Disentangling the Physics of the Attractive Hubbard Model via the Accessible and Symmetry-Resolved Entanglement Entropies
arXiv:2312.11746 · doi:10.1103/PhysRevB.109.195119
Abstract
The complicated ways in which electrons interact in many-body systems such as molecules and materials have long been viewed through the lens of local electron correlation and associated correlation functions. However, quantum information science has demonstrated that more global diagnostics of quantum states, like the entanglement entropy, can provide a complementary and clarifying lens on electronic behavior. One particularly useful measure that can be used to distinguish between quantum and classical sources of entanglement is the accessible entanglement, the entanglement available as a quantum resource for systems subject to conservation laws, such as fixed particle number, due to superselection rules. In this work, we introduce an algorithm and demonstrate how to compute accessible and symmetry-resolved entanglements for interacting fermion systems. This is accomplished by combining an incremental version of the swap algorithm with a recursive Auxiliary Field Quantum Monte Carlo algorithm recently developed by the authors. We apply these tools to study the pairing and charge density waves exhibited in the paradigmatic attractive Hubbard model via entanglement. We find that the particle and spin symmetry-resolved entanglements and their related full probability distribution functions show very clear - and unique - signatures of the underlying electronic behavior even when those features are less pronounced in more conventional correlation functions. Overall, this work provides a systematic means of characterizing the entanglement within quantum systems that can grant a deeper understanding of the complicated electronic behavior that underlies quantum phase transitions and crossovers in many-body systems.
arXiv comment19 pages, 9 figures
References in corpus (75)
- Quantum entanglement
- Entanglement Entropy and Quantum Field Theory
- Entanglement in quantum critical phenomena
- Topological entanglement entropy
- Detecting topological order in a ground state wave function
- Scaling of Entanglement close to a Quantum Phase Transitions
- Resonant Inelastic X-ray Scattering Studies of Elementary Excitations
- Measuring entanglement entropy through the interference of quantum many-body twins
- Reference frames, superselection rules, and quantum information
- Quantum entanglement in condensed matter systems
- Probing entanglement entropy via randomized measurements
- Probing entanglement in a many-body-localized system
- Measuring Renyi Entanglement Entropy with Quantum Monte Carlo
- A Constrained Path Monte Carlo Method for Fermion Ground States
- The entanglement of indistinguishable particles shared between two parties
- Quantum Monte Carlo method using phase-free random walks with Slater determinants
- Automated Selection of Active Orbital Spaces
- Symmetry-resolved entanglement in many-body systems
- Measuring orbital interaction using quantum information theory
- Fidelity susceptibility, scaling, and universality in quantum critical phenomena
- Choreographed entangle dances: topological states of quantum matter
- Entanglement Measures for Single- and Multi-Reference Correlation Effects
- Ab initio computations of molecular systems by the auxiliary-field quantum Monte Carlo method
- Superselection rules and quantum protocols
- Orbital entanglement in bond-formation processes
- Quasiparticle dynamics of symmetry resolved entanglement after a quench: the examples of conformal field theories and free fermions
- Quantum Monte Carlo calculation of entanglement Renyi entropies for generic quantum systems
- Entanglement as Measure of Electron-Electron Correlation in Quantum Chemistry Calculations
- Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
- Quantum Entanglement of Interacting Fermions in Monte Carlo
- Orbital entanglement in quantum chemistry
- Measurement Protocol for the Entanglement Spectrum of Cold Atoms
- Rényi generalization of the operational entanglement entropy
- Entanglement in indistinguishable particle systems
- Entanglement constrained by superselection rules
- Entanglement equipartition in critical random spin chains
- Entanglement of indistinguishable particles in condensed matter physics
- Nonlocal resources in the presence of Superselection Rules
- Operationally accessible entanglement of one dimensional spinless fermions
- Particle Number Fluctuations, Rényi and Symmetry-resolved Entanglement Entropy in Two-dimensional Fermi Gas from Multi-dimensional Bosonization
- Universal Signatures of Fractionalized Quantum Critical Points
- Symmetry decomposition of negativity of massless free fermions
- Fidelity susceptibility made simple: A unified quantum Monte Carlo approach
- Quantum Simulation of the Hubbard Model: The Attractive Route
- Symmetry resolved entanglement in integrable field theories via form factor bootstrap
- Symmetry resolved entanglement in two-dimensional systems via dimensional reduction
- Measuring Fermionic Entanglement: Entropy, Negativity, and Spin Structure
- Finite-size corrections in critical symmetry-resolved entanglement
- Renyi Entropy of the Interacting Fermi Liquid
- Boundary effects on symmetry resolved entanglement
- Entanglement entropy from nonequilibrium work
- Stable Quantum Monte Carlo Simulations for Entanglement Spectra of Interacting Fermions
- Quantifying Complexity in Quantum Phase Transitions via Mutual Information Complex Networks
- Bounds on the entanglement entropy by the number entropy in non-interacting fermionic systems
- Entanglement entropy and mutual information across the Mott transition in the two-dimensional Hubbard model
- Renyi Entropies of Interacting Fermions from Determinantal Quantum Monte Carlo Simulations
- Symmetry-resolved entanglement in critical non-Hermitian systems
- 1/4 is the new 1/2 when topology is intertwined with Mottness
- Finite Temperature Auxiliary Field Quantum Monte Carlo in the Canonical Ensemble
- Entanglement resolution of free Dirac fermions on a torus
- Universal features of entanglement entropy in the honeycomb Hubbard model
- Theory of Non-Interacting Fermions and Bosons in the Canonical Ensemble
- A hybrid Monte Carlo approach to the entanglement entropy of interacting fermions
- Stable computation of entanglement entropy for 2D interacting fermion systems
- Quantum Monte Carlo measurement of the chemical potential of helium-4
- Numerical stabilization of entanglement computation in auxiliary field quantum Monte Carlo simulations of interacting many-fermion systems
- Direct calculation of the Entanglement Spectrum in Quantum Monte Carlo with application to \textit{ab initio} Hamiltonians
- How much entanglement can be created in a closed system?
- Quasilocal entanglement across the Mott-Hubbard transition
- Entangling qubit registers via many-body states of ultracold atoms
- Inaccessible entanglement in symmetry protected topological phases
- Fractionalized Excitations Revealed by Entanglement Entropy
- A Stable, Recursive Auxiliary Field Quantum Monte Carlo Algorithm in the Canonical Ensemble: Applications to Thermometry and the Hubbard Model
- Symmetry-Resolved Entanglement: General considerations, calculation from correlation functions, and bounds for symmetry-protected topological phases
- A Path Integral Ground State Monte Carlo Algorithm for Entanglement of Lattice Bosons