The phenomenon of many-body localised (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalise, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localised systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density-density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.
The phenomenon of many-body localised (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalise, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localised systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density-density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.
The phenomenon of many-body localized (MBL) systems has attracted significant interest in recent years, for its intriguing implications from a perspective of both condensed-matter and statistical physics: they are insulators even at non-zero temperature and fail to thermalize, violating expectations from quantum statistical mechanics. What is more, recent seminal experimental developments with ultra-cold atoms in optical lattices constituting analog quantum simulators have pushed many-body localized systems into the realm of physical systems that can be measured with high accuracy. In this work, we introduce experimentally accessible witnesses that directly probe distinct features of MBL, distinguishing it from its Anderson counterpart. We insist on building our toolbox from techniques available in the laboratory, including on-site addressing, super-lattices, and time-of-flight measurements, identifying witnesses based on fluctuations, density–density correlators, densities, and entanglement. We build upon the theory of out of equilibrium quantum systems, in conjunction with tensor network and exact simulations, showing the effectiveness of the tools for realistic models.
The ability of classical thermodynamics to predict phenomena using only handful of parameters is miraculous. Moreover, this framework contrasts with other theories with its ability to describe our day to day experience, i. e. we know intuitively that an ice cube melts in a cold beverage on a hot summer day. A similarly powerful yet significantly less intuitive theory is quantum mechanics which describes the world at its tiniest length scales. Given this foundational position, we would expect to be able to derive all physical theories from quantum mechanics only. Unfortunately this would require knowing the quantum state of all particles which is costly as quantum mechanics requires resources growing exponentially in the system size to describe even relatively innocent many-body systems. Given this uncontrollable growth of parameters, it is highly desirable to apply the principles of thermodynamics to quantum many-body systems as a means to describe them ef- ficiently. Yet, the two theories are not obviously compatible. Subtle differences such as the definition of thermalisation already puzzled founding fathers like John von Neumann. While these have been understood by now, the focus shifted to gaining a thorough understanding of the process of thermalisation in the quantum regime, meaning that the state of the system can be described by a thermal ensemble locally after an initial out-of-equilibrium situation. In the recent past the field of quantum thermodynamics and specifically out-of-equilibrium dynamics has witnessed many successes notably the advent of highly controllable analogue quantum simulators which allow to probe out-of-equilibrium physics to an unprecedented precision. It has been established that thermalisation takes place in quantum many-body systems, but the underlying reasons and a comprehensive theory are still elusive. Only very recently, a class of systems exhibiting many-body localisation has been identi ed that defy this paradigm of thermalisation by localising their constituent particles despite many-body interactions. This can be captured using an effective description in terms of local constants of motion. Understanding the emergence of these physically relevant operators that hinder thermalisation hopefully sheds light also on the mechanism of thermalisation itself. In this thesis, we investigate the relation between thermodynamics and quantum mechanics in the context of out-of-equilibrium physics for many-body localisation. We give numerical evidence for the stability of localisation in large, closed onedimensional chains. Furthermore, we connect the established phenomenology of many-body localisation to experiments with ultra-cold atoms in optical lattices and give a blue print of measurements that can be performed with existing technology to show that the simulator indeed exhibits many-body localisation. We then set out to obtain a deeper understanding of the underlying theory of many-body localisation by devising an algorithm that explicitly constructs exact constants of motion allowing us to put the existing theoretical framework of many-body localisation to the test. It is our firm belief that understanding local constants of motion is indispensable to not only understand thermalisation in quantum many-body systems but is also of great use in other fields. A connection of this type is displayed by an extension of our algorithm to finding edge modes in spin chains with symmetry protected order.
