SciPost Phys. Lect. Notes 11 (2019) ·
published 4 December 2019
|
· pdf
Perhaps the most important aspect of symmetry in physics is the idea that a
state does not need to have the same symmetries as the theory that describes
it. This phenomenon is known as spontaneous symmetry breaking. In these lecture
notes, starting from a careful definition of symmetry in physics, we introduce
symmetry breaking and its consequences. Emphasis is placed on the physics of
singular limits, showing the reality of symmetry breaking even in small-sized
systems. Topics covered include Nambu-Goldstone modes, quantum corrections,
phase transitions, topological defects and gauge fields. We provide many
examples from both high energy and condensed matter physics. These notes are
suitable for graduate students.
SciPost Phys. 7, 071 (2019) ·
published 29 November 2019
|
· pdf
I studied the non-equilibrium response of an initial N\'{e}el state under
time evolution with the Kitaev honeycomb model. With isotropic interactions
($J_x = J_y = J_z$) the system quickly loses its antiferromagnetic order and
crosses over into a steady state valence bond solid, which can be inferred from
the long-range dimer correlations. There is no signature of a dynamical phase
transition. Upon including anisotropy ($J_x = J_y \neq J_z$), an exponentially
long prethermal regime appears with persistent magnetization oscillations whose
period derives from an effective toric code.
