Matrix product ansatz for Fermi fields in one dimension

Abstract

We present an implementation of a continuous matrix product state for two-component fermions in one-dimension. We propose a construction of variational matrices with an efficient parameterization that respects the translational symmetry of the problem (without being overly constraining) and readily meets the regularity conditions that arise from removing the ultraviolet divergences in the kinetic energy. We test the validity of our approach on an interacting spin-1/2 system and observe that the ansatz correctly predicts the ground state magnetic properties for the attractive spin-1/2 Fermi gas, including the phase-oscillating pair correlation function in the partially polarized regime.

6 pages, 5 figures

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• Continuous matrix product states with periodic boundary conditions and an application to atomtronics
• Continuous matrix product states for non-relativistic quantum fields: a lattice algorithm for inhomogeneous systems
• Quantum Gross-Pitaevskii Equation
• 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
• Derivation of matrix product states for the Heisenberg spin chain with open boundary conditions
• Continuous matrix product states solution for the mixing/demixing transition in one-dimensional quantum fields
• Magic entanglement renormalization for quantum fields
• Entanglement renormalization for gauge invariant quantum fields
• Continuous matrix-product states in inhomogeneous systems with long-range interactions
• Numerical continuum tensor networks in two dimensions
• Entanglement Renormalization of the class of Continuous Matrix Product States