Projected Entangled Pair States with non-Abelian gauge symmetries: an SU(2) study

Abstract

Over the last years, Projected Entangled Pair States have demonstrated great power for the study of many body systems, as they naturally describe ground states of gapped many body Hamiltonians, and suggest a constructive way to encode and classify their symmetries. The PEPS study is not only limited to global symmetries, but has also been extended and applied for local symmetries, allowing to use them for the description of states in lattice gauge theories. In this paper we discuss PEPS with a local, SU(2) gauge symmetry, and demonstrate the use of PEPS features and techniques for the study of a simple family of many body states with a non-Abelian gauge symmetry. We present, in particular, the construction of fermionic PEPS able to describe both two-color fermionic matter and the degrees of freedom of an SU(2) gauge field with a suitable truncation.

48 pages, 26 Figures

References in corpus (13)

• The density-matrix renormalization group in the age of matrix product states
• Classification of topological insulators and superconductors in three spatial dimensions
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Computational complexity and fundamental limitations to fermionic quantum Monte Carlo simulations
• Observation of long-range near-side angular correlations in proton-lead collisions at the LHC
• A Formulation of Lattice Gauge Theories for Quantum Simulations
• Gauging quantum states: from global to local symmetries in many-body systems
• Quantum simulation of the Schwinger model: A study of feasibility
• Lattice Gauge Tensor Networks
• Transfer Matrices and Excitations with Matrix Product States
• Diagnosing Deconfinement and Topological Order
• Chiral projected entangled-pair state with topological order
• The temperature dependence of the chiral condensate in the Schwinger model with Matrix Product States

Cited by in corpus (16)

• Digital lattice gauge theories
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Efficient Basis Formulation for (1+1)-Dimensional SU(2) Lattice Gauge Theory: Spectral calculations with matrix product states
• Systematic construction of spin liquids on the square lattice from tensor networks with SU(2) symmetry
• Towards overcoming the Monte Carlo sign problem with tensor networks
• Finding the ground state of a lattice gauge theory with fermionic tensor networks: a $2+1d$ ${\mathbb{Z}}_2$ demonstration
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Simulating both parity sectors of the Hubbard Model with Tensor Networks
• Local Manipulation and Measurement of Nonlocal Many-Body Operators in Lattice Gauge Theory Quantum Simulators
• Simulating quantum circuits using efficient tensor network contraction algorithms with subexponential upper bound
• Entanglement and confinement in lattice gauge theory tensor networks
• Half a state, half an operator: a general formulation of stators
• Gauged Gaussian PEPS -- A High Dimensional Tensor Network Formulation for Lattice Gauge Theories
• Fermionic Gaussian PEPS in $3+1d$: Rotations and Relativistic Limits
• Internal structure of gauge-invariant Projected Entangled Pair States
• Projected Entangled Pair States for Lattice Gauge Theories with Dynamical Fermions