Exact ground states and correlation functions of chain and ladder models of interacting hardcore bosons or spinless fermions

TL;DR

This paper derives exact ground states and correlation functions for one-dimensional and ladder models of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion, revealing surprising power-law decay behaviors.

Contribution

It introduces a novel mapping and the intervening-particle expansion to compute correlation functions exactly in these strongly interacting models.

Findings

Correlation functions decay with unexpected power-law exponents.

Exact ground states are mapped to the one-dimensional Fermi sea.

Results apply to both chain and ladder models with infinite repulsion.

Abstract

By removing one empty site between two occupied sites, we map the ground states of chains of hardcore bosons and spinless fermions with infinite nearest-neighbor repulsion to ground states of chains of hardcore bosons and spinless fermions without nearest-neighbor repulsion respectively, and ultimately in terms of the one-dimensional Fermi sea. We then introduce the intervening-particle expansion, where we write correlation functions in such ground states as a systematic sum over conditional expectations, each of which can be ultimately mapped to a one-dimensional Fermi-sea expectation. Various ground-state correlation functions are calculated for the bosonic and fermionic chains with infinite nearest-neighbor repulsion, as well as for a ladder model of spinless fermions with infinite nearest-neighbor repulsion and correlated hopping in three limiting cases. We find that the decay of these correlation functions are governed by surprising power-law exponents.