Dissipative quantum disordered models

We study several dynamical properties of a recently proposed implementation of the quantum transverse-field Ising chain in the framework of circuit QED. Particular emphasis is placed on the effects of disorder on the nonequilibrium behavior of the system. We show that small amounts of fabrication-induced disorder in the system parameters do not jeopardize the observation of previously-predicted phenomena. Based on a numerical extraction of the mean free path of the system, we...

The aim of this article is to give a pedagogical introduction to the exact equilibrium and nonequilibrium properties of free fermionic quantum spin chains. In a first part we present in full details the canonical diagonalisation procedure and review quickly the equilibrium dynamical properties. The phase diagram is analysed and possible phase transitions are discussed. The two next chapters are concerned with the effect of aperiodicity and quenched disorder on the critical pr...

It is widely believed that many-body localisation in one dimension is fragile and can be easily destroyed by thermal inclusions, however there are still many open questions regarding the stability of the localised phase and under what conditions it breaks down. Here I construct models with dilute disorder, which interpolate between translationally invariant and fully random models, in order to study the breakdown of localisation. This opens up the possibility to controllably ...

Over the last few years it was pointed out that certain observables of time-evolving quantum systems may have singularities at certain moments in time, mimicking the singularities physical systems have when undergoing phase transitions. These were given the name of dynamical phase transitions. They were shown to exist in certain integrable (exactly solvable) quantum systems, and were seen experimentally in some setups related (but not identical) to these solvable models. The ...

A phase transition indicates a sudden change in the properties of a large system. For temperature-driven phase transitions this is related to non-analytic behavior of the free energy density at the critical temperature: The knowledge of the free energy density in one phase is insufficient to predict the properties of the other phase. In this paper we show that a close analogue of this behavior can occur in the real time evolution of quantum systems, namely non-analytic behavi...

We show that short-range correlations have a dramatic impact on the steady-state phase diagram of quantum driven-dissipative systems. This effect, never observed in equilibrium, follows from the fact that ordering in the steady state is of dynamical origin, and is established only at very long times, whereas in thermodynamic equilibrium it arises from the properties of the (free) energy. To this end, by combining the cluster methods extensively used in equilibrium phase trans...

We use Monte Carlo simulations to study chains of Ising- and XY-spins with dissipation coupling to the site variables. The phase diagram and critical exponents of the dissipative Ising chain in a transverse magnetic field have been computed previously, and here we consider a universal ratio of susceptibilities. We furthermore present the phase diagram and exponents of the dissipative XY-chain, which exhibits a second order phase transition. All our results compare well with t...

We study nonlinear response in quantum spin systems {near infinite-randomness critical points}. Nonlinear dynamical probes, such as two-dimensional (2D) coherent spectroscopy, can diagnose the nearly localized character of excitations in such systems. {We present exact results for nonlinear response in the 1D random transverse-field Ising model, from which we extract information about critical behavior that is absent in linear response. Our analysis yields exact scaling forms...

We study the dynamics of lattice models of quantum spins one-half, driven by a coherent drive and subject to dissipation. Generically the meanfield limit of these models manifests multistable parameter regions of coexisting steady states with different magnetizations. We introduce an efficient scheme accounting for the corrections to meanfield by correlations at leading order, and benchmark this scheme using high-precision numerics based on matrix-product-operators in one- an...

Disorder is everywhere in nature and it has a fundamental impact on the behavior of many quantum systems. The presence of a small amount of disorder, in fact, can dramatically change the coherence and transport properties of a system. Despite the growing interest in this topic, a complete understanding of the issue is still missing. An open question, for example, is the description of the interplay of disorder and interactions, which has been predicted to give rise to exotic ...