Quantum Information Meets Quantum Matter -- From Quantum Entanglement to Topological Phase in Many-Body Systems

Abstract

This is the draft version of a textbook, which aims to introduce the quantum information science viewpoints on condensed matter physics to graduate students in physics (or interested researchers). We keep the writing in a self-consistent way, requiring minimum background in quantum information science. Basic knowledge in undergraduate quantum physics and condensed matter physics is assumed. We start slowly from the basic ideas in quantum information theory, but wish to eventually bring the readers to the frontiers of research in condensed matter physics, including topological phases of matter, tensor networks, and symmetry-protected topological phases.

Updated figures. Minor updates elsewhere. This draft is by no means final. More comments welcome

References in corpus (10)

• Local stabilizer codes in three dimensions without string logical operators
• Lieb-Robinson bounds and the generation of correlations and topological quantum order
• Topological Mott Insulators
• Doped Kagome System as Exotic Superconductor
• Fractional topological insulators in three dimensions
• Gapped quantum liquids and topological order, stochastic local transformations and emergence of unitarity
• Braided fusion categories, gravitational anomalies, and the mathematical framework for topological orders in any dimensions
• Mutual Chern-Simons theory for Z_2 topological order
• Classification of quantum phases and topology of logical operators in an exactly solved model of quantum codes
• Reduced Density Matrices and Topological Order in a Quantum Dimer Model

Cited by in corpus (75)

• Quantum enhanced measurements without entanglement
• One-Dimensional Symmetry Protected Topological Phases and their Transitions
• Quantum Simulating Nature's Fundamental Fields
• A Separability-Entanglement Classifier via Machine Learning
• Thirty Years of Composite Fermions and Beyond
• Wavefunctionology: The Special Structure of Certain Fractional Quantum Hall Wavefunctions
• Floquet topological phases with symmetry in all dimensions
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Characterization of topological states via dual multipartite entanglement
• Multipartite Entanglement at Finite Temperature
• Spin Currents and Magnon Dynamics in Insulating Magnets
• Simulating the dynamics of braiding of Majorana zero modes using an IBM quantum computer
• Lieb-Schultz-Mattis type theorems for quantum spin chains without continuous symmetry
• General Lieb-Schultz-Mattis type theorems for quantum spin chains
• Breakdown of topological Thouless pumping in the strongly interacting regime
• Symmetry-protected topological phases with uniform computational power in one dimension
• Dynamical phase transitions in sampling complexity
• Non-Abelian SU(N-1)-singlet fractional quantum Hall states from coupled wires
• The Uhlmann connection in fermionic systems undergoing phase transitions
• Multipartitioning topological phases by vertex states and quantum entanglement
• Correlation Length versus Gap in Frustration-Free Systems
• Topological phase transition and ${\mathbb{Z}}_2$ index for $S=1$ quantum spin chains
• Negativity Spectra in Random Tensor Networks and Holography
• Charged Topological Entanglement Entropy
• Measurement-based quantum computation in finite one-dimensional systems: string order implies computational power
• Entropy of a subalgebra of observables and the geometric entanglement entropy
• Bifurcating subsystem symmetric entanglement renormalization in two dimensions
• Visualizing Quasiparticles from Quantum Entanglement for general 1D phases
• Scaling of geometric phase versus band structure in cluster-Ising models
• Brane parity orders in the insulating state of Hubbard ladders
• Cornering gapless quantum states via their torus entanglement
• Complexity and Floquet dynamics: non-equilibrium Ising phase transitions
• Entanglement properties of the critical quench of O(N) bosons
• Determining system Hamiltonian from eigenstate measurements without correlation functions
• Lieb-Schultz-Mattis theorem with a local twist for general one-dimensional quantum systems
• Gamma Spaces and Information
• Boltzmann-Gibbs states in topological quantum walks and associated many-body systems: Fidelity and Uhlmann parallel transport analysis of Phase Transitions
• Multipartite entanglement of the topologically ordered state in a perturbed toric code
• Entanglement and interaction in a topological quantum walk
• Inaccessible entanglement in symmetry protected topological phases
• Entanglement entropy, dualities, and deconfinement in gauge theories
• Detecting Consistency of Overlapping Quantum Marginals by Separability
• Quantum effects and magnetism in the spatially distributed DNA molecules
• The structure of fixed-point tensor network states characterizes patterns of long-range entanglement
• "Haldane" phases with ultracold fermionic atoms in double-well optical lattices
• Entanglement properties of Floquet Chern insulators
• Quantum ground state isoperimetric inequalities for the energy spectrum of local Hamiltonians
• A unified diagrammatic approach to topological fixed point models
• The entanglement spectrum and Rényi entropies of non-relativistic conformal fermions
• Structure of the Entanglement Entropy of (3+1)D Gapped Phases of Matter
• Universal quantum computation with symmetric qubit clusters coupled to an environment
• From Rényi Entropy Power to Information Scan of Quantum States
• Topological states in strongly correlated systems
• Entanglement in topological systems
• Properties of the simplest inhomogeneous and homogeneous Tree-Tensor-States for Long-Ranged Quantum Spin Chains with or without disorder
• Entanglement entropy for the valence bond solid phases of two-dimensional dimerized Heisenberg antiferromagnets
• Hagedorn transition and topological entanglement entropy
• Non-Markovian quantum dynamics: Extended correlated projection superoperators
• Charge-conserving unitaries typically generate optimal covariant quantum error-correcting codes
• Multipartite States under Elementary Local Operations
• Engineering of Anyons on M5-Probes via Flux Quantization
• Quantum Adiabatic Evolution for Global Optimization in Big Data
• The ${\mathbb{Z}}_2$ toric-code and the double-semion topological order of hardcore Bose-Hubbard-type models in the strong-interaction limit
• Quantum circuit complexity and unsupervised machine learning of topological order
• Approximate recovery with locality and symmetry constraints
• On the simplest scale invariant Tree-Tensor-States preserving the quantum symmetries of the antiferromagnetic XXZ chain
• Local density matrices of many-body states in the constant weight subspaces
• Anomalous gapped boundaries between surface topological orders in higher-order topological insulators and superconductors with inversion symmetry
• Les Houches Lecture Notes on Tensor Networks
• Model Checking Applied to Quantum Physics
• Interference Effect of Beam Splitter Current in Iron-Pnictide Superconductors
• Explicit properties of the simplest inhomogeneous Matrix-Product-State including the Riemann metric of the MPS manifold
• Quantum entanglement in the t-J chain: From charge-spin separation to recombination
• Braiding properties of worldline configurations in hardcore lattice bosons
• Parafermionic representation of Potts-based cluster chain