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Physical review. B./Physical review. B

Observing quasiparticles through the entanglement lens

Yizhi You, Elisabeth Wybo, Frank Pollmann, Shivaji L. Sondhi

Published Oct 10, 2022• 10 citations
Publisher

Abstract

The quantum entanglement of a wave function generates the information entropy carried by each qubit of the many-body system and correspondingly creates unique quantum matter. In this work, the authors attempt to visualize distinct quasiparticles and collective motions from an entanglement perspective. Remarkably, many salient features of the quasiparticles, including their quantum numbers, locality, and fractionalization, are reflected in the entanglement spectrum and in the mutual information.

DOI
10.1103/physrevb.106.l161104

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The quantum entanglement of a wave function generates the information entropy carried by each qubit of the many-body system and correspondingly creates unique quantum matter. In this work, the authors attempt to visualize distinct quasiparticles and collective motions from an entanglement perspective. Remarkably, many salient features of the quasiparticles, including their quantum numbers, locality, and fractionalization, are reflected in the entanglement spectrum and in the mutual information.
The low energy physics of interacting quantum systems is typically understood through the identification of the relevant quasiparticles or low energy excitations and their quantum numbers. We present a quantum information framework that goes beyond this to examine the nature of the entanglement in the corresponding quantum states. We argue that the salient features of the quasiparticles, including their quantum numbers, locality and fractionalization are reflected in the entanglement spectrum and in the mutual information. We illustrate these ideas in the specific context of the d=1d=1d=1 transverse field Ising model with an integrability breaking perturbation.
The statistical physics of well isolated nonequilibrium quantum systems has been drawing intense interest recently, providing new paradigms for understanding equilibration and ergodicity (and failure thereof). Tools from the field of quantum information, such as quantum entanglement, have been instrumental in this development. Past investigations of the entanglement structure in localized and thermalizing phases have focused on diagnostics, such as entanglement entropy, which provide a useful but only partial characterization of the pattern of entanglement. In this work, inspired by random matrix theory, the authors examine localization and thermalization through the lens of the entanglement spectrum. This approach provides a complete characterization of the pattern of entanglement and yields new insights into many-body localization, thermalization, and nonequilibrium statistical mechanics.
We investigate the quantum entanglement content of quasiparticle excitations in extended many-body systems. We show that such excitations give an additive contribution to the bipartite von Neumann and Rényi entanglement entropies that takes a simple, universal form. It is largely independent of the momenta and masses of the excitations and of the geometry, dimension, and connectedness of the entanglement region. The result has a natural quantum information theoretic interpretation as the entanglement of a state where each quasiparticle is associated with two qubits representing their presence within and without the entanglement region, taking into account quantum (in)distinguishability. This applies to any excited state composed of finite numbers of quasiparticles with finite de Broglie wavelengths or finite intrinsic correlation length. This includes particle excitations in massive quantum field theory and gapped lattice systems, and certain highly excited states in conformal field theory and gapless models. We derive this result analytically in one-dimensional massive bosonic and fermionic free field theories and for simple setups in higher dimensions. We provide numerical evidence for the harmonic chain and the two-dimensional harmonic lattice in all regimes where the conditions above apply. Finally, we provide supporting calculations for integrable spin chain models and other interacting cases without particle production. Our results point to new possibilities for creating entangled states using many-body quantum systems.
In this paper, we present a quantum information framework for the entanglement behavior of the low-energy quasiparticle (QP) excitations in various quantum phases in one-dimensional (1D) systems. We first establish an exact correspondence between the correlation matrix and the QP entanglement Hamiltonian for free fermions and find an extended in-gap state in the QP entanglement Hamiltonian as a consequence of the position uncertainty of the QP. A more general understanding of such an in-gap state can be extended to a Kramers theorem for the QP entanglement Hamiltonian, which also applies to strongly interacting systems. Further, we present a set of ubiquitous entanglement spectrum features, dubbed entanglement fragmentation, conditional mutual information, and measurement-induced nonlocal entanglement for QPs in 1D symmetry protected topological phases. Our result thus provides another framework to identify different phases of matter in terms of their QP entanglement.
The quantum-mechanical description of assemblies of particles whose motion is confined to two (or one) spatial dimensions offers many possibilities that are distinct from bosons and fermions. We call such particles anyons. The simplest anyons are parameterized by an angular phase parameter θθθ. θ=0,πθ= 0, πθ=0,π correspond to bosons and fermions respectively; at intermediate values we say that we have fractional statistics. In two dimensions, θθθ describes the phase acquired by the wave function as two anyons wind around one another counterclockwise. It generates a shift in the allowed values for the relative angular momentum. Composites of localized electric charge and magnetic flux associated with an abelian U(1) gauge group realize this behavior. More complex charge-flux constructions can involve non-abelian and product groups acting on a spectrum of allowed charges and fluxes, giving rise to nonabelian and mutual statistics. Interchanges of non-abelian anyons implement unitary transformations of the wave function within an emergent space of internal states. Anyons of all kinds are described by quantum field theories that include Chern--Simons terms. The crossings of one-dimensional anyons on a ring are uni-directional, such that a fractional phase θθθ acquired upon interchange gives rise to fractional shifts in the relative momenta between the anyons. The quasiparticle excitations of fractional quantum Hall states have long been predicted to include anyons. Recently the anyon behavior predicted for quasiparticles in the ν=1/3ν= 1/3ν=1/3 fractional quantum Hall state has been observed both in scattering and in interferometric experiments. Excitations within designed systems, notably including superconducting circuits, can exhibit anyon behavior. Such systems are being developed for possible use in quantum information processing.
Information theory has its particles, bits and qubits, just as physics has electrons and photons. However, in physics we have a special category of objects with no clear counterparts in information theory: quasiparticles. They are introduced to simplify complex emergent phenomena making otherwise very difficult calculations possible and providing additional insight into the inner workings of the system. We show that we can adopt a similar approach in information theory. We introduce the hyperbits, information quasiparticles which we prove to be a resource equivalent to entanglement and classical communication, and we give examples of how they can be used to simplify calculations and get more insight into communication protocols.