Thermal masses and trapped-ion quantum spin models: a self-consistent approach to Yukawa-type interactions in the $\lambda {\varphi }^4$ model

Abstract

The quantum simulation of magnetism in trapped-ion systems makes use of the crystal vibrations to mediate pairwise interactions between spins, which are encoded in the internal electronic states of the ions, and measured in experiments that probe the real-time dynamics. These interactions can be accounted for by a long-wavelength relativistic theory, where the phonons are described by a coarse-grained Klein-Gordon field $\varphi (x)$ locally coupled to the spins that acts as a carrier, leading to an analogue of pion-mediated Yukawa interactions. In the vicinity of a structural transition of the ion crystal, one must go beyond the Klein-Gordon fields, and include additional $\lambda {\varphi }^4$ terms responsible for phonon-phonon scattering. This leads to quantum effects that can be expressed by Feynman loop integrals that modify the range of the Yukawa-type spin interactions; an effect that could be used to probe the underlying fixed point of this quantum field theory (QFT). Unfortunately, the rigidity of the trapped-ion crystal makes it challenging to observe genuine quantum effects, such as the flow of the critical point with the quartic coupling $\lambda$. We hereby show that thermal effects, which can be controlled by laser cooling, can unveil this flow through the appearance of thermal masses in interacting QFTs. We perform self-consistent calculations that resum certain Feynman diagrams and, additionally, go beyond mean-field theory to predict how measurements on the trapped-ion spin system can probe key properties of the $\lambda {\varphi }^4$ QFT.

References in corpus (95)

