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Cold atom simulation of interacting relativistic quantum field theories
J. Ignacio Cirac, Paolo Maraner, Jiannis K. Pachos
TL;DR
Many QFT problems call for non-perturbative insight, yet analytic methods seem intractable in three and four dimensions. The paper proposes optical-lattice cold-atom Hamiltonians whose low-energy behavior realizes interacting Dirac models. These setups target a Thirring mass gap and dynamical mass generation in the Gross-Neveu model.
Problem
Many open QFT problems, including infrared QCD, call for non-perturbative insight, while analytic methods seem intractable in three and four dimensions.
Source: p. 1Method
The paper designs cold-atom optical-lattice Hamiltonians whose low-energy sectors realize Thirring fermions and Dirac fermions coupled to a dynamic scalar field.
Source: p. 1Results
The Thirring effective mass is the zero-momentum gap, and the Gross-Neveu setup can detect dynamically generated mass.
Source: pp. 3–4Takeaways & Limitations
Cold atoms provide a controlled physical platform that naturally avoids the sign problem in numerical lattice-gauge simulations.
Source: p. 1The proposed QED2 extension additionally requires a bosonic kinetic term and an atomic Gauss constraint, and is presented elsewhere.
Source: p. 4
Abstract
from arXiv · showhide
We demonstrate that Dirac fermions self-interacting or coupled to dynamic scalar fields can emerge in the low energy sector of designed bosonic and fermionic cold atom systems. We illustrate this with two examples defined in two spacetime dimensions. The first one is the self-interacting Thirring model. The second one is a model of Dirac fermions coupled to a dynamic scalar field that gives rise to the Gross-Neveu model. The proposed cold atom experiments can be used to probe spectral or correlation properties of interacting quantum field theories thereby presenting an alternative to lattice gauge theory simulations.