Exploring entanglement in finite-size quantum systems with degenerate ground state
arXiv:2410.00515 · doi:10.1103/PhysRevB.111.054443
Abstract
We develop an approach for characterizing non-local quantum correlations in spin systems with exactly or nearly degenerate ground states. Starting with linearly independent degenerate eigenfunctions calculated with exact diagonalization we generate a finite set of their random linear combinations with Haar measure, which guarantees that these combinations are uniformly distributed in the space spanned by the initial eigenstates. Estimating the von Neumann entropy of the random wave functions helps to reveal previously unknown features of the quantum correlations in the phases with degeneracy of the ground state. For instance, spin spiral phase of the quantum magnet with Dzyaloshinskii-Moriya interaction is characterized by the enhancement of the entanglement entropy, which can be qualitatively explained by the changes in behaviour of two- and three-spin correlation functions. To establish the connection between our theoretical findings and real experiments we elaborate on the problem of estimating observables on the basis of the single-shot measurements of numerous degenerate eigenstates. By the example of solving a simple Ising model it is shown that digital quantum simulations performed with quantum computers can provide accurate description of the entanglement of the degenerate systems even in the presence of noise. We also discuss the ground state properties of degenerate fermionic and bosonic models, which can be useful for theoretical analysis of the experiments with ultracold atoms.
References in corpus (42)
- Many-Body Physics with Ultracold Gases
- Decoherence, einselection, and the quantum origins of the classical
- Entanglement Entropy and Quantum Field Theory
- Hardware-efficient Variational Quantum Eigensolver for Small Molecules and Quantum Magnets
- Probing many-body dynamics on a 51-atom quantum simulator
- Solving the Quantum Many-Body Problem with Artificial Neural Networks
- Predicting Many Properties of a Quantum System from Very Few Measurements
- Programmable Quantum Simulations of Spin Systems with Trapped Ions
- Programmable quantum simulation of 2D antiferromagnets with hundreds of Rydberg atoms
- Quantum Darwinism
- Induced measures in the space of mixed quantum states
- Observation of Time-Crystalline Eigenstate Order on a Quantum Processor
- Dynamical crystallization in a low-dimensional Rydberg gas
- Efficient variational simulation of non-trivial quantum states
- Neural Quantum States of frustrated magnets: generalization and sign structure
- Ground-State Energy and Spin Gap of Spin-1/2 Kagome Heisenberg Antiferromagnetic Clusters: Large Scale Exact Diagonalization Results
- Diagonalization- and Numerical Renormalization-Group-Based Methods for Interacting Quantum Systems
- Many-body physics in the NISQ era: quantum programming a discrete time crystal
- Stable Quantum-Correlated Many Body States through Engineered Dissipation
- Logarithmic divergence of the block entanglement entropy for the ferromagnetic Heisenberg model
- Entanglement entropy of highly degenerate states and fractal dimensions
- Optimizing quantum phase estimation for the simulation of Hamiltonian eigenstates
- Sublattice Coding Algorithm and Distributed Memory Parallelization for Large-Scale Exact Diagonalizations of Quantum Many-Body Systems
- Probing the topology of the quantum analog of a classical skyrmion
- Permutation operators, entanglement entropy, and the XXZ spin chain in the limit Δ-> -1
- Witnessing Entanglement and Quantum Correlations in Condensed Matter: A Review
- Quantifying genuine multipartite correlations and their pattern complexity
- Entangling power of permutation invariant quantum states
- Quantum Skyrmion Lattices in Heisenberg Ferromagnets
- Chiral entanglement in triangular lattice models
- lattice-symmetries: A package for working with quantum many-body bases
- Certification of quantum states with hidden structure of their bitstrings
- Estimating Patterns of Classical and Quantum Skyrmion States
- Reconstruction of classical skyrmions from Anderson towers: quantum Darwinism in action
- Entanglement in permutation symmetric states, fractal dimensions, and geometric quantum mechanics
- Tutorial: Extracting entanglement signatures from neutron spectroscopy
- Ground State Properties of Quantum Skyrmions described by Neural Network Quantum States
- Many-body quantum sign structures as non-glassy Ising models
- Benchmarking a boson sampler with Hamming nets
- Neural network agent playing spin Hamiltonian games on a quantum computer
- Quantifying spatio-temporal patterns in classical and quantum systems out of equilibrium
- Achieving the volume-law entropy regime with random-sign Dicke states