Quantum strong-interaction physics can yield collective phenomena over a vast range of energy scales and kinematics. We seek the emergence of quantum collective phenomena from underlying inter-particle interactions using advanced computational approaches with detailed theoretical analyses on both a low-energy (non-relativistic) and a high-energy (relativistic) scale. We select alpha-clustering in light nuclei for the non-relativistic phenomenon and a phase transition in quantum field theory for the relativistic phenomenon. Both problems are defined by microscopic Hamiltonians from the underlying theory and solved with advanced computational techniques. Detailed investigation of the results yields insights into remarkable emergent phenomena. This work proposes novel analytical and computational tools that lead to demonstrations on how non-perturbative quantum many-body theory in the Hamiltonian framework produces results that predict collective phenomena.
Quantum strong-interaction physics can yield collective phenomena over a vast range of energy scales and kinematics. We seek the emergence of quantum collective phenomena from underlying inter-particle interactions using advanced computational approaches with detailed theoretical analyses on both a low-energy (non-relativistic) and a high-energy (relativistic) scale. We select alpha-clustering in light nuclei for the non-relativistic phenomenon and a phase transition in quantum field theory for the relativistic phenomenon. Both problems are defined by microscopic Hamiltonians from the underlying theory and solved with advanced computational techniques. Detailed investigation of the results yields insights into remarkable emergent phenomena. This work proposes novel analytical and computational tools that lead to demonstrations on how non-perturbative quantum many-body theory in the Hamiltonian framework produces results that predict collective phenomena.
Quantum many-body systems are comprised of complex networks of microscopic interactions that work together to produce novel collective phases and phenomena. \nFor strongly-interacting systems, the connection between the underlying atomic-scale behaviour and the resulting emergent observable phenomena is exponentially (and, in practice, infinitely) complicated such that it becomes impossible to fully understand the connection between the physics at the microscopic and macroscopic levels. \nThe most promising theoretical approaches to addressing this infinite complexity utilize microscopic coarse-graining along with powerful computational simulations and strategies. \nIn this thesis, we apply numerical methods to effective lattice models and field theories with the goal of shedding light onto universal critical behaviour and exotic low-temperature phases in condensed matter physics. \n \nWe start by exploring universal features of critical non-interacting systems, for which several analytical strategies are readily available for calculating certain observables. \nWe study the behaviour of the system's entanglement for various entangling geometries, and utilize numerical techniques in order to isolate new universal features of Gaussian fixed points, which provide insight into the underlying critical theory's renormalization group flow. \nWe then proceed to examine computational strategies and, in particular, Monte Carlo simulations for studying more general interacting models. \nWe focus on the application of such strategies to the field of high-temperature superconductivity, for which we develop a coarse-grained model, simulate macroscopic observables and compare our results with those of recent experiments. \nWe conclude that lattice field theories together with innovative computational methods offer new perspectives on both universality and emergent phenomena in quantum matter.
Quantum computing introduces a revolutionary approach to solving problems that are computationally beyond the reach of classical systems. Among its most promising applications is the simulation of many-body systems, where strong particle interactions lead to complex quantum behaviors. Traditional computational techniques often fail due to exponential resource requirements, but quantum simulators can efficiently model these interactions through entanglement and superposition. Recent advances in superconducting qubits, trapped ions, and photonic quantum devices have enabled small- scale experimental demonstrations of spin models, Hubbard systems, and correlated electron dynamics. These developments offer new insights into condensed matter physics and quantum phase transitions. As quantum technologies continue to evolve, they hold the potential to transform the study of materials, superconductivity, and other many-body phenomena with remarkable precision and scalability.
