Probing the conformal Calabrese-Cardy scaling with cold atoms

Abstract

We demonstrate that current experiments using cold bosonic atoms trapped in one-dimensional optical lattices and designed to measure the second-order Renyi entanglement entropy S_2, can be used to verify detailed predictions of conformal field theory (CFT) and estimate the central charge c. We discuss the adiabatic preparation of the ground state at half-filling where we expect a CFT with c=1. This can be accomplished with a very small hoping parameter J, in contrast to existing studies with density one where a much larger J is needed. We provide two complementary methods to estimate and subtract the classical entropy generated by the experimental preparation and imaging processes. We compare numerical calculations for the classical O(2) model with a chemical potential on a 1+1 dimensional lattice, and the quantum Bose-Hubbard Hamiltonian implemented in the experiments. S_2 is very similar for the two models and follows closely the Calabrese-Cardy scaling, (c/8)\ln(N_s), for N_s sites with open boundary conditions, provided that the large subleading corrections are taken into account.

arXiv comment5 pages, 4 figures, uses revtex, references added, intro modified, supplemental material added at the end

References in corpus (47)

• Entanglement Entropy and Quantum Field Theory
• Entanglement in quantum critical phenomena
• Measuring entanglement entropy through the interference of quantum many-body twins
• Quantum thermalization through entanglement in an isolated many-body system
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Probing the relaxation towards equilibrium in an isolated strongly correlated 1D Bose gas
• Quantum trajectories and open many-body quantum systems
• Experimental realization of a long-range antiferromagnet in the Hubbard model with ultracold atoms
• Solving the 3D Ising Model with the Conformal Bootstrap
• Universality of Entropy Scaling in 1D Gap-less Models
• Quantum Simulations of Lattice Gauge Theories using Ultracold Atoms in Optical Lattices
• Single-atom imaging of fermions in a quantum-gas microscope
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• A Quantum Gas Microscope for Fermionic Atoms
• Ultracold Quantum Gases and Lattice Systems: Quantum Simulation of Lattice Gauge Theories
• Phases of the one-dimensional Bose-Hubbard model
• Site-resolved Imaging of Fermionic Lithium-6 in an Optical Lattice
• Conformality Lost
• Observation of scale invariance and universality in two-dimensional Bose gases
• Microscopic Observation of Pauli Blocking in Degenerate Fermionic Lattice Gases
• Parity effects in the scaling of block entanglement in gapless spin chains
• Non-equilibrium dynamics of bosonic atoms in optical lattices: Decoherence of many-body states due to spontaneous emission
• Optical Abelian Lattice Gauge Theories
• Unusual Corrections to Scaling in Entanglement Entropy
• Universal parity effects in the entanglement entropy of XX chains with open boundary conditions
• Numerical study of entanglement entropy in SU(2) lattice gauge theory
• Gauge-invariant implementation of the Abelian Higgs model on optical lattices
• Spatially Resolved Detection of a Spin-Entanglement Wave in a Bose-Hubbard Chain
• Exact blocking formulas for spin and gauge models
• Multipartite entanglement detection in bosons
• Detecting Quantum Critical Points using Bipartite Fluctuations
• Universal Thermal Corrections to Single Interval Entanglement Entropy for Conformal Field Theories
• Entanglement Entropy of 3-d Conformal Gauge Theories with Many Flavors
• Sudden expansion of Mott insulators in one dimension
• Thermal vs. Entanglement Entropy: A Measurement Protocol for Fermionic Atoms with a Quantum Gas Microscope
• Finite-size corrections of the Entanglement Entropy of critical quantum chains
• Progress towards quantum simulating the classical O(2) model
• CP(N-1) Quantum Field Theories with Alkaline-Earth Atoms in Optical Lattices
• Renyi Entropy and Parity Oscillations of the Anisotropic Spin-s Heisenberg Chains in a Magnetic Field
• The fine structure of the entanglement entropy in the classical XY model
• A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
• The two-dimensional O(3) model at nonzero density: from dual lattice simulations to repulsive bosons
• Detecting two-site spin-entanglement in many-body systems with local particle-number fluctuations
• Estimating the central charge from the Rényi entanglement entropy
• Lattice studies of QCD-like theories with many fermionic degrees of freedom
• Thermalization of strongly interacting bosons after spontaneous emissions in optical lattices
• An entropy perspective on the thermal crossover in a fermionic Hubbard chain

Cited by in corpus (14)

• Simulating Lattice Gauge Theories within Quantum Technologies
• Entanglement hamiltonian and entanglement contour in inhomogeneous 1D critical systems
• Quantum simulation of the universal features of the Polyakov loop
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• A gauge-invariant, rotor Hamiltonian from dual variables of 3D U(1) gauge theory
• O(3) nonlinear sigma model in 1+1 dimensions with matrix product states
• Entanglement and relative entropies for low-lying excited states in inhomogeneous one-dimensional quantum systems
• Truncation effects in the charge representation of the O(2) model
• Critical Entanglement for the Half-Filled Extended Hubbard Model
• Rényi entanglement entropies for the compactified massless boson with open boundary conditions
• Quantum Joule Expansion of One-Dimensional Systems
• Phase diagram of Rydberg atoms in a two-leg rectangular ladder
• Quantum simulation of spin-1/2 XYZ model using solid-state spin centers
• Critical behavior of SU(3) lattice gauge theory with 12 light flavors