  We investigate the evolution of holographic entanglement entropy (HEE) and
holographic complexity (HC) under a thermal quench in Einstein-Maxwell-Axion
theory (EMA), which is dual to a field theory with momentum relaxation on the
boundary. A strip-shaped boundary geometry is utilized to calculate HEE and HC
via `entropy=surface' and `complexity=volume' conjecture, respectively. By
fixing other parameters we claim that either large enough black hole charge or
width of the strip will introduce swallow-tail behaviors in HEE and
multi-values in HC due to the discontinuity of the minimum
Hubeny-Rangamani-Takayanagi (HRT) surface. Meanwhile, we explore the effects of
momentum relaxation on the evolution of HEE and HC. The results present that
the momentum relaxation will suppress the discontinuity to occur as it
increases. For large enough momentum relaxation the continuity of HEE and HC
will be recovered.
