Viacheslav Khrushchev

arXiv2026

QCommute: a tool for symbolic computation of nested commutators in quantum many-body spin-1/2 systems

We present QCommute, a software tool implemented in C++ for symbolic computation of nested commutators between a Hamiltonian and local observables in quantum many-body spin-1/2 systems on one-, two-, and three-dimensional hypercubic lattices. The computation is performed algebraically directly in the thermodynamic limit, and the Hamiltonian parameters are kept symbolic. Importantly, this way the entire parameter space is covered in a single run. The implementation supports extensive parallelization to achieve high computational performance. QCommute can serve as a computational backend for Heisenberg-picture approaches to quantum dynamics in strongly correlated regimes, ranging from direct Taylor expansion in time to advanced techniques such as the recursion method.

cond-mat.str-el↗

arXiv2026

Recursion method for quench dynamics: strengths and limitations

The recursion method, which solves coupled Heisenberg equations in a Lanczos operator basis, has recently emerged as a powerful nonperturbative tool for computing dynamical correlation functions in strongly correlated two- and three-dimensional quantum many-body systems. Motivated by this success, we investigate whether the method can be extended to expectation values of observables following a quantum quench. We find that such an extension encounters an obstacle absent in the computation of dynamical correlation functions. The latter are fully determined by the Lanczos coefficients $b_n$, which in generic systems exhibit universal behavior, enabling reliable extrapolation from the first few dozens of explicitly computed coefficients. In contrast, quench dynamics additionally requires "quench coefficients" $c_n$, defined as overlaps of Lanczos basis operators with the initial state. We show that, unlike the Lanczos coefficients, the quench coefficients exhibit no universal structure and cannot be reliably extrapolated, thereby limiting the time up to which the method yields accurate results. The behavior of quench coefficients is highly state-dependent, ranging from decaying to irregular or even growing sequences; typically, the less regular the sequence $c_n$, the shorter the accessible timescale. Nevertheless, for favorable initial states, the method remains competitive with state-of-the-art approaches. Moreover, its symbolic implementation allows a single computation to be reused across different Hamiltonian parameters and initial states, making it particularly advantageous in studies requiring extensive scans over Hamiltonian parameters or initial states.

cond-mat.str-el↗