# More current with less particles due to power-law hopping

## TL;DR

This paper uncovers a universal transport phase in one-dimensional fermionic systems with power-law hopping, where reducing particles enhances transport, especially for decay exponents between 1 and 2, with potential experimental signatures.

## Contribution

It reveals a novel phase with divergent zero-temperature Drude weight at low filling in power-law hopping models, extending understanding of transport in non-local quantum systems.

## Key findings

- Divergent Drude weight for 1<α<2 at zero temperature and low filling.
- Persistent current signatures of this phase survive at finite temperature.
- Transport behavior differs from short-range systems, decaying as a power law with temperature.

## Abstract

We reveal interesting universal transport behavior of ordered one-dimensional fermionic systems with power-law hopping. We restrict ourselves to the case where the power-law decay exponent $\alpha>1$, so that the thermodynamic limit is well-defined. We explore the quantum phase-diagram of the non-interacting model in terms of the zero temperature Drude weight, which can be analytically calculated. Most interestingly, we reveal that for $1<\alpha<2$, there is a phase where the zero temperature Drude weight diverges as filling fraction goes to zero. Thus, in this regime, counter intuitively, reducing number of particles increases transport and is maximum for a sub-extensive number of particles. Being a statement about zero-filling, this transport behavior is immune to adding number conserving interaction terms. We have explicitly checked this using two different interacting systems. We propose that measurement of persistent current due to a flux through a mesoscopic ring with power-law hopping will give an experimental signature of this phase. In persistent current, the signature of this phase survives up to a finite temperature for a finite system. At higher temperatures, a crossover is seen. The maximum persistent current shows a power-law decay at high temperatures. This is in contrast with short ranged systems, where the persistent current decays exponentially with temperature.