Ab-initio characterization of the quantum linear-zigzag transition using DMRG
arXiv:1311.2510 · doi:10.1103/PhysRevB.89.094103
Abstract
Ions of the same charge inside confining potentials can form crystalline structures which can be controlled by means of the ions density and of the external trap parameters. In particular, a linear chain of trapped ions exhibits a transition to a zigzag equilibrium configuration, which is controlled by the strength of the transverse confinement. Studying this phase transition in the quantum regime is a challenging problem, even when employing numerical methods to simulate microscopically quantum many-body systems. Here we present a compact analytical treatment to map the original long-range problem into a short-range quantum field theory on a lattice. We provide a complete numerical architecture, based on Density Matrix Renormalization Group, to address the effective quantum phi-four model. This technique is instrumental in giving a complete characterization of the phase diagram, as well as pinpoint the universality class of the criticality.
13 pages, 10 figures
References in corpus (19)
- Many-Body Physics with Ultracold Gases
- The density-matrix renormalization group in the age of matrix product states
- Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
- Matrix product states represent ground states faithfully
- DMRG and periodic boundary conditions: a quantum information perspective
- Tunable ion-photon entanglement in an optical cavity
- Structural phase transitions in low-dimensional ion crystals
- Quantum zigzag transition in ion chains
- Double wells, scalar fields and quantum phase transitions in ions traps
- Spontaneous nucleation of structural defects in inhomogeneous ion chains
- Transition from a one-dimensional to a quasi-one-dimensional state in interacting quantum wires
- An improved lattice measurement of the critical coupling in phi^4_2 theory
- Precise Experimental Investigation of Eigenmodes in a Planar Ion Crystal
- Density Matrix Renormalization Group for Dummies
- Dipolar bosons in a planar array of one-dimensional tubes
- Ground state of low dimensional dipolar gases: linear and zigzag chains
- Ion crystal transducer for strong coupling between single ions and single photons
- Quantum structural phase transition in chains of interacting atoms
- Ramsey interferometry with a spin embedded in a Coulomb chain
Cited by in corpus (13)
- The Tensor Networks Anthology: Simulation techniques for many-body quantum lattice systems
- Finite-density phase diagram of a (1+1)-d non-abelian lattice gauge theory with tensor networks
- Out-of-equilibrium dynamics of quantum many-body systems with long-range interactions
- Crossover from the classical to the quantum Kibble-Zurek scaling
- Hidden Frustrated Interactions and Quantum Annealing in Trapped Ion Spin-Phonon Chains
- Finite temperature spectrum at the symmetry-breaking linear-zigzag transition
- From classical to quantum criticality
- Non-equilibrium quantum thermodynamics in Coulomb crystals
- Buckling transitions and clock order of two-dimensional Coulomb crystals
- Ground-state electronic structure of quasi-one-dimensional wires in semiconductor heterostructures
- Structural transitions of nearly second order in classical dipolar gases
- Multi-mode Bose-Hubbard model for quantum dipolar gases in confined geometries
- Operator-based derivation of phonon modes and characterization of correlations for trapped ions at zero and finite temperature