Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration

Abstract

Tensor network states, and in particular Projected Entangled Pair States (PEPS) have been a strong ansatz for the variational study of complicated quantum many-body systems, thanks to their built-in entanglement entropy area law. In this work, we use a special kind of PEPS - Gauged Gaussian Fermionic PEPS (GGFPEPS) to find the ground state of $2+1d$ dimensional pure ${\mathbb{Z}}_2$ lattice gauge theories for a wide range of coupling constants. We do so by combining PEPS methods with Monte-Carlo computations, allowing for efficient contraction of the PEPS and computation of correlation functions. Previously, such numerical computations involved the calculation of the Pfaffian of a matrix scaling with the system size, forming a severe bottleneck; in this work we show how to overcome this problem. This paves the way for applying the method we propose and benchmark here to other gauge groups, higher dimensions, and models with fermionic matter, in an efficient, sign-problem-free way.

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Cited by in corpus (18)

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• Digital quantum simulation of a (1+1)D SU(2) lattice gauge theory with ion qudits
• Real-time scattering in the lattice Schwinger model
• Tensor Networks for Lattice Gauge Theories beyond one dimension: a Roadmap
• Topological Green's function zeros in an exactly solved model and beyond
• Entanglement and confinement in lattice gauge theory tensor networks
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Deep learning lattice gauge theories
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Parton Distribution Functions in the Schwinger model from Tensor Network States
• Efficient conversion from fermionic Gaussian states to matrix product states
• Internal structure of gauge-invariant Projected Entangled Pair States
• Wegner's Ising gauge spins versus Kitaev's Majorana partons: Mapping and application to anisotropic confinement in spin-orbital liquids
• Variational approach to open quantum systems with long-range competing interactions
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions
• Algorithmic Aspects of Gauged Gaussian Fermionic PEPS: Gauge Fixing and Translation Invariance
• Superselection-Resolved Entanglement in Lattice Gauge Theories: A Tensor Network Approach