Topological Gap Opening without Symmetry Breaking from Dynamical Quantum Correlations

The standard phenomenology for fermions to acquire a mass requires a spontaneous symmetry breaking, and is understood in terms of the Anderson-Higgs mechanism. Topological phase transitions are defined by global invariants that distinguish between phases of matter preserving the same symmetry, and they entail the closure of the energy gap. However, an analysis of the Bernevig-Hughes-Zhang model incorporating local interactions reveals that electronic correlations can significantly modify this paradigm [1].

Here we develop a theoretical framework, which we call Variational Gaussian Approximation [2], to identify the physical origin for the change of behavior of the topological transition. We demonstrate that dynamical quantum fluctuations can open a gap without any symmetry breaking [3]. Furthermore, we show that this phenomenon cannot be captured by a perturbative approach and is associated with the emergence of a massive Dirac fermion at the transition point, exhibiting Gross-Neveu critical behavior near the quantum critical endpoint. Our findings align with the concept of Symmetric Mass Generation recently proposed in [4], while conversely we identify the gap opening as a condensed matter analog of the Coleman-Weinberg mechanism.

[1] A. Amaricci, J. C. Budich, M. Capone, B. Trauzettel, and G. Sangiovanni. First- order character and observable signatures of topological

quantum phase transitions. Phys. Rev. Lett., 114:185701, May 2015. doi: 10.1103/PhysRevLett.114.185701.

[2] J. A. Hertz and M. A. Klenin. Fluctuations in itinerant-electron paramagnets. Phys. Rev. B, 10:1084–1096, Aug 1974.

doi: 10.1103/PhysRevB.10.1084.

[3] F. Paoletti, L. Fanfarillo, M. Capone, and A. Amaricci. Topological gap opening without symmetry breaking from dynamical quantum

correlations. Phys. Rev. B, 109:075148, Feb 2024. doi: 10.1103/PhysRevB.109.075148.

[4] J. Wang and Y.Z. You. Symmetric mass generation. Symmetry, 14(7), 2022. ISSN 2073-8994. doi: 10.3390/sym14071475