Abstract
We show that a Wilson-type discretization of the Gross–Neveu model, a fermionic N-flavor quantum field theory displaying asymptotic freedom and chiral symmetry breaking, can serve as a playground to explore correlated symmetry-protected phases of matter using techniques borrowed from high-energy physics. A large-N study, both in the Hamiltonian and Euclidean formalisms, yields a phase diagram with trivial, topological, and symmetry-broken phases separated by critical lines that meet at a tri-critical point. We benchmark these predictions using tools from condensed matter and quantum information science, which show that the large-N method captures the essence of the phase diagram even at N=1. Moreover, we describe a cold-atom scheme for the quantum simulation of this lattice model, which would allow to explore the single-flavor phase diagram.
Highlights
The understanding and classification of all possible phases of matter is one of the most important challenges of contemporary condensed-matter physics [1], and high-energy physics [2], finding important implications in quantum information science [3]
We show that a Wilson-type discretization of the Gross–Neveu model, a fermionic N-flavor quantum field theory displaying asymptotic freedom and chiral symmetry breaking, can serve as a playground to explore correlated symmetry-protected phases of matter using techniques borrowed from high-energy physics
We have described the existence of correlated symmetry-protected topological phases in a discretized version of the Gross–Neveu model
Summary
The understanding and classification of all possible phases of matter is one of the most important challenges of contemporary condensed-matter physics [1], and high-energy physics [2], finding important implications in quantum information science [3]. In contrast to the Higgs mechanism, where masses can be generated by introducing additional scalar fields that undergo spontaneous symmetry breaking themselves, here a physical mass (i.e. gap) is generated dynamically as a non-perturbative consequence of the four-fermion interactions These results are exact in the N → ∞ limit, and it is possible to calculate the leading corrections for a finite, but still large, N. By tuning this mass as a function of the interaction strength m(g2), one must search for a critical line m = mc(g2) where the renormalized mass of the Dirac fermion around k = 0 vanishes m 0 = 0, such that the correlation length fulfills ξ ≫ a (i.e. a second-order quantum phase transition) In this case, the physical quantities of interest become independent of the underlying lattice, and one expects to recover the desired continuum QFT.
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
