Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks

@inproceedings{Shachar2021ApproximatingRQ,
  title={Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks},
  author={Tom Shachar and Erez Zohar},
  year={2021}
}
We present a continuous tensor-network construction for the states of quantum fields called cPEPS (continuous projected entangled pair state), which enjoys the same spatial and global symmetries of ground-states of relativistic field theories. We explicitly show how such a state can approximate and eventually converge to the free field theory vacuum and suggest a regularization-independent way of estimating the convergence via a universal term in the fidelity per-site. We also present a… 

Figures from this paper

Wilson loops in the Hamiltonian formalism
In a gauge theory, the gauge invariant Hilbert space is unchanged by the coupling to arbitrary local operators. In the presence of Wilson loops, though, the physical Hilbert space must be enlarged by

References

SHOWING 1-10 OF 45 REFERENCES
Continuous Tensor Network States for Quantum Fields
We introduce a new class of states for bosonic quantum fields which extend tensor network states to the continuum and generalize continuous matrix product states (cMPS) to spatial dimensions $d\geq
Building Projected Entangled Pair States with a Local Gauge Symmetry
Tensor network states, and in particular projected entangled pair states (PEPS), suggest an innovative approach for the study of lattice gauge theories, both from a pure theoretic point of view, and
Continuum tensor network field states, path integral representations and spatial symmetries
A natural way to generalize tensor network variational classes to quantum field systems is via a continuous tensor contraction. This approach is first illustrated for the class of quantum field
Combining tensor networks with Monte Carlo methods for lattice gauge theories
Gauged gaussian Projected Entangled Pair States are particular tensor network constructions that describe lattice states of fermionic matter interacting with dynamical gauge fields. We show how one
Entanglement renormalization for quantum fields in real space.
TLDR
This work shows how to construct renormalization group (RG) flows of quantum field theories in real space, as opposed to the usual Wilsonian approach in momentum space, and argues that the full power of the construction should emerge in the case of interacting theories.
Class of quantum many-body states that can be efficiently simulated.
  • G. Vidal
  • Physics
    Physical review letters
  • 2008
We introduce the multiscale entanglement renormalization ansatz, a class of quantum many-body states on a D-dimensional lattice that can be efficiently simulated with a classical computer, in that
Renormalization and tensor product states in spin chains and lattices
TLDR
This work introduces several families of such states in terms of the known renormalization procedures, and highlights some of their properties, and shows how they can be used to describe a variety of systems.
Holographic geometry of entanglement renormalization in quantum field theories
A bstractWe study a conjectured connection between AdS/CFT and a real-space quantum renormalization group scheme, the multi-scale entanglement renormalization ansatz (MERA). By making a close contact
Normal projected entangled pair states generating the same state
Tensor networks are generated by a set of small rank tensors and define many-body quantum states in a succinct form. The corresponding map is not one-to-one: different sets of tensors may generate
Matrix product states and projected entangled pair states: Concepts, symmetries, theorems
The theory of entanglement provides a fundamentally new language for describing interactions and correlations in many body systems. Its vocabulary consists of qubits and entangled pairs, and the
...
1
2
3
4
5
...