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Glide Symmetry Breaking and Quantum Criticality in the Ising Magnet CoNb2O6
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Isolated Quantum Systems: Dynamics and Phase Structure Far From Equilibrium
Get PDFStatistical mechanics characterizes systems in or near equilibrium using in terms of a handful of "state" variables, e.g. temperature, rather than infinitely many degrees of freedom. Statistical physics describes the expansion of the early universe, aspects of black holes, and most fruitfully, phases of matter and their properties. Quantum considerations have improved this understanding over time and revealed new phenomena, especially in complicated "strongly correlated" systems. Topological phases of matter, e.g., are of both fundamental and practical interest: these phases cannot be distinguished locally, unlike ice and water, which also allows them to store and process quantum information in a "fault-tolerant" manner, recently proposed for application to quantum computation. However, above zero temperature, thermal effects can overwrite this information.Recent experiments on isolated systems have raised fundamental questions and revealed new routes to quantum computing. We now know that entanglement, generated dynamically as a quantum state evolves, "hides" local information about the past, producing familiar equilibrium states, described by a temperature. However, many systems do not thermalize: strong disorder can lead to MBL, which supports numerous phenomena forbidden in equilibrium and can protect quantum information at infinite temperature. In particular, both MBL and thermal systems are robust phases of matter, with a novel, athermal phase transition between them. This thesis begins with an overview of MBL and thermalization, followed by an overview of exactly soluble quantum systems. We then turn to an important result in the field by this author: we introduce the first nontrivial example of an integrable Floquet model and comment on its solution and salient features. We then discuss how integrable models can provide insight into quantum thermalization, e.g. in terms of entanglement growth and demonstrating that conserved charges diffuse. We then investigate thermalization away from the integrable limit, also known as "quantum chaos." We review the standard techniques in this field and, briefly, several important results, before reproducing work by this author establishing definitively the long-conjectured result that the onset of thermalization in the presence of a conserved charge is governed by diffusion of said charge. We then investigate the interplay of conventional and topological order with nonequilibrium phase structure, with applications to quantum computation in mind. We review localization-protected quantum order in several models. We then investigate two models with non-Abelian symmetry, and show that MBL in such models can only realize if the symmetry breaks spontaneously to an Abelian subgroup. Finally, we conclude by examining open quantum systems, where we find several counterintuitive results that show that baths can, in some cases, enhance localization in certain systems, which may have use in realizing quantum computation
Three studies on quantum phases of matter
Get PDFThis is a thesis in three parts regarding the study of quantum phases of matter.
In the first part, we show that the gapless boundary signatures — namely, chiral/helical hinge modes or localized zero modes — of three-dimensional higherorder topological insulators and superconductors with inversion symmetry can be gapped without symmetry breaking upon the introduction of non-Abelian surface topological order. In each case, the fractionalization pattern that appears on the surface is ‘anomalous’ in the sense that it can be made consistent with symmetry only on the surface of a three dimensional higher-order insulator/superconductor. Our results show that the interacting manifestation of higher-order topology is the appearance of ‘anomalous gapped boundaries’ between distinct topological orders whose quasiparticles are related by inversion, possibly in conjunction with other protecting symmetries such as TRS and charge conservation. This part is based on the published work: Ming-Hao Li, Titus Neupert, S. A. Parameswaran and Apoorv Tiwari, Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry, Phys. Rev. B 106, 125121.
In the second part, we extend the study of finite-entanglement scaling from onedimensional gapless models to two-dimensional systems with a Fermi surface. In particular, we show that the entanglement entropy of a contractible spatial region with linear size L scales as S ∼ Llog[ξf(L/ξ)] in the optimal tensor network, and hence area-law entangled, state approximation to a metallic state, where f(x) is a scaling function which depends on the shape of the Fermi surface and ξ is a finite correlation length induced by the restricted entanglement. Crucially, the scaling regime can be realized with numerically tractable bond dimensions. We also discuss the implications of the Lieb-Schultz-Mattis theorem at fractional filling for tensor network state approximations of metallic states. This part is based on parts of the published work: Quinten Mortier*, Ming-Hao Li*, Jutho Haegeman and Nick Bultinck, Finite-entanglement scaling of 2D metals, Phys. Rev. Lett. 131, 266202.
