Particles, holes and solitons: a matrix product state approach

Abstract

We introduce a variational method for calculating dispersion relations of translation invariant (1+1)-dimensional quantum field theories. The method is based on continuous matrix product states and can be implemented efficiently. We study the critical Lieb-Liniger model as a benchmark and excelent agreement with the exact solution is found. Additionally, we observe solitonic signatures of Lieb's Type II excitation. In addition, a non-integrable model is introduced where a U(1)-symmetry breaking term is added to the Lieb-Liniger Hamiltonian. For this model we find evidence of a non-trivial bound-state excitation in the dispersion relation.

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• Matrix product ansatz for Fermi fields in one dimension
• Diagonalizing transfer matrices and matrix product operators: a medley of exact and computational methods
• Shadows of Anyons
• Transfer Matrices and Excitations with Matrix Product States
• Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
• Scattering particles in quantum spin chains
• Ground-state energy and excitation spectrum of the Lieb-Liniger model : accurate analytical results and conjectures about the exact solution
• Particle-hole pairs and density-density correlations in the Lieb-Liniger model
• Exploring Interacting Quantum Many-Body Systems by Experimentally Creating Continuous Matrix Product States in Superconducting Circuits
• Approaching the Kosterlitz-Thouless transition for the classical XY model with tensor networks
• S matrix from matrix product states
• Many-body processes in black and grey matter-wave solitons
• Lieb-Liniger model with exponentially-decaying interactions: a continuous matrix product state study
• Continuous matrix product states for coupled fields: Application to Luttinger Liquids and quantum simulators
• Continuous matrix product states with periodic boundary conditions and an application to atomtronics
• Matrix product states and the nonabelian rotor model
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Quantum Gross-Pitaevskii Equation
• Quantum field tomography
• Continuous matrix product state tomography of quantum transport experiments
• Multiple phase separation in one-dimensional mixtures of mass- and population-imbalanced attractive Fermi gases
• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields
• Entanglement renormalization for gauge invariant quantum fields
• Charge density waves and their transitions in anisotropic quantum Hall systems
• Spectral gaps of two- and three-dimensional many-body quantum systems in the thermodynamic limit
• Entanglement Renormalization of the class of Continuous Matrix Product States
• On computing non-equilibrium dynamics following a quench
• Kac-Moody symmetries in one-dimensional bosonic systems
• Quantum simulation in the entanglement picture