Estimating entanglement in 2D Heisenberg model in the strong rung-coupling limit

Abstract

In this paper, we calculate entanglement in the isotropic Heisenberg model in a magnetic field on a two-dimensional rectangular zig-zag lattice in the strong rung-coupling limit, using the one-dimensional XXZ model as a proxy. Focusing on the leading order in perturbation, for arbitrary size of the lattice, we show how the one-dimensional effective description emerges. We point out specific states in the low-energy sector of the two-dimensional model that are well-approximated by the one-dimensional spin-1/2 XXZ model. We propose a systematic approach for mapping matrix-elements of operators defined on the two-dimensional model to their low-energy counterparts on the one-dimensional XXZ model. We also show that partial trace-based description of entanglement in the two-dimensional model can be satisfactorily approximated using the one-dimensional XXZ model as a substitute. We further show numerically that the one-dimensional XXZ model performs well in estimating entanglement quantified using a measurement-based approach in the two-dimensional model for specific choices of measured Hermitian operators.

23 pages, 9 figures, 1 table

References in corpus (28)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• The density-matrix renormalization group in the age of matrix product states
• Entanglement detection
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• 14-qubit entanglement: creation and coherence
• A class of quantum many-body states that can be efficiently simulated
• Topological Quantum Distillation
• Benchmarking quantum control methods on a 12-qubit system
• Topological Computation without Braiding
• Entanglement renormalization and topological order
• Entanglement and Quantum Phase Transition Revisited
• Quantum state transmission via a spin ladder as a robust data bus
• Entanglement Entropy of the Two-Dimensional Heisenberg Antiferromagnet
• Witnessing entanglement in quantum magnets using neutron scattering
• Multipartite entanglement detection via structure factors
• Simulation of time evolution with the MERA
• The low-$T$ phase diagram of $\mathrm{LiH}{\mathrm{o}}_{\mathrm{x}}{\mathrm{Y}}_{1-\mathrm{x}}{\mathrm{F}}_4$
• Dynamic properties of the spin-1/2 XY chain with three-site interactions
• Quantum Entanglement in the S=1/2 Spin Ladder with Ring Exchange
• Quantum spin systems for measurement-based quantum computation
• Exact solution of a spin-1/2 $XX$ chain with three-site interactions in a random transverse field: Influence of randomness on quantum phase transition
• Spin-1/2 Heisenberg ladder: variation of entanglement and fidelity measures close to quantum critical points
• Entanglement Spectra of Heisenberg Ladders of higher Spin
• Critical Lines and Massive Phases in Quantum Spin Ladders with Dimerization
• Twisted Order Parameter applied to Dimerized Ladders
• Quantum state transfer using 1D Heisenberg Hamiltonian on quasi-1D lattices
• Phase diagram of frustrated mixed-spin ladders in the strong-coupling limit