phi^4$ theory) in (1+1) dimensions on an infinite spatial lattice using matrix product states (MPS). We introduce and apply…
This work is devoted to the study Translation-Invariant (TI) Matrix Product State (MPS) representations of quantum states with periodic boundary conditions (PBC). We pursue two directions: we introduce new methods for constructing TI MPS…
We show that the time-dependent variational principle provides a unifying framework for time-evolution methods and optimisation methods in the context of matrix product states. In particular, we introduce a new integration scheme for…
Traditional numerical techniques for solving time-dependent partial-differential-equation (PDE) initial-value problems (IVPs) store a truncated representation of the function values and some number of their time derivatives at each time…
In order to model realistic quantum devices it is necessary to simulate quantum systems strongly coupled to their environment. To date, most understanding of open quantum systems is restricted either to weak system-bath couplings, or to…
A new approach to the theory and simulation of the non-Markovian dynamics of open quantum systems is presented. It is based on identification of a parameter which is uniformly small on wide time intervals: the occupation of the virtual…
We present a new paradigm for the dynamical simulation of interacting many-boson open quantum systems. The method relies on a variational ansatz for the $n$-boson density matrix, in terms of a superposition of photon-added coherent states.…
Vibrational dynamics of adsorbates near surfaces plays both an important role for applied surface science and as model lab for studying fundamental problems of open quantum systems. We employ a previously developed model for the relaxation…
We present an approach based upon binary tree tensor network (BTTN) states for computing steady-state current statistics for a many-particle 1D ratchet subject to volume exclusion interactions. The ratcheted particles, which move on a…
We demonstrate a surprising connection between pure steady state entanglement and relaxation timescales in an extremely broad class of Markovian open systems, where two (possibly many-body) systems $A$ and $B$ interact locally with a common…
The time-evolving matrix product operator (TEMPO) method is a powerful tool for simulating open system quantum dynamics. Typically, it is used in problems with diagonal system-bath coupling, where analytical expressions for discretized…
We study the evolution of one-dimensional quantum lattice systems when the ground state is perturbed by altering one site in the middle of the chain. For a large class of models, we observe a similar pattern of entanglement growth during…
We describe the quantum dynamics of the Hubbard model at semi-classical level, by implementing the Time-Dependent Variational Principle (TDVP) procedure on appropriate macroscopic wavefunctions constructed in terms of su(2)-coherent states.…
In this work we develop several new simulation algorithms for 1D many-body quantum mechanical systems combining the Matrix Product State variational ansatz with Taylor, Pad\'e and Arnoldi approximations to the evolution operator. By…
It is known that exact traveling wave solutions exist for families of (n+1)-states stochastic one-dimensional non-equilibrium lattice models with open boundaries provided that some constraints on the reaction rates are fulfilled. These…
Matrix product ansatz (MPA) is a powerful framework for constructing exact steady state weights of one dimensional non-equilibrium stochastic processes; but its generalization to higher dimensions is limited. Here, we introduce the MPA…
In this article we propose a dynamic quantum tomography model for open quantum systems with evolution given by phase-damping channels. Mathematically, these channels correspond to completely positive trace-preserving maps defined by the…
We consider the unitary time evolution of continuous quantum mechanical systems confined to a cavity in contact with a finite bath of variable size. Measures for Markovianity for such finite system-bath configurations are developed in terms…
I introduce a modification of continuous matrix product states (CMPS) that makes them adapted to relativistic quantum field theories (QFT). These relativistic CMPS can be used to solve genuine 1+1 dimensional QFT without UV cutoff and…