Collective excitations of holographic quantum liquids in a magnetic field

Abstract

Abstract:We use holography to study N = 4 supersymmetric SU (N c ) Yang-Mills theory in the large-N c and large-coupling limits coupled to a number N f N c of (n + 1)-dimensional massless supersymmetric hypermultiplets in the fundamental representation of SU (N c ), with n = 2, 3. We introduce a temperature T , a baryon number chemical potential µ, and a baryon number magnetic field B, and work in a regime with µ T, √ B. We study the collective excitations of these holographic quantum liquids by computing the poles in the retarded Green's function of the baryon number charge density operator and the associated peaks in the spectral function. We focus on the evolution of the collective excitations as we increase the frequency relative to T , i.e. the hydrodynamic/collisionless crossover. We find that for all B, at low frequencies the tallest peak in the spectral function is associated with hydrodynamic charge diffusion. At high frequencies the tallest peak is associated with a sound mode similar to the zero sound mode in the collisionless regime of a Landau Fermi liquid. The sound mode has a gap proportional to B, and as a result for intermediate frequencies and for B sufficiently large compared to T the spectral weight is strongly suppressed. We find that the hydrodynamic/collisionless crossover occurs at a frequency that is approximately B-independent.

A strongly coupled anyon material

“…Namely we find a sound-like mode that becomes gapped as ground state parameters are tuned. The difference between the original theory and the anyonised theory however is the following: a gapped zero sound in the original theory is a consequence of non-zero magnetic fields [10,11] while in the anyon theory it is a consequence of statistics. Curiously we shall also find the same qualitative behaviour for small statistical parameter although the zero sound mode will be distinct from that found in the large parameter regime.…”

“…Hence we should briefly review the physics of the D3-D5 probe brane at non-zero temperature, density and magnetic field. It is already well known that the strongly coupled theory described by the probe branes has zero sound and diffusion modes [10,11,[23][24][25]. Extending the Green's function to complex frequency and real momentum the diffusion mode is represented by a purely imaginary pole that starts at the origin as momentum goes to zero.…”

“…The result is two complex poles with opposite sign real parts i.e two imaginary poles join to produce two poles with real parts (see [11] for relevant diagrams). If the density is sufficiently large (see [11] for the meaning of sufficiently large) then the complex pole will have the dispersion relation associated with zero sound. When it is too small the resultant complex pole has a dispersion relation whose real part has a gradient closer to one.…”

“…It was observed that for small magnetic field in D3-D5 and D3-D7 probe brane systems [11] the qualitative motion of the poles at zero magnetic field continues to hold even though the zero sound mode becomes gapped [10,11,23]. This is because the thermal energy of the background is sufficiently high so as to overcome the gap.…”

“…Properties of the logarithm of the time component of the spectral function, log χ tt , for the D3-D5 system and its weakly anyonic counterpart against suitably normalised logarithms of frequency and momentum. The unusual axis normalisations are chosen to make comparison with the figures of [11] simple. Top: the time component of the spectral function of the D3-D5 system at non-zero temperature T , charge Q/(πV T ) = 10 6 N 5 and magnetic field B/(πT ) 2 = 10 3 (left) where V is the regulating spatial volume at the boundary.…”