Symmetry-resolved entanglement in many-body systems

Abstract

Similarly to the system Hamiltonian, a subsystem's reduced density matrix is composed of blocks characterized by symmetry quantum numbers (charge sectors). We present a geometric approach for extracting the contribution of individual charge sectors to the subsystem's entanglement measures within the replica trick method, via threading appropriate conjugate Aharonov-Bohm fluxes through a multi-sheet Riemann surface. Specializing to the case of 1+1D conformal field theory, we obtain general exact results for the entanglement entropies and spectrum, and apply them to a variety of systems, ranging from free and interacting fermions to spin and parafermion chains, and verify them numerically. We find that the total entanglement entropy, which scales as $\ln L$, is composed of $\sqrt{\ln L}$ contributions of individual subsystem charge sectors for interacting fermion chains, or even $\mathcal{O}(L^0)$ contributions when total spin conservation is also accounted for. We also explain how measurements of the contribution to the entanglement from separate charge sectors can be performed experimentally with existing techniques.

5+1 pages, 3 figures; v2: published version

References in corpus (12)

• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement negativity in quantum field theory
• Measuring entanglement growth in quench dynamics of bosons in an optical lattice
• Entanglement spectrum in one-dimensional systems
• Quantum Noise as an Entanglement Meter
• Rényi Entropies from Random Quenches in Atomic Hubbard and Spin Models
• Entanglement of low-energy excitations in Conformal Field Theory
• Unusual Corrections to Scaling in Entanglement Entropy
• Spin-resolved entanglement spectroscopy of critical spin chains and Luttinger liquids
• Relative Entropies in Conformal Field Theory
• Charged Renyi entropies and holographic superconductors
• Charged Rényi Entropies in CFTs with Einstein-Gauss-Bonnet Holographic Duals

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