Efficient MPS methods for extracting spectral information on rings and cylinders

Abstract

Based on the MPS formalism, we introduce an ansatz for capturing excited states in finite systems with open boundary conditions, providing a very efficient method for computing, e.g., the spectral gap of quantum spin chains. This method can be straightforwardly implemented on top of an existing DMRG or MPS ground-state code. Although this approach is built on open-boundary MPS, we also apply it to systems with periodic boundary conditions. Despite the explicit breaking of translation symmetry by the MPS representation, we show that momentum emerges as a good quantum number, and can be exploited for labeling excitations on top of MPS ground states. We apply our method to the critical Ising chain on a ring and the classical Potts model on a cylinder. Finally, we apply the same idea to compute excitation spectra for 2-D quantum systems on infinite cylinders. Again, despite the explicit breaking of translation symmetry in the periodic direction, we recover momentum as a good quantum number for labeling excitations. We apply this method to the 2-D transverse-field Ising model and the half-filled Hubbard model; for the latter, we obtain accurate results for, e.g., the hole dispersion for cylinder circumferences up to eight sites.

References in corpus (52)

• The density-matrix renormalization group in the age of matrix product states
• The density-matrix renormalization group
• Thermodynamic limit of the density matrix renormalization for the spin-1 Heisenberg chain
• Classical simulation of infinite-size quantum lattice systems in one spatial dimension
• Time-dependent variational principle for quantum lattices
• DMRG and periodic boundary conditions: a quantum information perspective
• From density-matrix renormalization group to matrix product states
• A class of ansatz wave functions for 1D spin systems and their relation to DMRG
• The Hubbard model: A computational perspective
• Studying Two Dimensional Systems With the Density Matrix Renormalization Group
• Variational optimization algorithms for uniform matrix product states
• Characterizing topological order by studying the ground states of an infinite cylinder
• Tangent-space methods for uniform matrix product states
• String patterns in the doped Hubbard model
• Evidence for Quasiparticle Decay in Photoemission from Underdoped Cuprates
• Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field
• Dynamics of the Kitaev-Heisenberg Model
• Variational matrix product ansatz for dispersion relations
• Matrix product states for critical spin chains: finite size scaling versus finite entanglement scaling
• Classifying Snapshots of the Doped Hubbard Model with Machine Learning
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Infinite size density matrix renormalization group, revisited
• Fermionic Matrix Product States and One-Dimensional Topological Phases
• Excitations and the tangent space of projected entangled-pair states
• Infinite boundary conditions for matrix product state calculations
• Hybrid-space density matrix renormalization group study of the doped two-dimensional Hubbard model
• Spinon confinement in a quasi one dimensional anisotropic Heisenberg magnet
• Efficient Matrix Product State Method for periodic boundary conditions
• Equal Time Correlations in Haldane Gap Antiferromagnets
• Simulating excitation spectra with projected entangled-pair states
• Density matrix renormalization group on a cylinder in mixed real and momentum space
• Evidence for composite nature of quasiparticles in the 2D t-J model
• Renormalization algorithm for the calculation of spectra of interacting quantum systems
• Parton theory of ARPES spectra in anti-ferromagnetic Mott insulators
• Excitations with projected entangled pair states using the corner transfer matrix method
• Time Evolution within a Comoving Window: Scaling of signal fronts and magnetization plateaus after a local quench in quantum spin chains
• Bound states and E_8 symmetry effects in perturbed quantum Ising chains
• Excitation Spectrum of $S=1$ Antiferromagnetic Chains
• Quasiparticles in quantum spin chains with long-range interactions
• Conformal data and renormalization group flow in critical quantum spin chains using periodic uniform matrix product states
• Exploiting translational invariance in Matrix Product State simulations of spin chains with periodic boundary conditions
• Scattering particles in quantum spin chains
• Variational Matrix Product Ansatz for Nonuniform Dynamics in the Thermodynamic Limit
• Excitation spectrum and Density Matrix Renormalization Group iterations
• Topological nature of spinons and holons: Elementary excitations from matrix product states with conserved symmetries
• SU(2)${}_1$ chiral edge modes of a critical spin liquid
• A matrix product state based algorithm for determining dispersion relations of quantum spin chains with periodic boundary conditions
• Continuous matrix product states with periodic boundary conditions and an application to atomtronics
• Spinon confinement and deconfinement in spin-1 chains
• Generating Function for Tensor Network Diagrammatic Summation
• Stiffness in 1D Matrix Product States with periodic boundary conditions
• Dynamic structure factor from real time evolution and exact correction vectors with matrix product states

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• Nonlinear spectroscopy of bound states in perturbed Ising spin chains
• Fermionic tensor network methods
• Fractional quantum Hall states with variational Projected Entangled-Pair States: a study of the bosonic Harper-Hofstadter model
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• Phase diagram of the chiral SU(3) antiferromagnet on the kagome lattice
• Projector formalism for kept and discarded spaces of matrix product states
• Twisting the Dirac cones of the SU(4) spin-orbital liquid on the honeycomb lattice
• Chiral polaron formation on the edge of topological quantum matter
• Variational adiabatic transport of tensor networks
• Momentum-resolved time evolution with matrix product states
• Extracting Nonlinear Dynamical Response Functions from Time Evolution
• 2D excitation information by MPS method on infinite helixes
• The Haldane gap in the SU(3) [3 0 0] Heisenberg chain
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Simulating chiral spin liquids with projected entangled-pair states
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Efficient and systematic calculation of arbitrary observables for the matrix product state excitation ansatz
• Spiral renormalization group flow and universal entanglement spectrum of the non-Hermitian 5-state Potts model
• Entanglement Spectrum as a diagnostic of chirality of Topological Spin Liquids: Analysis of an $\mathrm{SU}(3)$ PEPS
• A Generalised Haldane Map from the Matrix Product State Path Integral to the Critical Theory of the $J_1$-$J_2$ Chain