Density-curvature response and gravitational anomaly

Area of Science:

• Condensed matter physics
• Theoretical physics

Background:

• Two-dimensional gapped systems are crucial in condensed matter physics.
• Background magnetic fields significantly alter system responses.
• Galilean invariance is a fundamental symmetry principle.

Purpose of the Study:

• To investigate constraints imposed by Galilean invariance on physical responses.
• To derive exact relations between response functions in gapped systems.
• To uncover novel relationships beyond established ones.

Main Methods:

• Applying Ward identities to derive exact relations.
• Analyzing linear electromagnetic and elastic responses.
• Considering systems in a background magnetic field.

Main Results:

• Derived exact relations between response functions based on Galilean invariance.
• Confirmed known viscosity-conductivity relations.
• Discovered new relations involving density-curvature and thermal Hall responses.

Conclusions:

• Galilean invariance provides powerful constraints on system responses.
• The derived relations offer new insights into the behavior of 2D gapped systems.
• This work extends the understanding of transport phenomena in magnetic fields.