Excitations with projected entangled pair states using the corner transfer matrix method

Abstract

We present an extension of a framework for simulating single quasiparticle or collective excitations on top of strongly correlated quantum many-body ground states using infinite projected entangled pair states, a tensor network ansatz for two-dimensional wave functions in the thermodynamic limit. Our approach performs a systematic summation of locally perturbed states in order to obtain excited eigenstates localized in momentum space, using the corner transfer matrix method, and generalizes the framework to arbitrary unit cell sizes, the implementation of global Abelian symmetries and fermionic systems. Results for several test cases are presented, including the transverse Ising model, the spin-$\frac{1}{2}$ Heisenberg model and a free fermionic model, to demonstrate the capability of the method to accurately capture dispersions. We also provide insight into the nature of excitations at the $k=(\pi ,0)$ point of the Heisenberg model.

arXiv comment13 pages, 10 figures

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Cited by in corpus (37)

• The Hubbard model: A computational perspective
• Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Simulation of three-dimensional quantum systems with projected entangled-pair states
• Tensor network study of the $m=1/2$ magnetization plateau in the Shastry-Sutherland model at finite temperature
• Time evolution of an infinite projected entangled pair state: a neighborhood tensor update
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Direct sampling of projected entangled-pair states
• Variational methods for contracting projected entangled-pair states
• Generating Function for Tensor Network Diagrammatic Summation
• Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
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• TeNeS: Tensor Network Solver for Quantum Lattice Systems
• Generating function for projected entangled-pair states
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• Fractionalization Signatures in the Dynamics of Quantum Spin Liquids
• Corner transfer matrix renormalization group approach in the zoo of Archimedean lattices
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• Efficient tensor network algorithm for layered systems
• Momentum-resolved time evolution with matrix product states
• Spectral functions with infinite projected entangled-pair states
• Fermionic Isometric Tensor Network States in Two Dimensions
• Possible Observation of Quadrupole Waves in Spin Nematics
• Tensor network analysis of the maple-leaf antiferromagnet spangolite
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• 2D excitation information by MPS method on infinite helixes
• Gauge symmetry of excited states in projected entangled-pair state simulations
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• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Tangent Space Excitation Ansatz for Quantum Circuits
• Accelerating two-dimensional tensor network optimization by preconditioning
• Dynamical Spectral Function of the Kagome Quantum Spin Liquid
• Dispersion Relations in Two- and Three-Dimensional Quantum Systems
• Grassmann tensor networks