Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
arXiv:2401.14368 · doi:10.1103/PhysRevResearch.6.023128
Abstract
We present an expression for the spectral gap, opening up new possibilities for performing and accelerating spectral calculations of quantum many-body systems. We develop and demonstrate one such possibility in the context of tensor network simulations. Our approach requires only minor modifications of the widely used simple update method and is computationally lightweight relative to other approaches. We validate it by computing spectral gaps of the 2D and 3D transverse-field Ising models and find strong agreement with previously reported perturbation theory results.
1D Haldane chain model analyzed (7 pages and 5 figures)
References in corpus (28)
- The density-matrix renormalization group in the age of matrix product states
- Matrix Product States, Projected Entangled Pair States, and variational renormalization group methods for quantum spin systems
- Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
- Classical simulation of infinite-size quantum lattice systems in two spatial dimensions
- Accurate determination of tensor network state of quantum lattice models in two dimensions
- Time-evolving a matrix product state with long-ranged interactions
- Spin-orbital quantum liquid on the honeycomb lattice
- Efficient tensor network simulation of IBM's Eagle kicked Ising experiment
- Tensor Network Algorithms: a Route Map
- Developments in the Tensor Network -- from Statistical Mechanics to Quantum Entanglement
- Transfer Matrices and Excitations with Matrix Product States
- Fast convergence of imaginary time evolution tensor network algorithms by recycling the environment
- Efficient tensor network simulation of IBM's largest quantum processors
- Evaluating energy differences on a quantum computer with robust phase estimation
- Automatic differentiation applied to excitations with Projected Entangled Pair States
- Simulation of three-dimensional quantum systems with projected entangled-pair states
- Efficient MPS methods for extracting spectral information on rings and cylinders
- Gauging tensor networks with belief propagation
- Tensor-based algorithms for image classification
- A beginner's guide to non-abelian iPEPS for correlated fermions
- Time evolution of an infinite projected entangled pair state: a gradient tensor update in the tangent space
- Thermodynamics of 3D Kitaev quantum spin liquids via tensor networks
- Extracting the Speed of Light from Matrix Product States
- tgEDMD: Approximation of the Kolmogorov Operator in Tensor Train Format
- Thermal bosons in 3d optical lattices via tensor networks
- Spectral estimation for Hamiltonians: a comparison between classical imaginary-time evolution and quantum real-time evolution
- Detection of energy levels of a spin system on a quantum computer by probe spin evolution
- 2D excitation information by MPS method on infinite helixes