Exotic phases of matter represent a paradigm shift in condensed matter physics, transcending classical thermodynamic states and embracing quantum mechanical principles. These phases, including topological insulators, quantum spin liquids, and time crystals, exhibit emergent properties driven by symmetry breaking, entanglement, and quantum coherence. This paper explores the fundamental principles governing these novel phases, recent breakthroughs in their realization, and their implications for quantum computing and materials science. Emphasis is placed on theoretical models such as the Kitaev honeycomb lattice and experimental advances in ultracold atom traps and strongly correlated electron systems. By reviewing current challenges and prospects, this study outlines a roadmap for navigating this new frontier in physics.
Exotic phases of matter represent a paradigm shift in condensed matter physics, transcending classical thermodynamic states and embracing quantum mechanical principles. These phases, including topological insulators, quantum spin liquids, and time crystals, exhibit emergent properties driven by symmetry breaking, entanglement, and quantum coherence. This paper explores the fundamental principles governing these novel phases, recent breakthroughs in their realization, and their implications for quantum computing and materials science. Emphasis is placed on theoretical models such as the Kitaev honeycomb lattice and experimental advances in ultracold atom traps and strongly correlated electron systems. By reviewing current challenges and prospects, this study outlines a roadmap for navigating this new frontier in physics.
Quantum matter (novel phases of matter at zero temperature with exotic properties) is a growing field with applications in its own domain, and in providing foundational support to quantum sciences fields more generally. The ability to characterize and manipulate matter at the smallest scales continues to advance in fundamental ways. This review provides a plain-language, non-technical description of contemporary activity in quantum matter for a general science audience, and an example of these methods applied to quantum neuroscience. Quantum matter is the study of topologically governed phases of matter at absolute zero temperature that exhibit new kinds of emergent order and exotic properties related to topology and symmetry, entanglement, and electronic charge and magnetism, which may be orchestrated to create new classes of materials and computational devices (including in the areas of spintronics, valleytronics, and quantum computing). The paper is organized to discuss recent developments in quantum matter on the topics of short-range topologically protected materials (namely, topological semimetals), long-range entangled materials (quantum spin liquids and fractional quantum Hall states), and codes for characterizing and controlling quantum systems. A key finding is that a shift in the conceptualization of the field of quantum matter may be underway to expand the core focus on short-range topologically protected materials to also include geometry-based approaches and long-range entanglement as additionally important tools for the understanding, characterization, and manipulation of topological materials.
The exploration of quantum phases in strongly correlated electron systems represents a frontier in condensed matter physics, offering insights into phenomena such as high-temperature superconductivity, Mott insulation, and quantum spin liquids. Traditional theoretical approaches, relying on perturbative or mean-field approximations, often fall short in capturing the intricate interplay of electron correlations that drive these exotic phases. This paper delves into the critical role of exact and highly accurate diagrammatic expansions as powerful, non-perturbative tools for unraveling the emergence and characterization of quantum phases. We review the theoretical foundations of these methods, including advanced techniques like Dynamical Mean-Field Theory extensions and the Functional Renormalization Group, and discuss their ability to systematically incorporate non-local correlations. By examining their application to canonical models, we illustrate how these expansions provide a robust framework for constructing phase diagrams, predicting novel quantum states, and discerning the mechanisms underlying quantum phase transitions. We highlight the computational advancements, such as diagrammatic Monte Carlo, that enable the practical implementation of these complex theories. Finally, we discuss current challenges and future prospects, emphasizing the potential of exact diagrammatic expansions to deepen our understanding of quantum matter and guide the discovery of new materials with tailored functionalities.
