Quantum Gross-Pitaevskii Equation

Abstract

We introduce a non-commutative generalization of the Gross-Pitaevskii equation for one-dimensional quantum gasses and quantum liquids. This generalization is obtained by applying the time-dependent variational principle to the variational manifold of continuous matrix product states. This allows for a full quantum description of many body system ---including entanglement and correlations--- and thus extends significantly beyond the usual mean-field description of the Gross-Pitaevskii equation, which is known to fail for (quasi) one-dimensional systems. By linearizing around a stationary solution, we furthermore derive an associated generalization of the Bogoliubov -- de Gennes equations. This framework is applied to compute the steady state response amplitude to a periodic perturbation of the potential.

4.ε pages + references and 4 pages supplementary material (small revisions + extended discussion of periodic potential example)

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Cited by in corpus (16)

• Matrix Product States and Projected Entangled Pair States: Concepts, Symmetries, and Theorems
• Tangent-space methods for uniform matrix product states
• Matrix product ansatz for Fermi fields in one dimension
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Variational Neural-Network Ansatz for Continuum Quantum Field Theory
• Variational optimization of continuous matrix product states
• Energy level splitting for weakly interacting bosons in a harmonic trap
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Domain wall melting in spin-1 chains
• Magic entanglement renormalization for quantum fields
• Entanglement renormalization for gauge invariant quantum fields
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• On symmetry-resolved generalized entropies
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Kac-Moody symmetries in one-dimensional bosonic systems
• Revisiting Many-body Localization with Random Networks of Tensors