Constructs explicit physical local operators whose expectation values match twist field actions in MPS, exact in the injectivity limit and at the center of orthogonality, with numerical tests in the transverse-field Ising model.
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Topological entanglement entropy
Canonical reference. 86% of citing Pith papers cite this work as background.
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86% of classified citations
abstract
We formulate a universal characterization of the many-particle quantum entanglement in the ground state of a topologically ordered two-dimensional medium with a mass gap. We consider a disk in the plane, with a smooth boundary of length L, large compared to the correlation length. In the ground state, by tracing out all degrees of freedom in the exterior of the disk, we obtain a marginal density operator \rho for the degrees of freedom in the interior. The von Neumann entropy S(\rho) of this density operator, a measure of the entanglement of the interior and exterior variables, has the form S(\rho)= \alpha L -\gamma + ..., where the ellipsis represents terms that vanish in the limit L\to\infty. The coefficient \alpha, arising from short wavelength modes localized near the boundary, is nonuniversal and ultraviolet divergent, but -\gamma is a universal additive constant characterizing a global feature of the entanglement in the ground state. Using topological quantum field theory methods, we derive a formula for \gamma in terms of properties of the superselection sectors of the medium.
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representative citing papers
Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
Entanglement entropy in a holographic QCD model with a magnetic field develops a swallow-tail and becomes multivalued at large chemical potential, mirroring the model's own thermodynamic phase transitions.
For dual massive RG flows, the gapped-phase module is spanned by smeared Ishibashi states and cannot be reduced to the boundary-critical Cardy-state module, even in the simplest tricritical-Ising to Ising flow.
Quantum many-body scars in the PXP model display extensive ergotropy that scales with system size and can be charged via coherent rotation resets, enabling their use for quantum many-body batteries.
Disk path integrals of timelike Liouville theory yield one-loop Hartle-Hawking-like wavefunctions in a fixed extrinsic-curvature representation, with a conjectured all-loop form and a K-independent pairing that may define a cosmological inner product.
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
Pseudo entropy distinguishes topological from trivial phases in the SSH model via sign of averaged excess entropy ΔS12 and tracks quench critical times with its imaginary part.
The vecro hypothesis introduces a lattice model of the gravitational vacuum whose extended correlations nucleate fuzzballs that destroy semiclassical spacetime near trapped surfaces.
Coupling a colored particle to 2D Yang-Mills on a cylinder reduces the dynamics, for SU(N), to the singular Calogero-Sutherland model.
Edge partition functions for totally symmetric tensors in dS_{d+1} are decomposed under so(d), with the linearized gravity case receiving contributions from shift-symmetric fields on S^{d-1} suggesting an embedded brane interpretation.
The talk summarizes the quantum simulation program for lattice gauge theories, covering target problems in dense matter, algorithmic strategies, recent progress, and remaining challenges.
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.
citing papers explorer
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Mapping twist fields to local operators via tensor networks
Constructs explicit physical local operators whose expectation values match twist field actions in MPS, exact in the injectivity limit and at the center of orthogonality, with numerical tests in the transverse-field Ising model.
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dS$^4$ Metamorphosis
Higher spin gravity path integral on S^4 glues to an Sp(N) or superconformal S^3 boundary theory, giving leading contribution 2^N with one-loop cancellations.
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de Sitter Vacua & pUniverses
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
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Holographic entanglement entropy under external magnetic field from the EMD model
Entanglement entropy in a holographic QCD model with a magnetic field develops a swallow-tail and becomes multivalued at large chemical potential, mirroring the model's own thermodynamic phase transitions.
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Characterizing gapped phases by smeared boundary conformal field theories: Duality in unusual ordering with spontaneously broken generalized symmetries
For dual massive RG flows, the gapped-phase module is spanned by smeared Ishibashi states and cannot be reduced to the boundary-critical Cardy-state module, even in the simplest tricritical-Ising to Ising flow.
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Ergotropy of quantum many-body scars
Quantum many-body scars in the PXP model display extensive ergotropy that scales with system size and can be charged via coherent rotation resets, enabling their use for quantum many-body batteries.
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Quantum Liouville Cosmology
Disk path integrals of timelike Liouville theory yield one-loop Hartle-Hawking-like wavefunctions in a fixed extrinsic-curvature representation, with a conjectured all-loop form and a K-independent pairing that may define a cosmological inner product.
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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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Genuine multientropy, dihedral invariants and Lifshitz theory
Authors derive genuine multientropy for Lifshitz states as mutual information plus negativity, obtain its non-integer Rényi continuation, and prove dihedral invariants equal Rényi reflected entropies for general tripartite pure states.
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Conditional Independence of 1D Gibbs States with Applications to Efficient Learning
1D translation-invariant Gibbs states at positive temperature exhibit superexponential decay of Belavkin-Staszewski conditional mutual information, enabling efficient learning from local measurements and tensor network approximations.
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Separability and entanglement of resonating valence-bond states
Proves exact separability for disconnected subsystems in dimer RK states and exponentially suppressed entanglement for RVB states on arbitrary lattices, with negativity expressed via partition functions.
-
Pseudo entropy and topological phases of matter
Pseudo entropy distinguishes topological from trivial phases in the SSH model via sign of averaged excess entropy ΔS12 and tracks quench critical times with its imaginary part.
-
The magic of the gravitational vacuum
The vecro hypothesis introduces a lattice model of the gravitational vacuum whose extended correlations nucleate fuzzballs that destroy semiclassical spacetime near trapped surfaces.
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From 2D Yang-Mills to Calogero-Sutherland via a colored particle
Coupling a colored particle to 2D Yang-Mills on a cylinder reduces the dynamics, for SU(N), to the singular Calogero-Sutherland model.
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De Sitter Horizon Edge Partition Functions
Edge partition functions for totally symmetric tensors in dS_{d+1} are decomposed under so(d), with the linearized gravity case receiving contributions from shift-symmetric fields on S^{d-1} suggesting an embedded brane interpretation.
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Quantum Simulation of Gauge Theories for Particle and Nuclear Physics
The talk summarizes the quantum simulation program for lattice gauge theories, covering target problems in dense matter, algorithmic strategies, recent progress, and remaining challenges.
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Lectures on entanglement entropy in field theory and holography
Lecture notes surveying entanglement entropy in QFT and holography, emphasizing physical aspects and the Ryu-Takayanagi formula.