This book presents a detailed account of the theory and methods to tackle systems of strongly interacting particles from a bottom-up approach, which has been largely developed in the past decade by the authors and other experts in the field. This begins with a full characterisation of strongly interacting few-particle systems, which can be dealt with accurately using a variety of analytical and numerical techniques. These non-perturbative solutions can be used to gain qualitative and quantitative insight into more complex problems, especially the many-body problem. The book gives a detailed overview of the relevant and current research literature in the field, and is a valuable tool for researchers and graduate students.Part of IOP Series in Quantum Technology. Key features • Many worked examples of representative quantum systems, together with their physical interpretations and the main consequences of their solutions • Set of problems at the end of each chapter, not meant to complement the theory, but to give the reader dexterity in using the chapter’s methodologies • Timely discussion of a recently developed, and very active field summarised as “From Few- to Many-Body Quantum Physics of Strongly Interacting Particles”, and the physics of interacting quantum systems in inhomogeneous media • First, coherent, detailed monograph on the theory and methods of the field • Presents a rigorous account of the modern approaches to low-energy collisions and their use in few- and many-body physics, which have not appeared in book format • The book is relevant to a wide range of researchers and advanced students, from atomic and condensed matter physics, to photonics and nuclear physics • Written by pioneers and true experts in the field
The theory of the strong interaction, quantum chromodynamics (QCD), describes the generation of hadronic masses and the state of hadronic matter during the early stages of the evolution of the universe. As a complement, experiments with ultracold fermionic atoms provide a clean environment to benchmark our understanding of dynamical formation of condensates and the generation of bound states in strongly interacting many-body systems. Renormalization Group (RG) techniques offer great potential for theoretical advances in both hot and dense QCD and many-body physics, but their connections have not yet been investigated in great detail. We aim to take a further step to bridge this gap. A cross-fertilization is indeed promising since it may eventually provide us with an ab initio description of hadronization, condensation and bound-state formation in strongly interacting theories. After giving a thorough introduction to the derivation and analysis of fermionic RG flows, we give an introductory review of our present understanding of universal long-range behavior in various different theories, ranging from non-relativistic many-body problems to relativistic gauge theories, with an emphasis on scaling behavior of physical observables close to quantum phase transitions (i.e. phase transitions at zero temperature) as well as thermal phase transitions.
Liquids and solids, atoms and molecules, nuclei—all these clearly are interacting many-body systems. Even a nucleon may be regarded as a manyparticle system, not just because it is now known to consist of three quarks interacting via gluons, but because of the possibility in quantum field theory of virtual excitation of many particles from the vacuum. in the table page 56 we list some of the many-particle systems we encounter in the physical world at length scales that range from a few centimeters to a few fermis. Many of these systems exhibit phenomena—superconductivity in solids and fission in nuclei, for example—whose understanding does not follow immediately from knowledge of the constituents of the system and the interactions among the constituents, but requires new concepts and ideas. Many-body physics is the branch of theoretical physics that studies the new phenomena or “emergent properties” that arise from interactions among “elementary” constituents of a many-particle system and provides means and methods for carrying out precise calculations of such characteristic properties of these systems as may be compared with experimental results to verify hypotheses about the nature of the constituents and their interactions.
Experimental progress in atomic, molecular, and optical platforms in the last decade has stimulated strong and broad interest in the quantum coherent dynamics of many long-range interacting particles. The prominent collective character of these systems enables novel non-equilibrium phenomena with no counterpart in conventional quantum systems with local interactions. Much of the theory work in this area either focussed on the impact of variable-range interaction tails on the physics of local interactions or relied on mean-field-like descriptions based on the opposite limit of all-to-all infinite-range interactions. In this Report, we present a systematic and organic review of recent advances in the field. Working with prototypical interacting quantum spin lattices without disorder, our presentation hinges upon a versatile theoretical formalism that interpolates between the few-body mean-field physics and the many-body physics of quasi-local interactions. Such a formalism allows us to connect these two regimes, providing both a formal quantitative tool and basic physical intuition. We leverage this unifying framework to review several findings of the last decade, including the peculiar non-ballistic spreading of quantum correlations, counter-intuitive slowdown of entanglement dynamics, suppression of thermalization and equilibration, anomalous scaling of defects upon traversing criticality, dynamical phase transitions, and genuinely non-equilibrium phases stabilized by periodic driving. The style of this Report is on the pedagogical side, which makes it accessible to readers without previous experience in the subject matter.