Related papers: Krylov complexity as an order parameter for deconf…
We compare two order parameters for the deconfinement transition, induced by thermal and density effects, commonly used in the literature, namely the thermal and density evolution of the continuum threshold $s_{0}$, within the frame of the…
The simplest statistical-mechanical model of crystalline formation (or alloy formation) that includes electronic degrees of freedom is solved exactly in the limit of large spatial dimensions and infinite interaction strength. The solutions…
We develop an algorithm for computing the solution of a large system of linear ordinary differential equations (ODEs) with polynomial inhomogeneity. This is equivalent to computing the action of a certain matrix function on the vector…
We consider the statistics of the results of a measurement of the spreading operator in the Krylov basis generated by the Hamiltonian of a quantum system starting from a specified initial pure state. We first obtain the probability…
We present a Krylov space based theoretical framework for modeling inhomogeneous spin ensembles with arbitrary distributions of spin frequencies and couplings. The framework is then used to asymptotically large spin ensemble. In the…
The Krylov subspace methods, being one category of the most important classical numerical methods for linear algebra problems, can be much more powerful when generalised to quantum computing. However, quantum Krylov subspace algorithms are…
An a posteriori estimate for the error of a standard Krylov approximation to the matrix exponential is derived. The estimate is based on the defect (residual) of the Krylov approximation and is proven to constitute a rigorous upper bound on…
Duality places an important constraint on the renormalization group flows and the phase diagrams. For self-dual theories, the self-duality can be promoted as a symmetry, this leads to the multi-criticalities. This work investigates a…
We use methods of quantum field theory in toroidal topologies to study the $N$-component $D$-dimensional massive Gross-Neveu model, at zero and finite temperature, with compactified spatial coordinates. We discuss the behavior of the…
Thermalization of chaotic quantum many-body systems under unitary time evolution is related to the growth in complexity of initially simple Heisenberg operators. Operator growth is a manifestation of information scrambling and can be…
We summarize and extend evidence that the deconfinement phase transition in Yang-Mills theories can be viewed as change of effective non-perturbative degrees of freedom and of symmetries of their interactions. In short, the strings in four…
A Krylov subspace recycling method for the efficient evaluation of a sequence of matrix functions acting on a set of vectors is developed. The method improves over the recycling methods presented in [Burke et al., arXiv:2209.14163, 2022] in…
When a solution to an abstract inverse linear problem on Hilbert space is approximable by finite linear combinations of vectors from the cyclic subspace associated with the datum and with the linear operator of the problem, the solution is…
In a quantum many-body system, autocorrelation functions can determine linear responses nearby equilibrium and quantum dynamics far from equilibrium. In this letter, we bring out the connection between the operator complexity and the…
We compute the rate of growth of operator size in matrix models by probing the Lin-Maldacena class of geometries with classical probes. We consider massive point particle probes whose proper momentum equals the size of the gauge invariant…
Randomized block Krylov subspace methods form a powerful class of algorithms for computing the extreme eigenvalues of a symmetric matrix or the extreme singular values of a general matrix. The purpose of this paper is to develop new…
How can we define complexity in dS space from microscopic principles? Based on recent developments pointing towards a correspondence between a pair of double-scaled Sachdev-Ye-Kitaev (DSSYK) models/ 2D Liouville-de Sitter (LdS$_2$) field…
The effective potential of the order parameter for confinement is calculated within the variational approach to the Hamilton formulation of Yang-Mills theory. Compactifying one spatial dimension and using a background gauge fixing this…
We investigate the thermodynamics and phase structure of $SU(3)$ Yang-Mills theory on $\mathbb{T}^2\times\mathbb{R}^2$ in Euclidean spacetime in an effective-model approach. The model incorporates two Polyakov loops along two compactified…
We study the relation between the continuum threshold as function of the temperature $s_0(T)$ within finite energy sum rules and the trace of the Polyakov loop $\Phi$ in the framework of a nonlocal SU(2) chiral quark model, establishing a…