2D excitation information by MPS method on infinite helixes

Abstract

Understanding the excitation spectrum in two-dimensional quantum many-body systems has long been a challenging task. We present an approach by introducing an excitation ansatz based on an infinite matrix product state (MPS) on a helix structure. With the canonical form of MPS states, we can accurately extract key properties such as energy, degeneracy, spectrum weight, and scaling behavior of low-energy excited states simultaneously. To validate the effectiveness of this method, we begin by applying it to the critical point of the transverse-field Ising model. The extracted scaling exponent of the energy gap closely aligns with the conformal bootstrap results. Subsequently, we apply this approach to the $J_1$-$J_2$ Heisenberg model on a square lattice. We discover that the degeneracy of lowest-energy excitations serves as a reliable metric for distinguishing different phases. The phase boundary identified by our method is consistent with some of the previous findings. The present method provides a promising avenue for studying the excitation spectrum of two-dimensional quantum many-body systems.

References in corpus (42)

• The density-matrix renormalization group in the age of matrix product states
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Precision Islands in the Ising and $O(N)$ Models
• Resonating Valence Bond Theory of Coupled Heisenberg Chains
• Spin Liquid Ground State of the Spin-1/2 Square $J_1$-$J_2$ Heisenberg Model
• Plaquette Ordered Phase and Quantum Phase Diagram in the Spin-1/2 J1-J2 Square Heisenberg Model
• Variational optimization algorithms for uniform matrix product states
• Plaquette valence bond solid in the frustrated Heisenberg quantum antiferromagnet on the square lattice
• Magnetic order and disorder in the frustrated quantum Heisenberg antiferromagnet in two dimensions
• Dimer Order with Striped Correlations in the J_1-J_2 Heisenberg Model
• Direct evidence for a gapless $Z_2$ spin liquid by frustrating Néel antiferromagnetism
• Spontaneous plaquette dimerization in the $J_1-J_2$ Heisenberg model
• Tangent-space methods for uniform matrix product states
• Critical level crossings and gapless spin liquid in the square-lattice spin-$1/2$ $J_1$-$J_2$ Heisenberg antiferromagnet
• Ground-state phases of the spin-1/2 J_1-J_2 Heisenberg antiferromagnet on the square lattice: A high-order coupled cluster treatment
• The spin-1/2 J1-J2 Heisenberg antiferromagnet on the square lattice: Exact diagonalization for N=40 spins
• New valence bond crystal phase of a frustrated spin-1/2 square lattice antiferromagnet
• Variational matrix product ansatz for dispersion relations
• Exploring frustrated spin-systems using Projected Entangled Pair States (PEPS)
• The J1-J2 model: First order phase transition versus deconfinement of spinons
• Dirac-type nodal spin liquid revealed by refined quantum many-body solver using neural-network wave function, correlation ratio, and level spectroscopy
• 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
• High-energy magnon dispersion and multi-magnon continuum in the two-dimensional Heisenberg antiferromagnet
• Excitations and the tangent space of projected entangled-pair states
• Hierarchical mean-field approach to the $J_1$-$J_2$ Heisenberg model on a square lattice
• Ground-state phase diagram of the quantum $J_1-J_2$ model on the square lattice
• Gapless quantum spin liquid and global phase diagram of the spin-1/2 $J_1$-$J_2$ square antiferromagnetic Heisenberg model
• Spectral signatures of fractionalization in the frustrated Heisenberg model on the square lattice
• Direct Calculation of the Spin Stiffness in the $J_1$--$J_2$ Heisenberg Antiferromagnet
• Spin-1/2 J1-J2 Heisenberg antiferromagnet on a square lattice: a plaquette renormalized tensor network study
• Nonlinear Sigma model method for the J1-J2 Heisenberg model: disordered ground state with plaquette symmetry
• Excitations with projected entangled pair states using the corner transfer matrix method
• Investigation of the Néel phase of the frustrated Heisenberg antiferromagnet by differentiable symmetric tensor networks
• Plaquette valence-bond solid in the square lattice J1-J2 antiferromagnet Heisenberg model: a bond operator approach
• Automatic differentiation applied to excitations with Projected Entangled Pair States
• Spin Excitation Spectra of Anisotropic Spin-$1/2$ Triangular Lattice Heisenberg Antiferromagnets
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Generating Function for Tensor Network Diagrammatic Summation
• Continuous phase transition from Néel state to Z_2 spin liquid state on a square lattice
• Simulating a two-dimensional frustrated spin system with fermionic resonating-valence-bond states
• Emergent Symmetry in Quantum Phase Transitions: From Deconfined Quantum Critical Point to Gapless Quantum Spin Liquid
• One-dimensional projection of two-dimensional systems using spiral boundary conditions

Cited by in corpus (4)

• The Green's function Monte Carlo combined with projected entangled pair state approach to the frustrated $J_1$-$J_2$ Heisenberg model
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• A hybrid method integrating Green's function Monte Carlo and projected entangled pair states