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arXiv:1201.1764 · Physical review. D. Particles, fields, gravitation, and cosmology/Physical review. D. Particles and fields

Fermions on a Lifshitz background

Mohsen Alishahiha, M. Reza Mohammadi Mozaffar, Ali Mollabashi

Published Jul 3, 2012• 44 citations
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Abstract

We study a nonrelativistic fermionic retarded Green's function by making use of a fermion on the Lifshitz geometry with critical exponent $z=2$. With a natural boundary condition, respecting the symmetries of the model, the resultant retarded Green's function exhibits a number of interesting features including a flat band. We also study the finite temperature and finite chemical potential cases where the geometry is replaced by Lifshitz black hole solutions.

DOI
10.1103/physrevd.86.026002

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We study a nonrelativistic fermionic retarded Green's function by making use of a fermion on the Lifshitz geometry with critical exponent z=2z=2z=2. With a natural boundary condition, respecting the symmetries of the model, the resultant retarded Green's function exhibits a number of interesting features including a flat band. We also study the finite temperature and finite chemical potential cases where the geometry is replaced by Lifshitz black hole solutions.
We examine the behavior of the retarded Green's function in theories with Lifshitz scaling symmetry, both through dual gravitational models and a directeld theory approach. In contrast with the case of a relativistic CFT, where the Green's function is �xed (up to normalization) by symmetry, the generic Lifshitz Green's function can a priori depend on an arbitrary function G(^!), where ^ ! = !=j ~ kj z is the scale-invariant ratio of frequency to wavenumber, with dynamical exponent z. Nevertheless, we demonstrate that the imaginary part of the retarded Green's function (i.e. the spectral function) of scalar operators is exponentially suppressed in a window of frequencies near zero. This behavior is universal in all Lifshitz theories without additional constraining symmetries. On the gravity side, this result is robust against higher derivative corrections, while on theeld theory side we present two z = 2 examples where the exponential suppression arises from summing the perturbative expansion to innite order.
Some of the most interesting phenomena in condensed matter occur in high-temperature superconductors and heavy fermions, and arise from a parent non-Fermi-liquid background. Although the non-Fermi-liquid phase has metallic character, it is very different from typical metals in that the electronic excitations are not particlelike (no quasiparticles), and this has lead to these phases eluding a clear theoretical description. Here, the authors develop a model that provides a route to describe non-Fermi liquids realized in condensed matter systems. Building on the zero-dimensional Sachdev-Ye-Kitaev model that is inspired by connections between a non-Fermi liquid and black holes, the authors construct a model in a lattice system where the bands touch to give a divergent density of states (Lifshitz point). The resulting non-Fermi-liquid phases exhibit intriguing properties such as scaling symmetry, nontrivial power-law dependence of entropy on temperature, and fast information scrambling with rate linear in temperature, as well as dynamical transitions to more conventional phases with well-defined quasiparticles.
From ultracold atoms to quantum chromodynamics, reliable ab initio studies of strongly interacting fermions require numerical methods, typically in some form of quantum Monte Carlo calculation. Unfortunately, (non)relativistic systems at finite density (spin polarization) generally have a sign problem, such that those ab initio calculations are impractical. It is well-known, however, that in the relativistic case imaginary chemical potentials solve this problem, assuming the data can be analytically continued to the real axis. Is this feasible for nonrelativistic systems? Are the interesting features of the phase diagram accessible in this manner? By introducing complex chemical potentials, for real total particle number and imaginary polarization, the sign problem is avoided in the nonrelativistic case. To give a first answer to the above questions, we perform a mean-field study of the finite-temperature phase diagram of spin-1/2 fermions with imaginary polarization.
A bstract In this note, we reexamine decoherence effects in quantum field theories with gravity duals. The thought experiment proposed in [1, 2], which reveals novel decoherence patterns associated with black holes, also manifests itself from the perspective of the boundary theory. In particular, we consider a moving mirror coupled to quantum critical theories characterized by a dynamical exponent z that are dual to asymptotically Lifshitz geometries. The interference experiment occurs on the boundary, where a superposition of two spatially separated quantum states of a mirror is maintained for a finite time τ 0 before recombination. We find that the interaction with a quantum field at finite temperature, arising from the presence of a Lifshitz black hole, leads to a constant decoherence rate. In contrast, for the zero-temperature case corresponding to pure Lifshitz spacetime, the decoherence rate vanishes in the large-time limit τ 0 → ∞. Remarkably, in the zero-temperature regime, the decoherence exhibits a power-law decay at large τ 0 as z → ∞, a behavior reminiscent of the decoherence patterns seen in extremal black hole geometries. In addition, we investigate the decoherence of one particle in an EPR pair constructed holographically. Our results indicate that causality plays a crucial role in determining whether the entanglement leads to the suppression of decoherence in the other particle.