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Author ORCID Identifier


Open Access Dissertation

Document Type


Degree Name

Doctor of Philosophy (PhD)

Degree Program


Year Degree Awarded


Month Degree Awarded


First Advisor

Tigran Sedrakyan

Second Advisor

Nikolay Prokof’ev

Third Advisor

Boris Svistunov

Fourth Advisor

Owen Gwilliam

Subject Categories

Condensed Matter Physics | Quantum Physics | Statistical, Nonlinear, and Soft Matter Physics


Quantum criticality in low-dimensional quantum systems is known to host exotic behaviors. In quantum one-dimension (1D), the emerging conformal group contains infinite generators, and conformal techniques, e.g., operator product expansion, give accurate and universal descriptions of underlying systems. In quantum two-dimension (2D), the electronic interaction causes singular corrections to Fermi-liquids characteristics. Meanwhile, the Dirac fermions in topological 2D materials can greatly enrich emerging phenomena. In this thesis, we study the symmetry-breaking effects of low-dimensional quantum criticality. In 1D, we consider two cases: time-reversal symmetry (TRS) breaking in the Majorana conformal field theory (CFT) and the absence of conformal symmetry in the $z=2$ Lifshitz criticality. In both cases, universal features of quantum criticality exhibit exotic behaviors, e.g., the finite-size amplitude and entanglement entropy. In 2D, we study the effect of a weak perpendicular magnetic field on the doped graphene. We establish the chiral symmetry breaking mechanism induced by the field and explore its many-body consequences, e.g., thermodynamics and magnetoresistance.


Creative Commons License

Creative Commons Attribution 4.0 License
This work is licensed under a Creative Commons Attribution 4.0 License.