This thesis investigates quantum-many body systems out of equilibrium in a variety of physically relevant and intriguing settings. It provides an overview of the recent developments in this field and based on the author’s recent review illuminates many interesting connections and summarises open questions. In this general framework, the various results of the author are embedded. While they often rely on advanced mathematics, great care is taken to present them in an intuitive way and most technical material is discussed separately in appendices. In the context of equilibration, work created as part of this thesis is able to capture the Gaussification of correlated initial states for a large class of free models. This allows to significantly extend equilibration results of free models, which are of crucial importance, as they provide reasonable relaxation time scales and immediately connect to our physical intuition in terms of ballistic spreading. Building on two surprising connections between static and dynamic features of Hamiltonians, which in general are hard to obtain, the results of this thesis further greatly contribute to the recent debate on the true nature of quantum many- body localisation. For those interacting models, we derive the localised structure of eigenstates from a dynamical suppression of information propagation on the low-energy sector. Further, we show how a non-degenerate spectrum, indicating the presence of interactions, and the existence of an approximately local constant of motion are sufficient to show information propagation, if arbitrary energies are allowed. In the context of quantum phase transitions, we continue such connections between static and dynamic features. We specifically investigate the Mott-superfluid transition of the Bose-Hubbard model and ask to what extent it has a universal dynamical signature. In a joint experimental, numerical and analytical effort, complex behaviour of these dynamics is uncovered, thus challenging the common believe that the Kibble-Zurek mechanism is sufficient to fully capture such transitions. We embed such experimental investigation in the recent debate on quantum simulators, which give the exciting perspective of solving notoriously and even provably hard problems efficiently in the laboratory. For such devices, we argue that the final read-out of the results is an important out- standing problem to be solved. We approach this issue in the case of a continuous quantum field, in which the notion of reconstructing the quantum state is even conceptually unclear. Based on tensor network methods, we demonstrate that in an experiment of ultra-cold atoms in a continuous setup, states can nevertheless efficiently be obtained. Thus, this thesis constitutes not only an important review of the field of quantum many-body systems out of equilibrium, but, using advanced mathematical and numerical tools, has significantly contributed to our understanding of various important out- standing questions in interacting many-body systems.
Ultracold atoms in optical lattices provide one of the most promising platforms for analog quantum simulations of complex quantum many-body systems. Large-size systems can now routinely be reached and are already used to probe a large variety of different physical situations, ranging from quantum phase transitions to artificial gauge theories. At the same time, measurement techniques are still limited and full tomography for these systems seems out of reach. Motivated by this observation, we present a method to directly detect and quantify to what extent a quantum state deviates from a local Gaussian description, based on available noise correlation measurements from in situ and time-of-flight measurements. This is an indicator of the significance of strong correlations in ground and thermal states, as Gaussian states are precisely the ground and thermal states of noninteracting models. We connect our findings, augmented by numerical tensor network simulations, to notions of equilibration, disordered systems, and the suppression of transport in Anderson insulators.
We review some recent developments in the statistical mechanics of isolated quantum systems. We provide a brief introduction to quantum thermalization, paying particular attention to the eigenstate thermalization hypothesis (ETH) and the resulting single-eigenstate statistical mechanics. We then focus on a class of systems that fail to quantum thermalize and whose eigenstates violate the ETH: These are the many-body Anderson-localized systems; their long-time properties are not captured by the conventional ensembles of quantum statistical mechanics. These systems can forever locally remember information about their local initial conditions and are thus of interest for possibilities of storing quantum information. We discuss key features of many-body localization (MBL) and review a phenomenology of the MBL phase. Single-eigenstate statistical mechanics within the MBL phase reveal dynamically stable ordered phases, and phase transitions among them, that are invisible to equilibrium statistical mechanics and can occur at high energy and low spatial dimensionality, where equilibrium ordering is forbidden.
Entanglement is not only the key resource for many quantum technologies, but essential in understanding the structure of many-body quantum matter. At the interface of these two crucial areas are simulators, controlled systems capable of mimicking physical models that might escape analytical tractability. Traditionally, these simulations have been performed classically, where recent advancements such as tensor-networks have made explicit the limitation entanglement places on scalability. Increasingly however, analog quantum simulators are expected to yield deep insight into complex systems. This thesis advances the field in across various interconnected fronts. Firstly, we introduce schemes for verifying and distributing entanglement in a quantum dot simulator, tailored to specific experimental constraints. We then confirm that quantum dot simulators would be natural candidates for simulating many-body localization (MBL) - a recently emerged phenomenon that seems to evade traditional statistical mechanics. Following on from that, we investigate MBL from an entanglement perspective, shedding new light on the nature of the transition to it from a ergodic regime. As part of that investigation we make use of the logarithmic negativity, an entanglement measure applicable to many-body mixed states. In order to tie back into quantum simulators, we then propose an experimental scheme to measure the logarithmic negativity in realistic many-body settings. This method uses choice measurements on three or more copies of a mixed state along with machine learning techniques. We also introduce a fast method for computing many-body entanglement in classical simulations that significantly increases the size of system addressable. Finally, we introduce quimb, an open-source library for interactive but efficient quantum information and many-body calculations. It contains general purpose tensor-network support alongside other novel algorithms.