An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
Symmetry-resolved entanglement in many-body systems
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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.
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Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Numerical MPS study of the Moore-Read state finds approximate equipartition of symmetry-resolved entanglement entropy and good agreement with the Li-Haldane conjecture for the entanglement spectrum despite distinct neutral and charged velocities.
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Symmetry-Resolved Entanglement Entropy from Heat Kernels
An improved heat kernel framework with phase-factor reconstruction computes symmetry-resolved entanglement entropy for charged systems and derives a cMERA flow equation that agrees with CFT and holographic calculations.
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Typical entanglement entropy with charge conservation
Typical entanglement entropy with fixed global charge is given by the local thermal entropy at fixed charge density for both U(1) and SU(2) symmetries in the thermodynamic limit.
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Entangling Power: A Probe of Symmetry and Integrability in Quantum Many-Body Systems
Entangling power in Heisenberg spin chains shows a monotonic decrease with growing symmetry in small models, sharp dips at SU(2) and free-fermion points in finite chains, and vanishes at SU(2) points but maximizes at the free-fermion point in the thermodynamic limit for the S-matrix.
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The Quantum Complexity of String Breaking in the Schwinger Model
Quantum complexity measures applied to the Schwinger model reveal nonlocal correlations along the string and show that entanglement and magic give complementary views of string formation and breaking.
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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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Symmetry Resolved Entanglement Entropy in a Non-Abelian Fractional Quantum Hall State
Numerical MPS study of the Moore-Read state finds approximate equipartition of symmetry-resolved entanglement entropy and good agreement with the Li-Haldane conjecture for the entanglement spectrum despite distinct neutral and charged velocities.