Related papers: Operator growth bounds in a cartoon matrix model
We develop a Hamiltonian formalism for simulating interacting chiral fermions on the lattice while preserving unitarity and locality and without breaking the chiral symmetry. The fermion doubling problem is circumvented by constructing a…
We discuss the probability distribution for the "size" of a time-evolving operator in the SYK model. Scrambling is related to the fact that as time passes, the distribution shifts towards larger operators. Initially, the rate is exponential…
We use Majorana operators to study entanglement dynamics under random free fermion unitary evolution and projective measurements in one dimension. For certain choices of unitary evolution, namely those which swap neighboring Majorana…
To investigate the properties of the large $N$ limit of $\mathcal{N} = 1$ SUSY Yang-Mills theory, we have started a study for a reduced matrix model with an adjoint Majorana fermion. The gauge action is based on the Wilson action and the…
We study a class of models in which $N$ flavors of massless fermions on the half line are coupled by an arbitrary orthogonal matrix to $N$ rotors living on the boundary. Integrating out the rotors, we find the exact partition function and…
We propose that the size of an operator evolved under holographic renormalization group flow shall grow linearly with the scale and interpret this behavior as a manifestation of the saturation of the chaos bound. To test this conjecture, we…
We consider the Brownian SYK model of $N$ interacting Majorana fermions, with random couplings that are taken to vary independently at each time. We study the out-of-time-ordered correlators (OTOCs) of arbitrary observables and the…
We consider the exchange statistics of vortices, each of which traps an odd number ($N$) of Majorana fermions. We assume that the fermions in a vortex transform in the vector representation of the SO(N) group. Exchange of two vortices turns…
We investigate operator growth in a Brownian spin Sachdev--Ye--Kitaev (SYK) model with random all-to-all interactions, focusing on the full operator-size distribution. For Hamiltonians containing interactions of order two up to $L$, we…
Our objects of study are two-dimensional canonical systems that arise from indeterminate Hamburger moment problems and associated half-line Jacobi operators in limit circle case. The monodromy matrix of such a system coincides, up to a…
We propose a random matrix model as a representation for $D=1$ open strings. We show that the model is equivalent to $N$ fermions with spin in a central potential that also includes a long-range ferromagnetic interaction between the…
We investigate a one-dimensional free fermion model with nearest and next-nearest neighbor hopping, evolving in imaginary time from a product state with N consecutive fermions, and conditioned to go back to the same state after a given…
We analyze $(2+1)$-dimensional vector-vector type four-Fermi interaction (Thirring) model in the framework of the $1/N$ expansion. By solving the Dyson-Schwinger equation in the large-$N$ limit, we show that in the two-component formalism…
We formulate general plant-herbivore interaction models with monotone plant growth functions (rates). We study the impact of monotone plant growth functions in general plant-herbivore models on their dynamics. Our study shows that all…
Recently, a hypothesis on the complexity growth of unitarily evolving operators was presented. This hypothesis states that in generic, non-integrable many-body systems the so-called Lanczos coefficients associated with an autocorrelation…
We study a so-called semi-ergodic brickwork dual-unitary circuits where, in the infinite volume limit, the two-point correlation functions of single-site operators exhibit ergodic behavior along one light ray and non-ergodic behavior along…
We study theoretically entanglement and operator growth in a spin system coupled to an environment, which is modeled with classical dephasing noise. Using exact numerical simulations we show that the entanglement growth and its fluctuations…
A network of agents interacting both with competitive and/or cooperative mechanisms is modeled by using fermionic ladder operators. The time evolution of the network is assumed to be governed by a Hermitian time-independent Hamiltonian…
The phase structure of Nambu-Jona-Lasinio model with N-component fermions in curved space-time is studied in the leading order of the 1/N expansion. The effective potential for composite operator $\bar{\psi}\psi$ is calculated by using the…
In the theory of linear switching systems with discrete time, as in other areas of mathematics, the problem of studying the growth rate of the norms of all possible matrix products $A_{\sigma_{n}}\cdots A_{\sigma_{0}}$ with factors from a…