Causality and quantum criticality in long-range lattice models

Abstract

Long-range quantum lattice systems often exhibit drastically different behavior than their short-range counterparts. In particular, because they do not satisfy the conditions for the Lieb-Robinson theorem, they need not have an emergent relativistic structure in the form of a light cone. Adopting a field-theoretic approach, we study the one-dimensional transverse-field Ising model with long-range interactions, and a fermionic model with long-range hopping and pairing terms, explore their critical and near-critical behavior, and characterize their response to local perturbations. We deduce the dynamic critical exponent, up to the two-loop order within the renormalization group theory, which we then use to characterize the emergent causal behavior. We show that beyond a critical value of the power-law exponent of the long-range couplings, the dynamics effectively becomes relativistic. Various other critical exponents describing correlations in the ground state, as well as deviations from a linear causal cone, are deduced for a wide range of the power-law exponent.

20 page, 6 figures, a methods section added

References in corpus (18)

• Bose-Einstein Condensation of Erbium
• Observation of mesoscopic crystalline structures in a two-dimensional Rydberg gas
• Quantum Communication through Spin Chain Dynamics: an Introductory Overview
• Quantum degenerate dipolar Fermi gas
• Non-standard Hubbard models in optical lattices: a review
• Entanglement entropy for the long range Ising chain
• Kitaev chains with long-range pairing
• Nearly-linear light cones in long-range interacting quantum systems
• Topological phases in ultracold polar-molecule quantum magnets
• Exact quantum dynamics of bosons with finite-range time-dependent interactions of harmonic type
• Quantum correlations and entanglement in far-from-equilibrium spin systems
• Entanglement dynamics in short and long-range harmonic oscillators
• Condensate fragmentation as a sensitive measure of the quantum many-body behavior of bosons with long-range interactions
• Topological phases with long-range interactions
• Spectroscopy of interacting quasiparticles in trapped ions
• Designing spin-1 lattice models using polar molecules
• Quantum quench in long-range field theories
• Simulating the Haldane Phase in Trapped Ion Spins Using Optical Fields

Cited by in corpus (55)

• Programmable Quantum Simulations of Spin Systems with Trapped Ions
• Long-range interacting quantum systems
• Entanglement growth and correlation spreading with variable-range interactions in spin and fermionic tunnelling models
• Continuous symmetry breaking and a new universality class in 1D long-range interacting quantum systems
• Dynamical phase transitions in the collisionless pre-thermal states of isolated quantum systems: theory and experiments
• Multi-speed prethermalization in spin models with power-law decaying interactions
• Kaleidoscope of quantum phases in a long-range interacting spin-1 chain
• Entanglement area laws for long-range interacting systems
• Long-range topological insulators and weakened bulk-boundary correspondence
• Critical Phenomena and Kibble-Zurek Scaling in the Long-Range Quantum Ising Chain
• Entanglement and fluctuations in the XXZ model with power-law interactions
• Purely Long-Range Coherent Interactions in Two-Dimensional Structured Baths
• Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
• Fidelity and criticality of quantum Ising chain with long-range interactions
• Out-of-equilibrium phase diagram of long-range superconductors
• Fidelity Susceptibility Study of Quantum Long-Range Antiferromagnetic Ising Chain
• Absence of dynamical localization in interacting driven systems
• Condensed Matter Physics in Time Crystals
• Quasiparticle origin of dynamical quantum phase transitions
• Quasiparticles in quantum spin chains with long-range interactions
• Criticality of Spin Systems with Weak Long-Range Interactions
• Emergent locality in systems with power-law interactions
• Tightening the Lieb-Robinson Bound in Locally-Interacting Systems
• Dynamical criticality and domain-wall coupling in long-range Hamiltonians
• Tunable and robust long-range coherent interactions between quantum emitters mediated by Weyl bound states
• Floquet Many-body Engineering: Topological and Many-body Physics in Phase Space Lattices
• Singular dynamics and emergence of nonlocality in long-range quantum models
• Spreading of Correlations and Entanglement in the Long-Range Transverse Ising Chain
• Universality class of Ising critical states with long-range losses
• Spin transport in long-range interacting one-dimensional chain
• Scaling at quantum phase transitions above the upper critical dimension
• Algebraic Localization from Power-Law Interactions in Disordered Quantum Wires
• Correlation decay in fermionic lattice systems with power-law interactions at non-zero temperature
• Multipartite-Entanglement Tomography of a Quantum Simulator
• Quantum phase transitions in effective spin-ladder models for graphene zigzag nanoribbons
• Bound state dynamics in the long-range spin-$\frac{1}{2}$ XXZ model
• On the nature of the non-equilibrium phase transition in the non-Markovian driven Dicke model
• Quantum aging and dynamical universality in the long-range $O(N\to \infty )$ model
• Entanglement entropy of the long-range Dyson hierarchical model
• Emergent self-duality in long range critical spin chain: from deconfined criticality to first order transition
• Aging dynamics in quenched noisy long-range quantum Ising models
• Effective-Dimension Theory of Critical Phenomena above Upper Critical Dimensions
• Mimicking quantum correlation of a long-range Hamiltonian by finite-range interactions
• Exact Continuum Representation of Long-range Interacting Systems and Emerging Exotic Phases in Unconventional Superconductors
• Quantum phase diagrams of Dicke-Ising models by a wormhole algorithm
• Quasiballistic transport in long-range anisotropic Heisenberg model
• Concomitant Entanglement and Control Criticality Driven by Collective Measurements
• Long-range interactions from $U\left(1\right)$ gauge fields via dimensional mismatch
• Entanglement of weighted graphs uncovers transitions in variable-range interacting models
• Spatiotemporal Quenches in Long-Range Hamiltonians
• Slow decay rate of correlations induced by long-range extended Dzyaloshinskii-Moriya interactions
• Expediting quantum state transfer through the long-range extended XY model
• Photon-mediated interactions near a Dirac photonic crystal slab
• Berezinskii-Kosterlitz-Thouless phase transitions with long-range couplings
• Light Cones in Classical Dipole-Dipole Interacting Systems