Rate of cluster decomposition via Fermat-Steiner point

Abstract

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 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.

Krylov Complexity of Fermionic and Bosonic Gaussian States

“…Recent studies have explored Krylov complexity across a range of intriguing domains. [ 28–39 ] Krylov complexity provides an unambiguous definition of complexity, allowing for a genuine intrinsic assessment of spread of quantum state within the Hilbert space. This significantly distinguishes Krylov complexity from other quantum complexity definitions.…”

Krylov complexity in a natural basis for the Schrödinger algebra

“…Krylov complexity is conjectured to grow at a maximal rate for chaotic systems, although there are subtleties that need to be taken into account, especially for quantum field theories due to their infinite degrees of freedom in contrast to ordinary quantum mechanical systems, see discussions in [3][4][5][6][7][8][9][10]. When one considers quantum many body systems such as spin chains it is more straightforward to produce evidence that Krylov complexity can for example distinguish between integrable and chaotic dynamics as was argued in [11][12][13].…”

“…We believe that there are two main reasons. First, Krylov complexity can be applied to any quantum system making it computationally available, at least in principle, for a plethora of different cases including but not limited to condensed matter and many-body systems [13][14][15][16][17], quantum and conformal field theories [3][4][5][18][19][20], open systems [21][22][23][24][25], topological phases of matter [26,27] and many other topics related to aspects of the above and not only [28][29][30][31]. Second, it is related by its construction to inherent properties and characteristic parameters of the system, namely the Hamiltonian and the Hilbert space that it defines.…”