Pseudomode expansion of many-body correlation functions

TL;DR

This paper introduces a pseudomode expansion method for many-body correlation functions using the Heisenberg recursion approach, enabling efficient approximations with few pseudomodes in dissipative quantum systems.

Contribution

It develops a novel pseudomode expansion framework based on the Heisenberg recursion method and artificial dissipation, providing a new way to approximate many-body correlations.

Findings

Fast convergence of the expansion with few pseudomodes.

Effective approximation of autocorrelation functions in quantum spin models.

Localization in Krylov space aids the expansion's efficiency.

Abstract

We present an expansion of a many-body correlation function in a sum of pseudomodes -- exponents with complex frequencies that encompass both decay and oscillations. The pseudomode expansion emerges in the framework of the Heisenberg version of the recursion method. This method essentially solves Heisenberg equations in a Lanczos tridiagonal basis constructed in the Krylov space of a given observable. To obtain pseudomodes, we first add artificial dissipation satisfying the dissipative generalization of the universal operator growth hypothesis, and then take the limit of the vanishing dissipation strength. Fast convergence of the pseudomode expansion is facilitated by the localization in the Krylov space, which is generic in the presence of dissipation and can survive the limit of the vanishing dissipation strength. As an illustration, we present pseudomode expansions of infinite-temperature autocorrelation functions in the quantum Ising and $XX$ spin-$1/2$ models on the square lattice. It turns out that it is enough to take a few first pseudomodes to obtain a good approximation to the correlation function.