In the third part, we study fermionic quantum spin liquids (QSLs) on the threedimensonal trillium lattice of corner-sharing triangles. We are motivated by recent experimental and theoretical investigations that have explored various classical and quantum spin liquid states on similar networks of triangular motifs with strong geometric frutstration. Using the framework of Projective Symmetry Groups (PSG), we obtain a classification of all symmetric Z2 and U(1) QSLs on the trillium lattice. We find 2 Z2 spin-liquids, and a single U(1) spin-liquid which is proximate to one of the Z2 states. This small number of solutions reflecting the constraints imposed by the two non-symmorphic symmetries in the space group of trillium. This part is based on the unpublished work in collaboration with Dr. Sounak Biswas and Prof. S.A. Parameswaran
Topology and correlations in twisted bilayer graphene
Get PDFThis thesis studies several examples of how topology and interactions lead to novel electronic phenomena in magic-angle twisted bilayer graphene, a moire heterostructure that has attracted much attention owing its diversity of experimentally-observed correlated phases.
Part I focuses on neutral and charged excitations of the correlated insulators predicted within the strong coupling framework, which emphasizes the close connections of the central moire bands to quantum Hall ferromagnetism. In Chapter 3, we show that topological excitons can be formed from the quantized anomalous Hall insulator at filling factor , and explore the possibility of a new excitonic fractional quantum Hall hierarchy. In Chapter 4, we study the properties of the three classes of domain walls that separate topological domains in this insulator. In Chapter 5, we use microscopic Hartree-Fock numerics to analyze charged spin and pseudospin skyrmions at various integer fillings, with an emphasis on the pairing of pseudospin skyrmions and its consequences for skyrmion superconductivity.
Part II reconsiders the prevailing normal state phase diagrams of the strong coupling framework. In Chapter 6, we explore the effects of heterostrain, and demonstrate the emergence of a new electronic order, the incommensurate Kekule spiral, which possesses an unusual form of multiscale translation symmetry breaking. We argue that the phenomenology of the intermediate coupling regime is consistent with many experiments, and that strain and the incommensurate Kekule spiral are ingredients that should play important roles in any umbrella theory of twisted bilayer graphene
Quantum and classical Hilbert space fragmentation
Get PDFHilbert space fragmentation has provided fruitful grounds for the study of ergodicity violations and unusual symmetry structures in a variety of quantum systems. In this thesis, I use analytic and numerical approaches to examine these features in two contrasting Hilbert-space-fragmented models. One of these models exhibits "quantum fragmentation" (where the fragmentation can only be described in an entangled basis), the other displays "classical fragmentation" (where the fragmentation can be described in a product-state basis).
The quantum-fragmented system is an SU(M)-symmetric disordered bipartite spin model which, for M≥3, has a large non-trivial nullspace whose dimension grows exponentially with system size. This exponential growth leads to a rare example of Hilbert space fragmentation in a system with long-range interactions. I characterise the nullspace and the resulting fragmentation in detail, and show that the symmetry algebra responsible for the large degeneracy is a non-trivial subalgebra of the Read-Saleur commutant algebra. I also discuss perturbations of the model, including one that transforms certain states in the nullspace into quantum many-body scars.
The classically fragmented system is a family of quantum chains with local range-k interactions subject to the conservation of a total charge and its dipole moment. Such models exhibit a continuous "freezing" phase transition between weakly fragmented (ergodic) and strongly fragmented (non-ergodic) phases as the charge density ν is varied. I use a variety of innovative approaches to analyse these models, and show that the transition occurs at a critical charge density of ν꜀=(k-2)^(-1) independently of the onsite Hilbert space dimension. I also obtain numerous results characterising the properties of the different phases and their impact on the models' dynamical evolution. Together, the work in this thesis presents new insights into areas of fundamental importance to the exploration of Hilbert space fragmentation and ergodicity breaking
Dynamics and correlations in quantum many-body systems
Get PDFThis thesis is a collection of three exact results on correlation and response functions in integrable systems.
