Dirac fields in curved spacetime as Fermi-Hubbard model with non unitary tunnelings

Abstract

In this article we show that a Dirac Hamiltonian in a curved background spacetime can be interpreted, when discretized, as a tight binding Fermi-Hubbard model with non unitary tunnelings. We find the form of the nonunitary tunneling matrices in terms of the metric tensor. The main motivation behind this exercise is the feasibility of such Hamiltonians by means of laser assisted tunnelings in cold atomic experiments. The mapping thus provide a physical interpretation of such Hamiltonians. We demonstrate the use of the mapping on the example of time dependent metric in 2+1 dimensions. Studying the spin dynamics, we find qualitative agreement with known theoretical predictions, namely the particle pair creation in expanding universe.

9 pages, 4 figures. New results and figures added

References in corpus (10)

• Many-Body Physics with Ultracold Gases
• Quantum phase transition from a superfluid to a Mott insulator in a gas of ultracold atoms
• Ultracold atomic gases in optical lattices: mimicking condensed matter physics and beyond
• Creating, moving and merging Dirac points with a Fermi gas in a tunable honeycomb lattice
• Single-Spin Addressing in an Atomic Mott Insulator
• Bose Hubbard Models with Synthetic Spin-Orbit Coupling: Mott Insulators, Spin Textures and Superfluidity
• Cold atom simulation of interacting relativistic quantum field theories
• Dirac Equation For Cold Atoms In Artificial Curved Spacetimes
• Geometric Phase for Neutral Particle in the Presence of a Topological Defect
• Hermiticity of the Dirac Hamiltonian in Curved Spacetime

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• Horizon physics of quasi-one-dimensional tilted Weyl cones on a lattice
• Fermionic fields in a four-dimensional Bonnor-Melvin-Lambda space-time
• Fermion production at the boundary of an expanding universe: a cold-atom gravitational analogue
• Anisotropic optics and gravitational lensing of tilted Weyl fermions
• Hawking radiation on the lattice from Floquet and local Hamiltonian quench dynamics
• Interacting Dirac fields in an expanding universe: dynamical condensates and particle production
• Gauge fields induced by curved spacetime
• Quantum dynamics in 1D lattice models with synthetic horizons
• Synthetic horizons in an atomic chain: Horizon-induced effects and connections to quantum Hall systems