• Quantum Computing in the NISQ era and beyond
• Supplementary information for "Quantum supremacy using a programmable superconducting processor"
• Quantum computational advantage using photons
• Noisy intermediate-scale quantum (NISQ) algorithms
• Quantum computational chemistry
• Trapped-Ion Quantum Computing: Progress and Challenges
• An Open-System Quantum Simulator with Trapped Ions
• Suppressing quantum errors by scaling a surface code logical qubit
• Observation of a Many-Body Dynamical Phase Transition with a 53-Qubit Quantum Simulator
• Quantum algorithms: an overview
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Engineered 2D Ising interactions on a trapped-ion quantum simulator with hundreds of spins
• Many-body localization in a quantum simulator with programmable random disorder
• Effective quantum spin systems with ion traps
• Observation of entanglement propagation in a quantum many-body system
• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Real-time dynamics of lattice gauge theories with a few-qubit quantum computer
• Non-local propagation of correlations in long-range interacting quantum systems
• Entanglement and quantum computation with ions in thermal motion
• Demonstration of a small programmable quantum computer with atomic qubits
• High-fidelity two-qubit quantum logic gates using trapped calcium-43 ions
• High-fidelity quantum logic gates using trapped-ion hyperfine qubits
• The European Quantum Technologies Roadmap
• High-fidelity preparation, gates, memory and readout of a trapped-ion quantum bit
• Universal digital quantum simulation with trapped ions
• Self-Verifying Variational Quantum Simulation of the Lattice Schwinger Model
• Quantum Simulators: Architectures and Opportunities
• High-Fidelity Universal Gate Set for ${}^9$Be${}^{+}$ Ion Qubits
• Simulating Lattice Gauge Theories within Quantum Technologies
• Realization of a scalable Shor algorithm
• Emergence and Frustration of Magnetic Order with Variable-Range Interactions in a Trapped Ion Quantum Simulator
• Quantum chemistry calculations on a trapped-ion quantum simulator
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Experimental Quantum Computations on a Topologically Encoded Qubit
• Encoding a qubit in a trapped-ion mechanical oscillator
• A compact ion-trap quantum computing demonstrator
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Realization of an Error-Correcting Surface Code with Superconducting Qubits
• Quantum Simulation for High Energy Physics
• Demonstration of fault-tolerant universal quantum gate operations
• Basics of thermal field theory -- a tutorial on perturbative computations
• Complete methods set for scalable ion trap quantum information processing
• Lattice gauge theories simulations in the quantum information era
• Characterizing large-scale quantum computers via cycle benchmarking
• Complete 3-Qubit Grover Search on a Programmable Quantum Computer
• Quantum simulation of open-system dynamical maps with trapped ions
• Review on novel methods for lattice gauge theories
• Parallel Entangling Operations on a Universal Ion Trap Quantum Computer
• Standard Model Physics and the Digital Quantum Revolution: Thoughts about the Interface
• Quantum information processing with trapped ions
• Fault-tolerant quantum error detection
• Assessing the progress of trapped-ion processors towards fault-tolerant quantum computation
• Structural phase transitions in low-dimensional ion crystals
• Quantum gate teleportation between separated qubits in a trapped-ion processor
• Observation of Domain Wall Confinement and Dynamics in a Quantum Simulator
• High-fidelity trapped-ion quantum logic using near-field microwaves
• Repeated multi-qubit readout and feedback with a mixed-species trapped-ion register
• Digital Quantum Simulation of the Schwinger Model and Symmetry Protection with Trapped Ions
• Entangling logical qubits with lattice surgery
• Robust and resource-efficient microwave near-field entangling ${}^9$Be${}^{+}$ gate
• Quantum zigzag transition in ion chains
• Cold Trapped Ions as Quantum Information Processors
• Coherent Imaging Spectroscopy of a Quantum Many-Body Spin System
• Matrix product states and variational methods applied to critical quantum field theory
• Phonon-phonon interactions due to non-linear effects in a linear ion trap
• Observation of power-law scaling for phase transitions in linear trapped ion crystals
• An improved lattice measurement of the critical coupling in phi^4_2 theory
• Deterministic correction of qubit loss
• Long-range Heisenberg models in quasi-periodically driven crystals of trapped ions
• Tensor network analysis of critical coupling in two dimensional ${\varphi }^4$ theory
• High-Precision Calculations in Strongly Coupled Quantum Field Theory with Next-to-Leading-Order Renormalized Hamiltonian Truncation
• Demonstration of three- and four-body interactions between trapped-ion spins
• Quantum Simulations of Physics Problems
• Implementing Fault-tolerant Entangling Gates on the Five-qubit Code and the Color Code
• $\lambda {\varphi }^4$ Theory I: The Symmetric Phase Beyond NNNNNNNNLO
• Polarization-gradient cooling of 1D and 2D ion Coulomb crystals
• Density matrix renormalization group in a two-dimensional $\lambda {\varphi }^4$ Hamiltonian lattice model
• Controlling long ion strings for quantum simulation and precision measurements
• Hidden Frustrated Interactions and Quantum Annealing in Trapped Ion Spin-Phonon Chains
• Spin-Peierls Quantum Phase Transitions in Coulomb Crystals
• Systematic uncertainty due to background-gas collisions in trapped-ion optical clocks
• Temperature driven structural phase transition for trapped ions and its experimental detection
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Quantum sensors for the generating functional of interacting quantum field theories
• New MC determination of the critical coupling in ${\varphi }_2^4$ theory
• Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
• From classical to quantum criticality
• Ion-crystal demonstration of structural phase transition induced solely by temperature
• Investigations in 1+1 dimensional lattice ${\varphi }^4$ theory
• Optimizing Stabilizer Parities for Improved Logical Qubit Memories
• A room-temperature ion trapping apparatus with hydrogen partial pressure below $10^{-11}$ mBar
• Experiments towards quantum information with trapped Calcium ions
• Entanglement Generation and Decoherence in a Two-Qubit System Mediated by Relativistic Quantum Field
• Quantum advantage and stability to errors in analogue quantum simulators
• Long-range Ising interactions mediated by $\lambda {\varphi }^4$ fields: probing the renormalisation of sound in crystals of trapped ions