Topological concepts have been employed to understand a wide range of phenomena in physics. While a plethora of ground states are known to have topological underpinning, it is still quite unclear if and how topology manifests itself in the relaxation dynamics of strongly correlated many-body systems. In this Letter, we study time evolution of interacting bosons in a finite one-dimensional superlattice and uncover surprising emergent topological phenomena in the long-time stationary states. Beginning with simple product states, the system evolves into stationary states with high energy whose string correlation and entanglement are investigated. Based on extensive numerical simulations and effective-model analysis, it is demonstrated that the stationary states are nonthermal for a wide range of parameters, and they exhibit certain features that are characteristic of the symmetry-protected topological ground state of the Hamiltonian. In contrast, no topological feature is found in the stationary state as long as the system thermalizes. This difference is further corroborated by the distinct behavior of quantum entanglement and edge states of the system. Our theoretical prediction can be examined by current experimental techniques and paves the way for a more comprehensive understanding of topological phases in nonequilibrium settings.
Topological concepts have been employed to understand a wide range of phenomena in physics. While a plethora of ground states are known to have topological underpinning, it is still quite unclear if and how topology manifests itself in the relaxation dynamics of strongly correlated many-body systems. In this Letter, we study time evolution of interacting bosons in a finite one-dimensional superlattice and uncover surprising emergent topological phenomena in the long-time stationary states. Beginning with simple product states, the system evolves into stationary states with high energy whose string correlation and entanglement are investigated. Based on extensive numerical simulations and effective-model analysis, it is demonstrated that the stationary states are nonthermal for a wide range of parameters, and they exhibit certain features that are characteristic of the symmetry-protected topological ground state of the Hamiltonian. In contrast, no topological feature is found in the stationary state as long as the system thermalizes. This difference is further corroborated by the distinct behavior of quantum entanglement and edge states of the system. Our theoretical prediction can be examined by current experimental techniques and paves the way for a more comprehensive understanding of topological phases in nonequilibrium settings.
The topological features of quantum many-body wave functions are known to have profound consequences for the physics of ground-states and their low-energy excitations. We describe how topology influences the dynamics of many-body systems when driven far from equilibrium. Our results are succinctly captured by a nonequilibrium topological classification that can be used to predict universal aspects of generic isolated quantum systems as they evolve unitarily in time. By analogy to the classifications used to describe systems in equilibrium, we consider two short-ranged entangled wave functions to be topologically equivalent if they can be interconverted via finite-time unitary evolution governed by a symmetry-respecting Hamiltonian. We demonstrate that this definition captures the salient features of these systems in a broad range of nonequilibrium scenarios. As well as providing conceptual insights into the constraints imposed by topology on many-body dynamics, we discuss the practical implications of our findings. In particular, we show that the characteristic zero-frequency spectroscopic peaks associated with topologically protected edge modes will be broadened by external noise only when the system is trivial in the nonequilibrium classification.
The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges from a set of configurations enforced by another broken symmetry. This mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.
The Schrödinger equation is nearly a century old, yet we are still in the midst of uncovering the remarkable phenomena emerging in many-body quantum systems. From superconductivity to anyonic quasiparticles, nature consistently surprises with its rich self-organization. To elucidate and grasp this variety, it is paramount to understand the phases of matter that can occur in many-body ground states, as well as their emergent collective excitations. Of particular interest are topological phases of matter, characterized by exotic excitations or edge phenomena. There exist by now several universal frameworks for gapped systems, i.e., those with an energy gap above the ground state. However, in the last decade, a multitude of gapless quantum wires---effectively one-dimensional systems---have been reported to be topologically non-trivial. A framework for their understanding and classification is missing. In addition to ground state order---topological or otherwise---a more complete picture involves the properties of excitations above the ground state. Alas, little is known about excitations beyond the universal low-energy regime. In part, this is due to a lack of analytical and numerical methods able to describe excitations at finite energies, especially in strongly-interacting systems beyond one dimension. In this thesis, we address these issues: firstly, we build a general understanding of topological phases in one dimension, including both gapped and gapless cases. In particular, we unify previously studied examples into a single framework. Secondly, we develop a novel numerical method for obtaining spectral functions in two dimensions---these give direct insight into the properties of excitations and are moreover experimentally measurable. Using this numerical method, we uncover a variety of robust properties of excitations at finite energies. Part I of this thesis concerns gapped and gapless topological phases in one dimension. In Chapter 2, we first treat the case of non-interacting fermions. Therein, we review the known classification of gapped phases before extending it to the gapless case, showing that exponentially-localized Majorana zero modes can still emerge at the edge when the bulk is gapless. Interacting gapped phases are discussed in Chapter 3, with a focus on symmetry-protected topological order. These have already been classified; our contribution is to provide a non-technical review of this classification as well as showing that many paradigmatic model Hamiltonians can be related to one another. Finally, Chapter 4 introduces the notion of