Infinite boundary conditions for response functions and limit cycles within the infinite-system density matrix renormalization group approach demonstrated for bilinear-biquadratic spin-1 chains

摘要: Response functions $\langle\hat{A}_x(t)\hat{B}_y(0)\rangle$ for one-dimensional strongly correlated quantum many-body systems can be computed with matrix product state (MPS) techniques. Especially, when one is interested in spectral or dynamic structure factors of translation-invariant systems, the response some range $|x-y|<\ell$ needed. We demonstrate how number required time-evolution runs reduced substantially: (a) If finite-system simulations are employed, from $\ell$ to $2\sqrt{\ell}$. (b) To go beyond, employ infinite MPS (iMPS) such that two evolution suffice. this purpose, iMPS heterogeneous only around causal cone perturbation evolved time, i.e., simulation done so-called boundary conditions. Computing overlaps these states, spatially shifted relative each other, yields all distances $|x-y|$. As a specific application, we compute factor ground states bilinear-biquadratic spin-1 chains very high resolution and explain underlying low-energy physics. determine initial uniform simulations, infinite-system density-matrix renormalization group (iDMRG) employed. discuss that, depending on system chosen bond dimension, iDMRG cell size $n_c$ may converge non-trivial limit cycle length $m$. This then corresponds an enlarged unit $m n_c$.