Generating function for projected entangled-pair states

Abstract

Diagrammatic summation is a common bottleneck in modern applications of projected entangled-pair states, especially in computing low-energy excitations of a two-dimensional quantum many-body system. To solve this problem, here we extend the generating function approach for tensor network diagrammatic summation, a scheme previously proposed in the context of matrix product states. Taking the form of a one-particle excitation, we show that the excited state can be computed efficiently in the generating function formalism, which can further be used in evaluating the dynamical structure factor of the system. Our benchmark results for the spin-$1/2$ transverse-field Ising model and Heisenberg model on the square lattice provide a desirable accuracy, showing good agreement with known results. We then study the spin-$1/2$ $J_1$-$J_2$ model on the same lattice and investigate the dynamical properties of the putative gapless spin liquid phase. We conclude with a discussion on generalizations to multi-particle excitations.

13 pages, 6 figures

References in corpus (15)

• Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
• Tensor renormalization group approach to 2D classical lattice models
• Accurate determination of tensor network state of quantum lattice models in two dimensions
• Fractional excitations in the square-lattice quantum antiferromagnet
• Algorithms for finite Projected Entangled Pair States
• Resonating valence bond states in the PEPS formalism
• Quantum Spin Liquid in Spin 1/2 J1-J2 Heisenberg Model on Square Lattice: Many-Variable Variational Monte Carlo Study Combined with Quantum-Number Projections
• Nearly deconfined spinon excitations in the square-lattice spin-1/2 Heisenberg antiferromagnet
• Projected Entangled Pair States at Finite Temperature: Imaginary Time Evolution with Ancillas
• The antiferromagnetic spin-1/2 Heisenberg model on the square lattice in a magnetic field
• Finite correlation length scaling with infinite projected entangled pair states at finite temperature
• Investigation of the chiral antiferromagnetic Heisenberg model using PEPS
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Finite temperature tensor network study of the Hubbard model on an infinite square lattice
• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice

Cited by in corpus (12)

• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
• An introduction to infinite projected entangled-pair state methods for variational ground state simulations using automatic differentiation
• Simulating Spin Dynamics of Supersolid States in a Quantum Ising Magnet
• Spectral functions with infinite projected entangled-pair states
• Variationally optimizing infinite projected entangled-pair states at large bond dimensions: A split corner transfer matrix renormalization group approach
• Gauge symmetry of excited states in projected entangled-pair state simulations
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Tangent Space Excitation Ansatz for Quantum Circuits
• Variational optimization of projected entangled-pair states on the triangular lattice
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• Accurate computation of the energy variance and $⟨⟨{\mathcal{L}}^{†}\mathcal{L}⟩⟩$ using iPEPS