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arXiv:2009.04499 · Physical Review Letters

Emergent Fine Structure Constant of Quantum Spin Ice Is Large

Salvatore D. Pace, Siddhardh C. Morampudi, Roderich Moessner, Chris R. Laumann

Published Sep 9, 2021• 40 citations
arXivHTMLPDF

Abstract

Condensed-matter systems provide alternative "vacua" exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine structure constant α, which parametrizes how strongly matter couples to light: α_{QSI} is more than an order of magnitude greater than α_{QED}≈1/137. Furthermore, α_{QSI}, the emergent speed of light, and all other parameters of the emergent QED, are tunable by engineering the microscopic Hamiltonian. We find that α_{QSI} can be tuned all the way from zero up to what is believed to be the strongest possible coupling beyond which QED confines. In view of the small size of its constrained Hilbert space, this marks out quantum spin ice as an ideal platform for studying exotic quantum field theories and a target for quantum simulation. The large α_{QSI} implies that experiments probing candidate condensed-matter realizations of quantum spin ice should expect to observe phenomena arising due to strong interactions.

DOI
10.1103/physrevlett.127.117205

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Condensed-matter systems provide alternative "vacua" exhibiting emergent low-energy properties drastically different from those of the standard model. A case in point is the emergent quantum electrodynamics (QED) in the fractionalized topological magnet known as quantum spin ice, whose magnetic monopoles set it apart from the familiar QED of the world we live in. Here, we show that the two greatly differ in their fine structure constant α, which parametrizes how strongly matter couples to light: α_{QSI} is more than an order of magnitude greater than α_{QED}≈1/137. Furthermore, α_{QSI}, the emergent speed of light, and all other parameters of the emergent QED, are tunable by engineering the microscopic Hamiltonian. We find that α_{QSI} can be tuned all the way from zero up to what is believed to be the strongest possible coupling beyond which QED confines. In view of the small size of its constrained Hilbert space, this marks out quantum spin ice as an ideal platform for studying exotic quantum field theories and a target for quantum simulation. The large α_{QSI} implies that experiments probing candidate condensed-matter realizations of quantum spin ice should expect to observe phenomena arising due to strong interactions.
The low-energy physics of quantum spin ice is known to support an emergent form of quantum electrodynamics (QED), where magnetic monopoles exist and the fine-structure constant is material dependent. In this article, we show how this QED is modified via a coupling to dynamical matter on the centered pyrochlore lattice, a structure that has recently been synthesized using metal-organic frameworks. Specifically, we study the low-energy properties of the S = 1 / 2 quantum XXZ model on the centered pyrochlore lattice, with a focus on the sign-problem-free region. At fourth order in degenerate perturbation theory, this model hosts a quantum spin liquid distinct from the well-known U(1) quantum spin ice on the pyrochlore because of the presence of dynamical matter in the ground state. Exact diagonalization results are consistent with this quantum spin liquid over an extended region of the ground-state phase diagram, although potential quantum critical points within this region could indicate a richer phase structure. Our work thus expands the physics of quantum spin ice in an experimentally motivated geometry, showing how the emergent QED can be coupled to dynamical matter at zero temperature.
Frustrated spin-ice systems support emergent gauge fields and fractionalized quasiparticles that act as magnetic monopoles. Although artificial platforms have enabled their direct visualization, access to their quantum-coherent dynamics has remained limited. Here we realize a programmable dipolar square spin-ice model using a superconducting-qubit quantum annealer, providing access to a previously unexplored quantum-coherent regime of artificial spin ice. By implementing a direct one-to-one mapping between lattice spins and physical qubits, together with engineered extended couplings, we realize effective dipolar interactions on frustrated lattices comprising more than 400 vertices. Tuning transverse-field fluctuations enables us to probe the real-time dynamics of Dirac-string defects and interacting monopole plasmas. We observe super-diffusive monopole transport, with scaling exponents intermediate between classical diffusion and ballistic motion, indicating dynamics beyond classical stochastic relaxation and consistent with coherent propagation within an emergent gauge manifold. These results establish programmable quantum spin ice as a scalable platform for investigating fractionalized excitations and emergent gauge dynamics in engineered quantum matter.
