The concept of entanglement in many‑body physics has traditionally focused on spin or particle‑number degrees of freedom. Here we introduce a novel class of fermionic quantum phases in which orbital degrees of freedom of identical particles become entangled across spatially distinct sites. We construct the general form of the many‑body wavefunction for a system of N fermions occupying L orbitals per site, and show that the ground state of certain interacting Hamiltonians can be written as |\Psi> = \sum_{i,j} c_{ij} | \phi_i \phi_j >, where | \phi_i > and | \phi_j > denote single‑particle orbital states localized at different lattice sites. This entangled orbital structure leads to emergent properties distinct from conventional band insulators, Mott insulators, or spin liquids. We discuss the symmetry constraints, the role of fermionic statistics, and the topological aspects that arise when the orbital entanglement is global. Theoretical analysis predicts that FOEPs can host protected edge modes, exotic quasiparticles, and non‑Abelian statistics in two‑dimensional lattices. We also outline experimental signatures that could be observed in engineered cold‑atom systems, photonic lattices, or layered transition‑metal dichalcogenides, and argue that the discovery of FOEPs would open a new frontier in the search for quantum materials with high‑temperature superconductivity or quantum information processing capabilities.
The concept of entanglement in many‑body physics has traditionally focused on spin or particle‑number degrees of freedom. Here we introduce a novel class of fermionic quantum phases in which orbital degrees of freedom of identical particles become entangled across spatially distinct sites. We construct the general form of the many‑body wavefunction for a system of N fermions occupying L orbitals per site, and show that the ground state of certain interacting Hamiltonians can be written as |\Psi> = \sum_{i,j} c_{ij} | \phi_i \phi_j >, where | \phi_i > and | \phi_j > denote single‑particle orbital states localized at different lattice sites. This entangled orbital structure leads to emergent properties distinct from conventional band insulators, Mott insulators, or spin liquids. We discuss the symmetry constraints, the role of fermionic statistics, and the topological aspects that arise when the orbital entanglement is global. Theoretical analysis predicts that FOEPs can host protected edge modes, exotic quasiparticles, and non‑Abelian statistics in two‑dimensional lattices. We also outline experimental signatures that could be observed in engineered cold‑atom systems, photonic lattices, or layered transition‑metal dichalcogenides, and argue that the discovery of FOEPs would open a new frontier in the search for quantum materials with high‑temperature superconductivity or quantum information processing capabilities.
The concept of entanglement has long been central to quantum information science, yet most studies have focused on spin, charge, or spatial degrees of freedom. Here we introduce a new class of many‑body states, the Fermionic Orbital Entangled Phases (FOEP), in which the orbital degrees of freedom of itinerant fermions become entangled across the lattice. We construct a general formalism for describing orbital entanglement, derive the structure of the many‑body wavefunction, and discuss the symmetry constraints that allow such phases to emerge. The key feature of FOEP is the formation of a coherent superposition of orbital configurations that cannot be factorized into products of single‑particle orbitals. We propose that two‑dimensional materials with strong spin‑orbit coupling and multiple active orbitals, such as transition‑metal dichalcogenides and perovskite monolayers, provide fertile ground for realizing FOEP. We also outline experimental signatures, including anomalous orbital‑dependent transport, orbital‑selective quasiparticle interference patterns, and the emergence of new collective modes detectable by Raman or resonant inelastic X‑ray scattering. Finally, we discuss the potential impact of FOEP on quantum technologies and the prospects for discovering fundamentally new quantum matter that could attract Nobel‑level recognition.
The combination of quantum effects and interactions in quantum many-body systems can result in exotic phases with fundamentally entangled ground state wavefunctions -- topological phases. Topological phases come in two types, both of which will be studied in this thesis. In topologically ordered phases, the pattern of entanglement in the ground state wavefunction encodes the statistics of exotic emergent excitations, a universal indicator of a phase that is robust to all types of perturbations. In symmetry protected topological phases, the entanglement instead encodes a universal response of the system to symmetry defects, an indicator that is robust only to perturbations respecting the protecting symmetry.Finding and creating these phases in physical systems is a motivating challenge that tests all aspects - analytical, numerical, and experimental - of our understanding of the quantum many-body problem. Nearly three decades ago, the creation of simple ansatz wavefunctions - such as the Laughlin fractional quantum hall state, the AKLT state, and the resonating valence bond state - spurred analytical understanding of both the role of entanglement in topological physics and physical mechanisms by which it can arise. However, quantitative understanding of the relevant phase diagrams is still challenging. For this purpose, tensor networks provide a toolbox for systematically improving wavefunction ansatz while still capturing the relevant entanglement properties.In this thesis, we use the tools of entanglement and tensor networks to analyze ansatz states for several proposed new phases. In the first part, we study a featureless phase of bosons on the honeycomb lattice and argue that this phase can be topologically protected under any one of several distinct subsets of the crystalline lattice symmetries. We discuss methods of detecting such phases with entanglement and without.In the second part, we consider the problem of constructing fixed-point wavefunctions for intrinsically fermionic topological phases, i.e. topological phases contructed out of fermions with a nontrivial response to fermion parity defects. A zero correlation length wavefunction and a commuting projector Hamiltonian that realizes this wavefunction as its ground state are constructed. Using an appropriate generalization of the minimally entangled states method for extraction of topological order from the ground states on a torus to the intrinsically fermionic case, we fully characterize the corresponding topological order as Ising x (p - i p). We argue that this phase can be captured using fermionic tensor networks, expanding the applicability of tensor network methods.
