• Corpus ID: 247793761

Entanglement area law for 1D gauge theories and bosonic systems

  title={Entanglement area law for 1D gauge theories and bosonic systems},
  author={Nilin Abrahamsen and Yuan Su and Yu Tong and Nathan Wiebe},
We prove an entanglement area law for a class of 1D quantum systems involving infinite-dimensional local Hilbert spaces. This class of quantum systems include bosonic models such as the Hubbard-Holstein model, and both U(1) and SU(2) lattice gauge theories in one spatial dimension. Our proof relies on new results concerning the robustness of the ground state and spectral gap to the truncation of Hilbert space, applied within the approximate ground state projector (AGSP) framework from previous… 
1 Citations
Entanglement Witnessing for Lattice Gauge Theories
: Entanglement is assuming a central role in modern quantum many-body physics. Yet, for lattice gauge theories its certification remains extremely challenging. A key difficulty stems from the local


Statistics dependence of the entanglement entropy.
This work establishes scaling laws for entanglement in critical quasifree fermionic and bosonic lattice systems, without resorting to numerical means, and finds Lifshitz quantum phase transitions accompanied with a nonanalyticity in the prefactor of the leading order term.
Entanglement-area law for general bosonic harmonic lattice systems (14 pages)
We demonstrate that the entropy of entanglement and the distillable entanglement of regions with respect to the rest of a general harmonic-lattice system in the ground or a thermal state scale at
An Area Law for One Dimensional Quantum Systems
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
An area law for 2d frustration-free spin systems
We prove that the entanglement entropy of the ground state of a locally gapped frustration-free 2D lattice spin system satisfies an area law with respect to a vertical bipartition of the lattice into
Efficient basis formulation for 1+1 dimensional SU(2) lattice gauge theory: Spectral calculations with matrix product states
We propose an explicit formulation of the physical subspace for a (1+1)-dimensional SU(2) lattice gauge theory, where the gauge degrees of freedom are integrated out. Our formulation is completely
Improved Thermal Area Law and Quasilinear Time Algorithm for Quantum Gibbs States
A new thermal area law is proposed that holds for generic many-body systems on lattices and is based on a polynomial approximation to the exponential function which provides a relationship between the imaginary-time evolution and random walks.
Colloquium: Area laws for the entanglement entropy
Physical interactions in quantum many-body systems are typically local: Individual constituents interact mainly with their few nearest neighbors. This locality of interactions is inherited by a decay
Matrix Product States for Lattice Field Theories
The term Tensor Network States (TNS) refers to a number of families of states that represent different ans\"atze for the efficient description of the state of a quantum many-body system. Matrix
The mass spectrum of the Schwinger model with matrix product states
A bstractWe show the feasibility of tensor network solutions for lattice gauge theories in Hamiltonian formulation by applying matrix product states algorithms to the Schwinger model with zero and
Rigorous Rg Algorithms and Area Laws for Low Energy Eigenstates In 1D
A new algorithm is given, based on a rigorously justified RG type transformation, for finding low energy states for 1D Hamiltonians acting on a chain of n particles, which is natural and efficient.