The presence of multiple competing interactions in spin systems can lead to novel phases known as quantum spin liquids (QSLs). QSLs are disordered spin systems with long-range entanglement that realize the deconfined phase of emergent lattice gauge theories and host fractional excitations. A notable example of great experimental interest is quantum spin ice (QSI), a three-dimensional QSL that realizes an analog of quantum electrodynamics with emergent photons and interacting electric and magnetic charges. The current leading candidate materials for realizing QSI are dipolar-octupolar (DO) cerium-based pyrochlore compounds. These are believed to stabilize a U(1)U(1)U(1) QSL known as π\piπ-flux QSI, where translation symmetry acting on spinon excitations fractionalizes. In this thesis, we explore the physics of QSI, relying heavily on parton constructions, to make experimentally relevant predictions for DO materials. First, we explore the physics of symmetry fractionalization in QSI, whereby lattice symmetries are realized projectively when acting on fractional quasiparticles. Symmetry fractionalization is examined within the framework of gauge mean-field theory (GMFT), a parton construction designed explicitly for application to QSI. This study shows that the pyrochlore lattice space group strongly constrains possible symmetry fractionalization classes. It systematically explains how all space group transformations, beyond translation, fractionalize in π\piπ-flux QSI. Next, we apply this framework to DO materials and show how the equal-time structure factor predicted for π\piπ-flux QSI is consistent with recent energy-integrated inelastic neutron scattering experiments on certain candidate materials. We also predict that the dynamical spin structure factor of π\piπ-flux QSI is characterized by a broad continuum with three distinctive peaks of decreasing intensity that are approximately equally spaced. We argue that these peaks should be accessible with currently available experimental apparatus and offer a smoking-gun signature of π\piπ-flux QSI. We confirm those predictions by extending the exclusive boson representation and speculate on the thermodynamic behavior of cerium candidates. We close by commenting on recent experimental breakthroughs and possible future directions.
Quantum spin liquids are exotic phases of matter whose low-energy physics is described as the deconfined phase of an emergent gauge theory. With recent theory proposals and an experiment showing preliminary signs of Z 2 topological order [G. Semeghini , ], Rydberg atom arrays have emerged as a promising platform to realize a quantum spin liquid. In this work, we propose a way to realize a U(1) quantum spin liquid in three spatial dimensions, described by the deconfined phase of U(1) gauge theory in a pyrochlore lattice Rydberg atom array. We study the ground state phase diagram of the proposed Rydberg system as a function of experimentally relevant parameters. Within our calculation, we find that by tuning the Rabi frequency, one can access both the confinement-deconfinement transition driven by a proliferation of “magnetic” monopoles and the Higgs transition driven by a proliferation of “electric” charges of the emergent gauge theory. We suggest experimental probes for distinguishing the deconfined phase from ordered phases. This work serves as a proposal to access a confinement-deconfinement transition in three spatial dimensions on a Rydberg-based quantum simulator.
Quantum spin liquids are exotic phases of matter that are prevented from being frozen even at zero temperature, and appear disordered by local probes that monitor the subsystems. Driven by quantum fluctuations, topological spin liquids are manifested by their long-range entanglement, and are characterized by quasiparticles with fractional statistics. Here, we make contact of a 2D Rydberg ice to a QED vacuum of an ultra-high-finesse optical cavity, and dynamically promote the frustrated background field of the spin ice to a Z2\mathbb{Z}_2Z2​ spin liquid. We characterize the deconfined nature of the dynamical gauge theory residing in the strongly-correlated Rydberg matter with Wilsonian loops. We observe the proliferation of vison and spinon pairs by site-resolved fluorescence imaging, and detect the exchange statistical angle θtop∼π/2θ_{\text{top}}\simπ/2θtop​∼π/2 between the two anyons by monitoring the dynamical correlators of the fluctuating cavity photons. Our work provides the first microscopic detection of anyons in a topological quantum matter, and heralds the arrival of strongly-coupled many-body QED, where interacting matter and light are put on equal footing at the level of individual quanta.
We develop a theory of the dynamical response of a minimal model of quantum spin ice (QSI) by means of inelastic light scattering. In particular, we are interested in the Raman response of the fractionalized U(1) spin liquid realized in the XXZ QSI. We show that the low-energy Raman intensity is dominated by spinon and gauge fluctuations. We find that the Raman response in the QSI state of that model appears only in the T2g{T}_{2g}T2g​ polarization channel. We show that the Raman intensity profile displays a broad continuum from the spinons and coupled spinon and gauge fluctuations, and a low-energy peak arising entirely from gauge fluctuations. Both features originate from the exotic interaction between photon and the fractionalized excitations of QSI. Our theoretical results suggest that inelastic Raman scattering can in principle serve as a promising experimental probe of the nature of a U(1) spin liquid in QSI.