In this dissertation we study the properties of quantum many-body systems whose behavior is governed by strong correlation effects between large numbers of degrees of freedom. We begin with a review of various types of condensed matter settings and a general discussion of how interactions can lead to qualitatively new properties. In Chapter 2 we discuss a class of spin models which generate nontrivial realizations of a global symmetry, both in the presence and absence of topological order. In Chapter 3, we examine a model of a non-Fermi liquid. This model is built out of electron-like degrees of freedom and has a Fermi surface, yet has no stable quasiparticle excitations. In Chapter 4 we discuss some aspects of entanglement entropy in gapless multi-component systems, and suggest a way of measuring the topological properties of Kondo lattice wavefunctions.
Mott insulators, in which strong Coulomb interactions fully localize electrons on single atomic sites, play host to an incredibly rich and exciting array of strongly correlated physics. One can naturally extend this concept to cluster Mott insulators, wherein electrons localize not on single atoms but across clusters of atoms, forming "molecules in solids". The resulting localized degrees of freedom incorporate the full spectrum of electronic degrees of freedom, spin, orbital, and charge. These serve as the building blocks for cluster Mott insulators, and understanding them is an important first step toward understanding the many-body physics that emerges in candidate cluster Mott insulators. Here, we focus on elementary building blocks, neglecting some of the complexity present in real materials which can often obfuscate the underlying principles at play. Through an extensive set of exact theoretical calculations on clusters of varying geometry, number of orbitals, and number of electrons, we uncover some of the basic organizing principles of cluster Mott phases, particularly when interactions dominate and negate a simple single-particle picture. These include, for example, the identification of an additional "cluster Hund's rule", of cluster ground states that are best understood from a purely interacting perspective, and of several localized degrees of freedom which are protected by an unusual combination of discrete spatial or orbital symmetries. Finally, we discuss the impact of adding additional terms, relevant to material candidates, on the phase diagrams presented throughout, as well as the potential next steps in the journey to building a more complete picture of cluster Mott insulators.
The conventional description of fermionic matter relies on the dichotomy between Fermi liquid and non‑Fermi liquid behaviors. In both cases the microscopic degrees of freedom are governed by the Pauli exclusion principle, and the many‑body state is constructed by filling single‑particle orbitals up to a Fermi level. Recent theoretical and experimental developments have revealed that under extreme conditions large assemblies of fermions can develop correlations that defy the standard frameworks. Here we propose a new collective fermionic statistic, termed NCFS, which emerges when the number of fermionic excitations in a large system follows a non‑Gaussian probability distribution P(N) that incorporates higher‑order correlations beyond the two‑point function. We formulate the NCFS in terms of a set of collective variables s_1, s_2, …, s_K that encode multi‑particle correlations, derive the constraints imposed by the Pauli principle and conservation laws, and analyze the resulting entropy and correlation functions. The NCFS predicts novel transport anomalies, unusual spectral line shapes, and a distinct scaling of the specific heat. Potential physical realizations include ultracold fermionic gases tuned near a Feshbach resonance, heavy‑fermion compounds, and engineered quantum dot lattices. The emergence of NCFS opens a new frontier for discovering exotic quantum states, with implications that may justify high‑profile recognition, including a Nobel Prize.
In this thesis, I explore three classes of quantum phases of matter that cannot be un-derstood purely on the basis of symmetry, and can be regarded (to varying degrees) as having highly-entangled ground-states. The first Part describes topological super-conductors with non-Abelian defects, and develops realistic routes to constructing these exotic superconductors from more elementary materials. Particular attention is payed to practical issues such as disorder. The second Part examines the role of inter-actions in electron topological insulators (TIs). Non-perturbative definitions of the familiar topological band-insulator are given, and new strongly-correlated TIs with no band-structure analogs are identified. The last Part turns exotic gapless phases without quasi-particle excitations, focusing on topics related to recently discovered quantum spin-liquid (QSL) materials. The possibility of a gapless QSL in the vicin-ity of the metal-insulator transition in doped semiconductors is explored, and optical conductivity is developed as an experimental tool to examine the nature of the QSL