Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
An Area Law for One Dimensional Quantum Systems
6 Pith papers cite this work. Polarity classification is still indexing.
6
Pith papers citing it
abstract
We prove an area law for the entanglement entropy in gapped one dimensional quantum systems. The bound on the entropy grows surprisingly rapidly with the correlation length; we discuss this in terms of properties of quantum expanders and present a conjecture on completely positive maps which may provide an alternate way of arriving at an area law. We also show that, for gapped, local systems, the bound on Von Neumann entropy implies a bound on R\'{e}nyi entropy for sufficiently large $\alpha<1$ and implies the ability to approximate the ground state by a matrix product state.
representative citing papers
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
Real-time lattice Hamiltonian simulation of a three-particle Ising field theory suppresses Umklapp processes and produces relativistic hydrodynamics sound modes, extracting ζ/s=14.19±0.90 and c_s/c=0.76±0.02 at T≈7.14.
Gauged Gaussian PEPS ansatz demonstrated on Z2 gauge theory with dynamical fermions, agreeing with exact diagonalization on small lattices and feasible for larger ones.
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.
citing papers explorer
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Renormalization flows for 1D mixed states and a quantum Goursat lemma
Convergent renormalization trajectories of Hopf-algebra boundary MPDOs under on-site noise are classified by finite *-quantum hypergroups via a new quantum Goursat lemma.
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Algebras of order parameters in one-dimensional spin systems
String order parameters in 1D gapped phases with invertible or non-invertible symmetries organize into Lagrangian algebras in the Drinfel'd centre via tensor-network module categories.
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Tame the Umklapp Processes in Real-Time Lattice Simulation for Hydrodynamics: An Ising Field Theory Study
Real-time lattice Hamiltonian simulation of a three-particle Ising field theory suppresses Umklapp processes and produces relativistic hydrodynamics sound modes, extracting ζ/s=14.19±0.90 and c_s/c=0.76±0.02 at T≈7.14.
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Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
Gauged Gaussian PEPS ansatz demonstrated on Z2 gauge theory with dynamical fermions, agreeing with exact diagonalization on small lattices and feasible for larger ones.
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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.
- Topological Control of Quantum Chaos Diagnostics: OTOCs, Spectral Statistics, and Information Scrambling in Ising Model