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• W3136275772 abstract "This thesis is about the theory of open quantum many-body physics with a particular focus on driven-dissipative photonic and spin lattices. After a review of the main physical platforms and theoretical concepts, we describe our original results. In Chapter 2, we present a theory of the single-mode Kerr model with a time-dependent pump. This model describes a single-mode optical cavity with a third-order optical nonlinearity. In the regime of parameters where the semiclassical analysis shows bistability, we find that a dynamic hysteresis loop appears in the exact solution. The hysteresis area as a function of the sweep time shows a double power-law decay where the second exponent is independent of the system parameters. We show how these effects are related to the emergence of a dissipative phase transition. We also describe concisely the experimental results which have recently confirmed such theoretical predictions. In Chapter 3, we present the corner-space renormalization method. In order to obtain the steady-state density matrix of the lattice, we solve the Lindblad master equation in a subspace of the Hilbert space (the corner). The states spanning the corner space are selected iteratively using eigenvectors of the density matrix of smaller lattice systems, merging in real space two lattices at each iteration and selecting M pairs of states by maximizing their joint probability. The accuracy of the results is then improved by increasing the dimension M of the corner space until convergence is reached. The method has been benchmarked on a two-dimensional Bose-Hubbard model with coherent driving. The strength and limitations of the method are critically discussed.In Chapter 4, we investigate a dissipative phase transition in the two-dimensional anisotropic Heisenberg XYZ model. Using the corner-space renormalization method we present a finite-size analysis of steady-state observables. In particular, we show the critical behaviour of the magnetic susceptibility, the entropy growth and the entanglement witnesses, providing a first evaluation of the critical exponents characterizing the transition. A study of the dynamics of finite-size systems is also consistent with a critical slowing down. For comparison, we present the corresponding analysis for one-dimensional arrays, showing the absence of criticality due to the reduced dimension.In Chapter 5, we explore the non-equilibrium photonic phases of a dissipative Bose-Hubbard model with incoherent pumping of coupled two-level systems. Within a Gutzwiller mean-field approach, we determine the steady-state phase diagram of the system. We predict a second-order phase transition between an incompressible Mott-like phase and a coherent delocalized phase." @default.
• W3136275772 created "2021-03-29" @default.
• W3136275772 creator A5072804974 @default.
• W3136275772 date "2017-11-24" @default.
• W3136275772 modified "2023-09-27" @default.
• W3136275772 title "Dissipative phase transitions in open quantum lattice systems" @default.
• W3136275772 hasPublicationYear "2017" @default.
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