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arXiv:1902.02749 · Physical Review Letters

Fractionalized Excitations Revealed by Entanglement Entropy

Wen-Jun Hu, Yi Zhang, Andriy H. Nevidomskyy, Elbio R. Dagotto, Qimiao Si A, Hsin-Hua Lai

Published Jun 12, 2020• 9 citations
arXivHTMLPDF

Abstract

Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.

DOI
10.1103/physrevlett.124.237201

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Fractionalized excitations develop in many unusual many-body states such as quantum spin liquids, disordered phases that cannot be described using any local order parameter. Because these exotic excitations correspond to emergent degrees of freedom, how to probe them and establish their existence is a long-standing challenge. We present a general procedure to reveal the fractionalized excitations using real-space entanglement entropy in critical spin liquids that are particularly relevant to experiments. Moreover, we show how to use the entanglement entropy to construct the corresponding spinon Fermi surface. Our work defines a new pathway to establish and characterize exotic excitations in novel quantum phases of matter.
Quantum spin liquids (QSLs) are exotic phases of matter that host fractionalized excitations. It is difficult for local probes to characterize QSL, whereas quantum entanglement can serve as a powerful diagnostic tool due to its nonlocality. The kagome antiferromagnetic Heisenberg model is one of the most studied and experimentally relevant models for QSL, but its solution remains under debate. Here, we perform a numerical Aharonov-Bohm experiment on this model and uncover universal features of the entanglement entropy. By means of the density matrix renormalization group, we reveal the entanglement signatures of emergent Dirac spinons, which are the fractionalized excitations of the QSL. This scheme provides qualitative insights into the nature of kagome QSL and can be used to study other quantum states of matter. As a concrete example, we also benchmark our methods on an interacting quantum critical point between a Dirac semimetal and a charge-ordered phase.
Quantum spin liquids are phases of matter whose internal structure is not captured by a local order parameter. Particularly intriguing are critical spin liquids, where strongly interacting excitations control low energy properties. Here we calculate their bipartite entanglement entropy that characterizes their quantum structure. In particular we calculate the Renyi entropy S(2) on model wave functions obtained by Gutzwiller projection of a Fermi sea. Although the wave functions are not sign positive, S(2) can be calculated on relatively large systems (>324 spins) using the variational Monte Carlo technique. On the triangular lattice we find that entanglement entropy of the projected Fermi sea state violates the boundary law, with S(2) enhanced by a logarithmic factor. This is an unusual result for a bosonic wave function reflecting the presence of emergent fermions. These techniques can be extended to study a wide class of other phases.
Motivated by the recent proposal that several candidate materials such as YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​ could be spinon Fermi surface spin liquids, we explore the experimental consequences of the external magnetic fields on this exotic state. Specifically, we focus on the weak field regime where the spin-liquid state is well preserved and the spinon remains to be a good description of the magnetic excitations. From the spin-1/2 nature of the spinon excitation, we predict the unique features of the spinon continuum when the weak magnetic field is applied to the system. Due to the small energy scale of the exchange interactions between the local moments in the spin-liquid candidate like YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, our proposal for the spectral weight shifts and spectral crossing in the magnetic fields can be immediately tested by inelastic neutron scattering experiments. Several other experimental aspects about the spinon Fermi surface and the spinon excitations are discussed and proposed. Our work provides an experimental scheme to examine the fractionalized spinon excitation and the candidate spin-liquid states in YbMgGaO4{\mathrm{YbMgGaO}}_{4}YbMgGaO4​, the 6H-B phase of Ba3NiSb2O9{\mathrm{Ba}}_{3}{\mathrm{NiSb}}_{2}{\mathrm{O}}_{9}Ba3​NiSb2​O9​, and other relevant materials.
The Landau Fermi liquid theory and the Ginzburg-Landau phase transition theory stand as two pivotal cornerstones in traditional condensed matter physics, achieving significant success in addressing crucial physical phenomena such as BCS superconductors and liquid helium superfluids. However, marked by the discoveries of the quantum Hall effect and high-temperature superconductivity in the 1980s, it gradually became evident that for a broad class of novel quantum states, such as fractional quantum Hall states and quantum spin liquids, their properties transcend the Landau Fermi liquid theory and Ginzburg-Landau phase transition theory. Topological order and its related concepts of long-range many-body quantum entanglement and fractionalized excitation have become the key concepts to understand these exotic quantum states. Designing and identifying topologically ordered states of matter in quantum materials and quantum simulation systems, and probing and manipulating their fractionalized excitations, are important research directions in modern condensed matter physics. In recent years, great progress has been made in the quantum simulation and manipulation of topological order on highly controllable quantum simulation platforms, such as Rydberg atomic systems, superconducting quantum processors, and two-dimensional moiré superlattices. This article provides a brief overview of recent research advances and challenges in the study of topological order in traditional condensed matter systems and quantum simulation experimental platforms. It also provides prospects for the future developments of this field.
Emergence in systems of many electrons can lead to macroscopic demonstrations of quantum mechanics which are intrinsically many-body. A primary focus of this dissertation is the phenomena of fractionalization, where the effective quasiparticles which emerge at long distances exhibit fractional quantum numbers of the microscopic degrees of freedom. The interplay between these emergent degrees of freedom and the microscopic symmetries can lead to a number of exotic properties including competing orders and unconventional phase transitions. I explore this phenomena in a number of platforms. This includes quantum antiferromagnets which can give rise to \textit{quantum spin liquids}, where we predict critical properties of phase transitions between spin liquids and conventionally-ordered phases - due to the fractionalized excitations, such critical theories deviate from traditional Landau-Ginzburg predictions. I also study the interplay between fractionalized spin and charge excitations, as well as fractionalization in non-equilibrium contexts. The second goal of this dissertation is to investigate the properties of disordered, strongly interacting, zero dimensional systems which exemplify many notable properties of higher-dimensional systems, such as doping-induced quantum criticality and non-Fermi liquid transport. The effects of disorder play an essential role in these models, leading to phenomena such as spin glass phases and conductance fluctuations which we investigate through both numerical and analytical methods.
Quantum spin liquids are highly entangled ground states of insulating spin systems, in which magnetic ordering is prevented down to the lowest temperatures due to quantum fluctuations. One of the most extraordinary characteristics of quantum spin liquid phases is their ability to support fractionalized, low-energy quasiparticles known as spinons, which carry spin-1/2 but bear no charge. Relaxometry based on color centers in crystalline materials—of which nitrogen-vacancy (NV) centers in diamond are a well-explored example—provides an exciting new platform to probe the spin spectral functions of magnetic materials with both energy and momentum resolution and to search for signatures of these elusive, fractionalized excitations. In this work, we theoretically investigate the color-center relaxometry of two archetypal quantum spin liquids: the two-dimensional U(1) quantum spin liquid with a spinon Fermi surface and the spin-1/2 antiferromagnetic spin chain. The former is characterized by a metallic, spin-split ground state of mobile, interacting spinons, which closely resembles a spin-polarized Fermi liquid ground state but with neutral quasiparticles. We show that the observation of the Stoner continuum and the collective spin wave mode in the spin spectral function would provide a strong evidence for the existence of spinons and fractionalization. In one dimension, mobile spinons form a Luttinger liquid ground state. We show that the spin spectral function exhibits strong features representing the collective density and spin-wave modes, which are broadened in an algebraic fashion with an exponent characterized by the Luttinger parameter. The possibilities of measuring these collective modes and detecting the power-law decay of the spectral weight using NV relaxometry are discussed. We also examine how the transition rates are modified by marginally irrelevant operators in the Heisenberg limit. Published by the American Physical Society 2024