In the first part we study transport (two-point functions) in the 1D Hubbard model. First, we analyze the limit of large on-site repulsion and characterize spin transport as a function of temperature. Then, we consider the case where the model displays non-abelian symmetries, e.g., spin , and argue that in this case transport is anomalous with dynamical scaling exponent and follows \acrshort{kpz} scaling.
In the next two parts we focus instead on (perturbative) nonlinear response functions, which can be expressed as -point correlators with . Given the lack of a systematic understanding of the information which can be extracted from these, we compute them in integrable 1D systems. We therefore focus on two distinct scenarios. In the first scenario, we consider a finite temperature system perturbed by some inhomogeneous field coupling to local charges --- thus the perturbations can only accelerate quasiparticles, but not create/annihilate them. In this context, we develop a diagrammatic framework based on generalized hydrodynamics that allows a systematic calculation of nonlinear response functions. We show that, in the hydrodynamic limit, nonlinear response functions qualitatively distinguish between non-interacting and interacting systems. In the second scenario, we instead consider a zero temperature system whose ground state coincides with the quasiparticle vacuum. In this simpler setting we consider more general perturbations that can also create and annihilate quasiparticles. Focusing on the Ising chain as a paradigmatic model we show that the long-time limit of four-point functions (third-order response) grows linearly in time. We interpret these divergences in terms of semiclassical processes where quasiparticles propagate ballistically and scatter when their trajectories intersect
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Quantum quenches in closed and open spin chains: a thesis in two parts
Get PDFThis thesis is concerned with three studies of far from equilibrium dynamics in quantum spin chains. In all cases the nonequilibrium dynamics is generated by a protocol called a ‘quantum quench’, describing the time evolution after a sudden change in system parameters. Part A is concerned with closed systems, meaning those isolated from their environment and begins with Chapter 1, which introduces the quench protocol and motivates the study of quantum quenches through examples of its experimental relevance before providing a short survey of known theoretical results that will enable the reader to interpret the quenches in later chapters. Chapter 2 then introduces a paradigmatic spin chain — the transverse field Ising model (TFIM) — and details its solution, along with providing a worked elementary quench example, which shows that a class of local observables relax to stationary values following the quench.
The first chapter based on original research, Chapter 3, builds on this framework by considering the axial next-nearest neighbour Ising (ANNNI) model, an extension of the transverse field Ising model with an additional next-nearest neighbour Ising interaction. Whilst the TFIM is exactly solvable, the ANNNI is a generic quantum system and its behaviour far from equilibrium must be determined approximately. Quench dynamics in this system were recently used to investigate if signatures of proximate quantum critical points can be observed at early and intermediate times. Chapter 3 constructs a simple time-dependent mean-field theory that allows one to obtain a quantitatively accurate description of these quenches at short times and provides a simple framework for understanding the reported numerical results. In the process, this theory highlights fundamental limitations on detecting quantum critical points through quench dynamics. Moreover, the origin of the peculiar oscillatory behaviour seen in various observables is explained as arising from the formation of a long-lived bound state.
Chapter 4 continues the investigation into oscillations found in Chapter 3 by studying quench dynamics in systems that support kinematically protected gapped excitations at zero temperature, a class of which the ANNNI is a member. An open question in this context is whether such oscillations will ultimately decay. I will argue that strong support for the decay hypothesis can be obtained by considering spin models that can be mapped to systems of weakly interacting fermions, which in turn are amenable to an analysis by standard methods based on the Bogoliubov–Born–Green–Kirkwood–Yvon (BBGKY) hierarchy. By performing such a systematic perturbative analysis in a representative model, Chapter 4 finds a time scale beyond which the oscillations start to decay. Finally, in Part B I turn my attention to open quantum systems. Chapter 5 will contain a summary of the established physics involved with these, and in particular will introduce the Lindblad formalism applicable when such systems satisfy a Markov assumption as well as a ‘superoperator’ formalism for recasting Lindblad equations as (non-Hermitian) Schroedinger equations. Chapter 6 then calculates the full quench dynamics for a system described by a certain Lindblad equation for an initial product state. The Lindbladian in question is solved using an algebraic feature called ‘operator-space fragmentation’ which leads to exponentially many invariant subspaces. On each subspace the Lindblad dynamics projects to a model of free (non-Hermitian) fermions, which enables the solution
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