In recent years, topology has become increasingly prevalent in condensed matter physics. It has allowed us to understand, and even predict, a variety of striking and remarkable physical phenomena. The study of strongly interacting systems has similarly lavished us with a diverse range of exotic phases and unconventional transitions, many of which are still poorly understood. In this thesis we will explore the interplay between topology and interactions in an effort to uncover new and novel phases. First we study how interactions impact the quantum phase transition between a topologically non-trivial phase and a trivial phase. The combination of interactions and the low-energy degrees of freedom associated with the transition leads to the emergence of a dome of lattice-symmetry breaking nematic order. Such behaviour is reminiscent of a number of strongly correlated electronic systems. We move on to study the strongly interacting limit of one of the earliest and best-known non-interacting topological phases, Haldane's model of a Chern insulator. Recently realized with ultracold atoms in a shaken optical lattice, the model has a non-trivial topological invariant associated with its band structure. In the strongly interacting limit the spin degrees of freedom are all that survive and we find a rich phase diagram of magnetically ordered phases, using a combination of both classical and quantum techniques. Supplementing the model with an additional term we can `quantum-melt' one of these ordered states to produce a disordered, liquid state that we positively identify as a chiral spin liquid, a highly entangled state of matter with fractionalised excitations. We generalise this mechanism to other two dimensional lattices, uncovering a possible unifying framework with which to understand the emergence of chiral spin liquids in lattice spin models. Finally, motivated by groundbreaking experiments in the ultracold atoms community, we investigate a model of two-component bosons with an artificial spin-orbit coupling. The interplay between the lattice, interactions and spin-orbit coupling produces a variety of unusual superfluid phases. Using a novel Monte Carlo technique we reveal the finite temperature phase diagram that appears close to the Mott transition.
Quantum spin liquids have fascinated condensed matter physicists for decades because of their unusual properties such as spin fractionalization and long-range entanglement. Unlike conventional symmetry breaking, the topological order underlying quantum spin liquids is hard to detect experimentally. Even theoretical models are scarce for which the ground state is established to be a quantum spin liquid. The Kitaev honeycomb model and its generalizations to other tricoordinated lattices are chief counterexamples—they are exactly solvable, harbor a variety of quantum spin liquid phases, and are also relevant for certain transition metal compounds including the polymorphs of (Na,Li) 2 IrO 3 iridates and RuCl 3 . In this review, we give an overview of the rich physics of the Kitaev model, including two-dimensional and three-dimensional fractionalization as well as dynamic correlations and behavior at finite temperatures. We discuss the different materials and argue how the Kitaev model physics can be relevant even though most materials show magnetic ordering at low temperatures.
(English) In recent years, the evolution of quantum technologies has resulted in an unprecedented control over individual quantum particles and many-body systems. This remarkable progress has given rise to a new era, marked by the convergence of classical and quantum methodologies to investigate fundamental questions concerning the nature of quantum matter, improving our understanding of the role of entanglement in solid-state systems or the mechanisms behind high-energy physics. From analog quantum simulators to digital quantum computers, these advancements hold potential across diverse domains. This thesis explores the interplay between classical and quantum methods in understanding topological phases of matter. We concentrate on three distinct directions: non-conventional topological superconductors, interaction-induced topological phases in ultracold atom quantum simulators, and applications of variational quantum algorithms. Each trajectory relies on the combination of different techniques with the aim of understanding and characterizing topological phenomena in different settings. Exploring non-conventional topological superconductors involves extending the paradigmatic Kitaev chain model by incorporating additional terms in the Hamiltonian such as long-range interactions and quasi-periodic potentials. This investigation is relevant to better understand the impact of real-world conditions on the both the topological and localization properties of systems hosting non-local Majorana modes, which are promising candidates for topological quantum computation. In the realm of interacting systems, we explore the realization of interaction-induced topological phases in systems of ultracold atoms in optical lattices, both in one and two dimensions. The remarkable control and versatility of such platforms enable the simulation of both theoretical topological models and strongly correlated physics. Notably, the interplay between interactions and topology can give rise to intriguing phenomena, such as delocalized fractional charges and gapless topological phases,challenging existing intuition. We employ advanced numerical methods based on tensor networks to benchmark the experimental proposals that open the door to the realization and detection of novel many-body phases of matter, including topological quantum critical points and a higher-order topological Peierls insulator in Bose-Hubbard models with long-range interactions. Variational quantum algorithms, conversely, have the potential to efficiently tackle a wide range of problems, including ground state search, phase classification or accessing topological invariants. Despite current limitations in trainability and scalability, these hybrid classical-quantum algorithms provide practical insights into current quantum hardware capabilities and can inspire future architectures. We explore the application of variational quantum algorithms to shed light on topological phenomena, raising questions about their ability to discern topological phase transitions and compute topological invariants in situations where classical approaches fail. This thesis presents a comprehensive exploration of distinct approaches to topological quantum matter by leveraging quantum technologies and quantum-inspired classical algorithms. Our results not only advance our understanding of quantum systems but also pave the way for the realization and discovery of novel physics extending to quantum information processing, materials science, and beyond.