Gaussian Continuous Tensor Network States for Simple Bosonic Field Theories

Abstract

Tensor networks states allow to find the low energy states of local lattice Hamiltonians through variational optimization. Recently, a construction of such states in the continuum was put forward, providing a first step towards the goal of solving quantum field theories (QFTs) variationally. However, the proposed manifold of continuous tensor network states (CTNSs) is difficult to study in full generality, because the expectation values of local observables cannot be computed analytically. In this paper, we study a tractable subclass of CTNSs, the Gaussian CTNSs (GCTNSs), and benchmark them on simple quadratic and quartic bosonic QFT Hamiltonians. We show that GCTNSs provide arbitrarily accurate approximations to the ground states of quadratic Hamiltonians, and decent estimates for quartic ones at weak coupling. Since they capture the short distance behavior of the theories we consider exactly, GCTNSs even allow to renormalize away simple divergences variationally. In the end, our study makes it plausible that CTNSs are indeed a good manifold to approximate the low energy states of QFTs.

arXiv comment8 + 4 pages

References in corpus (27)

• The density-matrix renormalization group
• Entanglement spectrum of a topological phase in one dimension
• Symmetry protected topological orders and the group cohomology of their symmetry group
• Classification of Gapped Symmetric Phases in 1D Spin Systems
• Classifying quantum phases using Matrix Product States and PEPS
• Renormalization algorithms for Quantum-Many Body Systems in two and higher dimensions
• Renormalization and tensor product states in spin chains and lattices
• PEPS as ground states: degeneracy and topology
• Continuous Matrix Product States for Quantum Fields
• Gradient methods for variational optimization of projected entangled-pair states
• Anyons and matrix product operator algebras
• Hamiltonian Truncation Study of the Phi^4 Theory in Two Dimensions
• Approximating Gibbs states of local Hamiltonians efficiently with PEPS
• Geometry of variational methods: dynamics of closed quantum systems
• Matrix product states and variational methods applied to critical quantum field theory
• Simulating excitation spectra with projected entangled-pair states
• Conformal Data from Finite Entanglement Scaling
• Applying the variational principle to (1+1)-dimensional quantum field theories
• A scaling hypothesis for matrix product states
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Algorithms for entanglement renormalization: boundaries, impurities and interfaces
• Gaussian time dependent variational principle for the Bose-Hubbard model
• Continuous Tensor Network States for Quantum Fields
• Conjectures about the ground-state energy of the Lieb-Liniger model at weak repulsion
• A tensor network study of the complete ground state phase diagram of the spin-1 bilinear-biquadratic Heisenberg model on the square lattice
• Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
• Computing the renormalization group flow of two-dimensional ${\varphi }^4$ theory with tensor networks

Cited by in corpus (8)

• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Relativistic continuous matrix product states for quantum fields without cutoff
• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension
• Variational method in relativistic quantum field theory without cutoff
• Cut-Off Kinks
• Tensor Renormalization Group for interacting quantum fields
• Symmetries and field tensor network states
• Holographic Tensor Networks as Tessellations of Geometry