symmetry-enriched quantum criticality, which we propose as a framework for classifying gapless phases. The key message is that in the presence of symmetries, a universality class can divide into distinct phases, characterized by the symmetry action on the low-energy scaling operators. This includes gapless topological phases, with examples hiding in plain sight; we clarify their stability and reinterpret previously studied examples. Part II studies the excitations above the ground states of two-dimensional quantum spin models. The main object of our study is the dynamic spin structure factor; this type of spectral function is reviewed in the first part of Chapter 5. The second part of this chapter introduces a novel matrix-product-state-based algorithm to efficiently compute it, opening a new window on the dynamics of two-dimensional quantum systems. We benchmark this numerical method in Chapter 6 on the exactly-solvable Kitaev model---a paradigmatic topological model realizing a quantum spin liquid. By adding non-integrable Heisenberg perturbations, we identify the first unequivocal theoretical realization of a proximate spin liquid: the ground state becomes conventionally ordered, yet the high-energy spectral properties are structurally similar to those of the nearby Kitaev spin liquid. The latter agrees with aspects of recent inelastic neutron scattering experiments on alpha-RuCl3. In Chapter 7, we turn to one of the oldest models in many-body quantum physics: the spin-1/2 Heisenberg antiferromagnet on the square lattice. Despite its venerable history, there is still disagreement about the physical origin of high-energy spectral features which low-order spin wave theory cannot account for. We provide a simple picture for this strongly-interacting-magnon feature by connecting it to a simple Ising limit. Lastly, Chapter 8 discusses the stability of quasiparticles---collective excitations behaving like a single emergent entity, of which magnons are a prime example. These are often known to be stable at the lowest energies and are presumed to decay whenever this is seemingly allowed by energy and momentum conservation. However, we show that strong interactions can prevent this from happening. We numerically confirm this principle of avoided decay in the (slightly-detuned) Heisenberg antiferromagnet on the triangular lattice. Moreover, we can even identify its fingerprints in existing experimental data on Ba3CoSb2O9 and superfluid helium. In this thesis, we thus enlarge our understanding of quantum phases and their excitations. The identification of the key principles of gapless topological phases in one dimension calls for direct analogues in higher dimensions, waiting to be uncovered. With regard to the robust properties of the excitations identified in this thesis, we are hopeful that these can be extended into a theory of quasiparticle properties away from the universal low-energy regime.
Abstract The dual role played by symmetry in many-body physics manifests itself through two fundamental mechanisms: spontaneous symmetry breaking and topological symmetry protection. These two concepts, ubiquitous in both condensed matter and high energy physics, have been applied successfully in the last decades to unravel a plethora of complex phenomena. Their interplay, however, remains largely unexplored. Here we report how, in the presence of strong correlations, symmetry protection emerges from a set of configurations enforced by another broken symmetry. This mechanism spawns different intertwined topological phases, where topological properties coexist with long-range order. Such a singular interplay gives rise to interesting static and dynamical effects, including interaction-induced topological phase transitions constrained by symmetry breaking, as well as a self-adjusted fractional pumping. This work paves the way for further exploration of exotic topological features in strongly-correlated quantum systems.
We study the nonequilibrium dynamics of a one-dimensional topological Kondo insulator, modelled by a p-wave Anderson lattice model, following a quantum quench of the on-site interaction strength. Our goal is to examine how the quench influences the topological properties of the system, and therefore our main focus is the time evolution of the string order parameter, entanglement spectrum, and the topologically protected edge states. We point out that postquench local observables can be well captured by a thermal ensemble up to a certain interaction strength. Our results demonstrate that the topological properties after the interaction quench are preserved. Though the absolute value of the string order parameter decays in time, the analysis of the entanglement spectrum, Loschmidt echo and the edge states indicates the robustness of the topological properties in the time-evolved state. These predictions could be directly tested in state-of-the-art cold-atom experiments.
Interactions among atoms can lead to emergent phenomena, one of the most fascinating being topological order. Topological phases are important in understanding high-temperature superconductors and fault-tolerant quantum computing. Quantum spin liquids, a key example of topologically ordered phases, exhibit unique properties such as long-range entanglement in the ground state and support of anyonic excitations, making them an exciting focus in the study of strongly correlated systems. This thesis explores the detection and learning of topological phases in quantum many-body systems, including quantum spin models, cuprate superconductors and ultracold atomic platform of Rydberg atom arrays. Guided by the experiments on Kitaev materials, we begin by using spinon mean-field theory of quantum spin liquids to explain the transition from a quantized thermal Hall effect to an unquantized values. Making closer connections to experiments in cuprates, we include additional interactions with phonons present in the system. We examine how spinon-phonon interactions, characterized by symmetry analysis, give rise to a chiral phonon Hall viscosity and can also contribute to the thermal Hall effect. In the second part, we turn to Rydberg atom arrays, which have recently been shown to realize a Z2 quantum spin liquid phase—an elusive state in conventional solid-state materials. We study how Rydberg interactions and lattice geometries lead to the emergence of Z2 gauge theories and distinct classes of topological quantum spin liquids. Finally, we study a variational tensor network tomography method for learning topological states from randomized measurements on Rydberg atom arrays. We demonstrate its efficiency in characterizing complex two-dimensional states that could be realized in future experiments.