Continuous matrix product states with periodic boundary conditions and an application to atomtronics

Abstract

We introduce a time evolution algorithm for one-dimensional quantum field theories with periodic boundary conditions. This is done by applying the Dirac-Frenkel time-dependent variational principle to the set of translational invariant continuous matrix product states with periodic boundary conditions. Moreover, the ansatz is accompanied with additional boundary degrees of freedom to study quantum impurity problems. The algorithm allows for a cutoff in the spectrum of the transfer matrix and thus has an efficient computational scaling. In particular we study the prototypical example of an atomtronic system - an interacting Bose gas rotating in a ring shaped trap in the presence of a localised barrier potential.

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Cited by in corpus (17)

• Tangent-space methods for uniform matrix product states
• Continuous Matrix Product States for Quantum Fields: an Energy Minimization Algorithm
• Continuous Tensor Network States for Quantum Fields
• Efficient MPS methods for extracting spectral information on rings and cylinders
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Variational optimization of continuous matrix product states
• Characterizing the quantum field theory vacuum using temporal Matrix Product states
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Quantum Coherent States of Interacting Bose-Fermi Mixtures in One Dimension
• Density-Matrix Renormalization Group for Continuous Quantum Systems
• Magic entanglement renormalization for quantum fields
• Entanglement renormalization for gauge invariant quantum fields
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Finite-size scaling on the torus with periodic projected entangled-pair states
• Entanglement Renormalization of the class of Continuous Matrix Product States
• Kac-Moody symmetries in one-dimensional bosonic systems
• Holographic Tensor Networks as Tessellations of Geometry