Tensor renormalization group in bosonic field theory

Abstract

We compute the partition function of a massive free boson in a square lattice using a tensor network algorithm. We introduce a singular value decomposition (SVD) of continuous matrices that leads to very accurate numerical results. It is shown the emergence of a CDL fixed point structure. In the massless limit, we reproduce the results of conformal field theory including a precise value of the central charge.

5+8 pages, 4+2 figures

References in corpus (34)

• The density-matrix renormalization group
• Efficient classical simulation of slightly entangled quantum computations
• A Practical Introduction to Tensor Networks: Matrix Product States and Projected Entangled Pair States
• Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
• Entanglement spectrum of a topological phase in one dimension
• Entanglement renormalization
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Tensor-Entanglement-Filtering Renormalization Approach and Symmetry Protected Topological Order
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Entanglement Renormalization and Holography
• Holographic quantum error-correcting codes: Toy models for the bulk/boundary correspondence
• Classifying quantum phases using Matrix Product States and PEPS
• Tensor renormalization group approach to 2D classical lattice models
• DMRG and periodic boundary conditions: a quantum information perspective
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Tensor Network Renormalization
• Liouville Action as Path-Integral Complexity: From Continuous Tensor Networks to AdS/CFT
• Continuous Matrix Product States for Quantum Fields
• Matrix-product-groundstates for one-dimensional spin-1 quantum antiferromagnets
• Density Matrix Renormalization Group Method for 2D Classical Models
• Entanglement renormalization for quantum fields
• Equivalence of the Variational Matrix Product Method and the Density Matrix Renormalization Group applied to Spin Chains
• cMERA as Surface/State Correspondence in AdS/CFT
• Entanglement renormalization, scale invariance, and quantum criticality
• Tensor network renormalization yields the multi-scale entanglement renormalization ansatz
• Quantum MERA Channels
• Continuous Tensor Network States for Quantum Fields
• Efficient evaluation of partition functions of frustrated and inhomogeneous spin systems
• Continuum tensor network field states, path integral representations and the encoding of spatial symmetries
• Renormalization Group Circuits for Weakly Interacting Continuum Field Theories
• Information Geometry of Entanglement Renormalization for free Quantum Fields
• Holographic codes
• Continuous tensor network renormalization for quantum fields
• The Density Matrix Renormalization Group, Quantum Groups and Conformal Field Theory

Cited by in corpus (8)

• Simulating Lattice Gauge Theories within Quantum Technologies
• Review on novel methods for lattice gauge theories
• Tensor lattice field theory with applications to the renormalization group and quantum computing
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks
• Collective Monte Carlo updates through tensor network renormalization
• Lattice regularisation and entanglement structure of the Gross-Neveu model
• Tensor Renormalization Group for interacting quantum fields
• Integrability and scattering of the boson field theory on a lattice