Randomness & quantum criticality
Randomness can change the universality of a quantum critical point or generate critical states through dynamics. I study both quenched disorder in Hamiltonians and random non-unitary evolution, focusing on how spatial and temporal randomness affect correlations and entanglement. Developing analytical descriptions that can be tested against numerical calculations is central to understanding the resulting scaling behavior.
Papers
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Entanglement entropy of (2+1)D quantum critical points with quenched disorder: Dimensional reduction approach
Physical Review B 106, 195152 (2022)
We develop a dimensional-reduction method for entropy calculations at disordered (2+1)-dimensional quantum critical points. Applied to Dirac fermions in a random magnetic field, it reveals area-law entanglement with a disorder-dependent coefficient. We also derive a universal subleading term controlled by the correlation length and disorder strength, linking entanglement to the scaling of disordered critical points.
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Quantum criticality in the nonunitary dynamics of (2+1)-dimensional free fermions
Physical Review B 103, 174303 (2021)
Non-unitary evolution with randomness in space and time drives two-dimensional free fermions into a critical steady state over a continuous range of non-unitary strengths. We find a logarithmic violation of the entanglement area law, algebraic correlations, and dynamical scaling with z = 1. A quasiparticle-pair picture explains the entanglement scaling, while a classical nonlinear master equation captures the evolution of correlations.