Attraction from frustration in ladder systems

Abstract

We analyze the formation of multi-particle bound states in ladders with frustrated kinetic energy in two component bosonic and two component fermionic systems. We focus on the regime of light doping relative to insulating states at half-filling, spin polarization close to 100 percent, and strong repulsive interactions. A special feature of these systems is that the binding energy scales with single particle tunneling t rather than exchange interactions, since effective attraction arises from alleviating kinetic frustration. For two component Fermi systems on a zigzag ladder we find a bound state between a hole and a flipped spin (magnon) with a binding energy that can be as large as 0.6t. We demonstrate that magnon-hole attraction leads to formation of clusters comprised of several holes and magnons and expound on antiferromagentic correlations for the transverse spin components inside the clusters. We identify several many-body states that result from selforganization of multi-particle bound states, including a Luttinger liquid of hole -magnon pairs and a density wave state of two hole -three magnon composites. We establish a symmetry between the spectra of Bose and Fermi systems and use it to establish the existence of antibound states in two component Bose mixtures with SU(2) symmetric repulsion on a zigzag ladder. We also consider Bose and Fermi systems on a square ladder with flux and demonstrate that both systems support bound states. We discuss experimental signatures of multi-particle bound states in both equilibrium and dynamical experiments. We point out intriguing connections between these systems and the quark bag model in QCD.

A two-dimensional programmable tweezer array of fermions

“…For example, two-leg triangular ladder systems can be used to explore the J 1 − J 2 model, including the special case of the Majumdar-Ghosh model and its valence-bond solid ground states [45]. Furthermore, upon introducing spin-imbalance and hole-doping, a triangular two-leg ladder is predicted to host magnon-hole binding at energy scales set by the tunneling, rather than the superexchange [46]. Multi-leg triangular ladders may potentially host other exotic states such as a chiral spin liquid at half filling and intermediate U/t that evolves to a 120 •antiferromagnetic order at strong U/t [47].…”

Site-resolved observables in the doped spin-imbalanced triangular Hubbard model

“…We interpret this as signatures for repulsive pairing effects between the minority (|↓ ) and holes as discussed in refs. [42,43]. This spin-hole relationship can also be probed experimentally.…”

Exploring kinetically induced bound states in triangular lattices with ultracold atoms: Spectroscopic approach

“…This phenomenon can arise when a lattice exhibits closed loops composed of either an odd or even number of links. In this scenario, different quantum propagation paths of a single hole destructively interfere due to their opposite contribution to the energy when the hopping integral is positive (t > 0) [1,82,[94][95][96]. This obstruction to kinetic energy of a hole can be alleviated if the hole binds a spin flip excitation.…”

“…On the theoretical side, most efforts have been focused on understanding magnetic polarons in square lattices, with similar results expected to hold for all bipartite lattices [52,. However several theoretical studies considered non-bipartite triangular lattices and pointed out intriguing effects of frustration on magnetic polarons [1,[82][83][84][85]. Specifically, antiferromagnetic polarons appear when a Mott insulator in a triangular lattice is doped with a low density of holes.…”

“…The characteristic binding energy of such composite objects is determined by the tunneling strength and not the superexchange interaction. This makes them promising candidates for experimental studies with cold atoms simulators, which are still limited in how low they can go in temperature [1,82]. In particular, recent cold atom experiments have simulated the Hubbard model in the triangular lattice [2][3][4][86][87][88] and explored the emergence of kinetic magnetism with fermionic atoms loaded in triangular geometries [2].…”