Entanglement Renormalization of the class of Continuous Matrix Product States

Abstract

Continuous tensor network gives a variational ansatz for the ground state of the quantum field theories (QFTs). The notable examples are the continuous matrix product state (cMPS) and the continuous multiscale entanglement renormalization ansatz (cMERA). While cMPS is just adapted to the non-relativistic QFTs, only the Gaussian cMERA is well-understood which we can not use to approximate the ground state of the interacting relativistic QFTs. But instead, cMERA also corresponds to a real-space renormalization group flow in the context of the wave functions. In this letter, we investigate the backward Gaussian cMERA renormalization group flow of the class of cMPS by putting the standard cMPS at the IR scale. At the UV scale, for the bosonic systems in the thermodynamic limit, we achieve the variational class of states that has been proposed recently as the relativistic cMPS (RCMPS) is adapted to the relativistic QFTs without requiring to introduce of any additional IR or UV cut-off. We also extend the RCMPS to fermionic systems and theories on a finite circle.

6 pages, 1 figure

References in corpus (14)

• Matrix product states represent ground states faithfully
• Tensor renormalization group approach to 2D classical lattice models
• Continuous Matrix Product States for Quantum Fields
• The Dynamics of 1D Quantum Spin Systems Can Be Approximated Efficiently
• Gauging quantum states: from global to local symmetries in many-body systems
• Matrix product ansatz for Fermi fields in one dimension
• Density Induced Phase Transitions in the Schwinger Model: A Study with Matrix Product States
• Matrix Product States: Symmetries and Two-Body Hamiltonians
• From Path Integrals to Tensor Networks for AdS/CFT
• Continuous matrix product states with periodic boundary conditions and an application to atomtronics
• Classification of Matrix Product States with a Local (Gauge) Symmetry
• Relativistic continuous matrix product states for quantum fields without cutoff
• Approximating Relativistic Quantum Field Theories with Continuous Tensor Networks
• Variational method in relativistic quantum field theory without cutoff