Energetical self-organization of a few strongly interacting particles

TL;DR

This paper investigates the quantum self-organization of few strongly interacting particles on a 2D Hubbard lattice, revealing persistent bond order, distinct phases, and topological invariants across ground and excited states.

Contribution

It introduces a novel analysis using Euler characteristics to quantify bond order and identifies new quantum phases and topological features in strongly interacting particle systems.

Findings

Bond order persists for strong interactions at various fillings.

Distinct density-wave and clustering phases are identified.

Excited states exhibit self-tuned superpositions maintaining topological invariants.

Abstract

We study the quantum self-organization of a few interacting particles with strong short-range interactions. The physical system is modeled via a 2D Hubbard square lattice model, with a nearest-neighbor interaction term of strength U and a second nearest-neighbor hopping t. For t=0 the energy of the system is determined by the number of bonds between particles that lie on adjacent sites in the Hubbard lattice. We find that this bond order persists for the ground and some of the excited states of the system, for strong interaction strength, at different fillings of the system. For our analysis we use the Euler characteristic of the network/graph grid structures formed by the particles in real space (Fock states), which helps to quantify the energetical(bond) ordering. We find multiple ground and excited states, with integer Euler numbers, whose values persist from the $t=0$ case, for strong interaction $U>>t$. The corresponding quantum phases for the ground state contain either density-wave-order(DWO) for low fillings, where the particles stay apart form each other, or clustering-order(CO) for high fillings, where the particles form various structures as they condense into clusters. In addition, we find various excited states containing superpositions of Fock states, whose probability amplitudes are self-tuned in a way that preserves the integer value of the Euler characteristic from the $t=0$ limit.