13 research outputs found

### Chiral transport in curved spacetime via holography

We consider a holographic model of strongly interacting plasma with a
gravitational anomaly. In this model, we compute parity-odd responses of the
system at finite temperature and chemical potential to external electromagnetic
and gravitational fields. Working within the linearized fluid/gravity duality,
we performed the calculation up to the third order in gradient expansion.
Besides reproducing the chiral magnetic(CME) and vortical (CVE) effects we also
obtain gradient corrections to the CME and CVE due to the gravitational
anomaly. Additionally, we find energy-momentum and current responses to the
gravitational field similarly determined by the gravitational anomaly. The
energy-momentum response is the first purely gravitational transport effect
that has been related to quantum anomalies in holographic theories.Comment: 21 page

### Interactions Remove the Quantization of the Chiral Photocurrent at Weyl Points.

The chiral photocurrent or circular photogalvanic effect (CPGE) is a photocurrent that depends on the sense of circular polarization. In a disorder-free, noninteracting chiral Weyl semimetal, the magnitude of the effect is approximately quantized with a material-independent quantum e^{3}/h^{2} for reasons of band topology. We study the first-order corrections due to the Coulomb and Hubbatrd interactions in a continuum model of a Weyl semimetal in which known corrections from other bands are absent. We find that the inclusion of interactions generically breaks the quantization. The corrections are similar but larger in magnitude than previously studied interaction corrections to the (nontopological) linear optical conductivity of graphene, and have a potentially observable frequency dependence. We conclude that, unlike the quantum Hall effect in gapped phases or the chiral anomaly in field theories, the quantization of the CPGE in Weyl semimetals is not protected but has perturbative corrections in interaction strength

### Rate of cluster decomposition via Fermat-Steiner point

In quantum field theory with a mass gap correlation function between two
spatially separated operators decays exponentially with the distance. This
fundamental result immediately implies an exponential suppression of all higher
point correlation functions, but the predicted exponent is not optimal. We
argue that in a general quantum field theory the optimal suppression of a
three-point function is determined by total distance from the operator
locations to the Fermat-Steiner point. Similarly, for the higher point
functions we conjecture the optimal exponent is determined by the solution of
the Euclidean Steiner tree problem. We discuss how our results constrain
operator spreading in relativistic theories.Comment: 16 pages; journal version, appendix A adde

### Rate of Cluster Decomposition via Fermat-Steiner Point

In quantum field theory with a mass gap correlation function between two spatially separated operators decays exponentially with the distance. This fundamental result immediately implies an exponential suppression of all higher point correlation functions, but the predicted exponent is not optimal. We argue that in a general quantum field theory the optimal suppression of a three-point function is determined by total distance from the operator locations to the Fermat-Steiner point. Similarly, for the higher point functions we conjecture the optimal exponent is determined by the solution of the Euclidean Steiner tree problem. We discuss how our results constrain operator spreading in relativistic theories

### A Universal Operator Growth Hypothesis

We present a hypothesis for the universal properties of operators evolving
under Hamiltonian dynamics in many-body systems. The hypothesis states that
successive Lanczos coefficients in the continued fraction expansion of the
Green's functions grow linearly with rate $\alpha$ in generic systems, with an
extra logarithmic correction in 1d. The rate $\alpha$ --- an experimental
observable --- governs the exponential growth of operator complexity in a sense
we make precise. This exponential growth even prevails beyond semiclassical or
large-$N$ limits. Moreover, $\alpha$ upper bounds a large class of operator
complexity measures, including the out-of-time-order correlator. As a result,
we obtain a sharp bound on Lyapunov exponents $\lambda_L \leq 2 \alpha$, which
complements and improves the known universal low-temperature bound $\lambda_L
\leq 2 \pi T$. We illustrate our results in paradigmatic examples such as
non-integrable spin chains, the Sachdev-Ye-Kitaev model, and classical models.
Finally we use the hypothesis in conjunction with the recursion method to
develop a technique for computing diffusion constants.Comment: 18+9 pages, 10 figures, 1 table; accepted versio

### Direct Geometric Probe of Singularities in Band Structure

The band structure of a crystal may have points where two or more bands are
degenerate in energy and where the geometry of the Bloch state manifold is
singular, with consequences for material and transport properties. Ultracold
atoms in optical lattices have been used to characterize such points only
indirectly, e.g., by detection of an Abelian Berry phase, and only at
singularities with linear dispersion (Dirac points). Here, we probe
band-structure singularities through the non-Abelian transformation produced by
transport directly through the singular points. We prepare atoms in one Bloch
band, accelerate them along a quasi-momentum trajectory that enters, turns, and
then exits the singularities at linear and quadratic touching points of a
honeycomb lattice. Measurements of the band populations after transport
identify the winding numbers of these singularities to be 1 and 2,
respectively. Our work opens the study of quadratic band touching points in
ultracold-atom quantum simulators, and also provides a novel method for probing
other band geometry singularities

### Beyond the Berry Phase: Extrinsic Geometry of Quantum States

Consider a set of quantum states $| \psi(x) \rangle$ parameterized by $x$
taken from some parameter space $M$. We demonstrate how all geometric
properties of this manifold of states are fully described by a scalar
gauge-invariant Bargmann invariant $P^{(3)}(x_1, x_2,
x_3)=\operatorname{tr}[P(x_1) P(x_2)P(x_3)]$, where $P(x) = |\psi(x)\rangle
\langle\psi(x)|$. Mathematically, $P(x)$ defines a map from $M$ to the complex
projective space $\mathbb{C}P^n$ and this map is uniquely determined by
$P^{(3)}(x_1,x_2,x_3)$ up to a symmetry transformation. The phase $\arg
P^{(3)}(x_1,x_2,x_3)$ can be used to compute the Berry phase for any closed
loop in $M$, however, as we prove, it contains other information that cannot be
determined from any Berry phase. When the arguments $x_i$ of
$P^{(3)}(x_1,x_2,x_3)$ are taken close to each other, to the leading order, it
reduces to the familiar Berry curvature $\omega$ and quantum metric $g$. We
show that higher orders in this expansion are functionally independent of
$\omega$ and $g$ and are related to the extrinsic properties of the map of $M$
into $\mathbb{C}P^n$ giving rise to new local gauge-invariant objects, such as
the fully symmetric 3-tensor $T$. Finally, we show how our results have
immediate applications to the modern theory of polarization, calculation of
electrical response to a modulated field and physics of flat bands