# Spectral Function of a Boson Ladder in an Artificial Gauge Field

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## Abstract

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## 1. Introduction

## 2. Model

## 3. Spectral Function in the Meissner Phase for Weak Interchain Hopping

## 4. Spectral Function in the Vortex Phase for Weak Interchain Hopping

## 5. Spectral Functions in the Weakly Interacting Regime From Bosonization

## 6. Spectral Function in the Bogoliubov Theory

## 7. Conclusions

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Phase diagram for a hard-core bosonic system on a ladder as a function of flux per plaquette $\lambda $ and $\mathsf{\Omega}$, at the filling value $n=1$. The black solid line that joins solid dots is the phase boundary between the Meissner and the Vortex phase, while the dashed red line is the prediction for this boundary in the non-interacting system. In the insets, we show the different behavior of the spin-current ${J}_{s}\left(\lambda \right)$ for two values of interchain coupling $\mathsf{\Omega}$ when there is the Meissner–Vortex transition and where there is not, respectively, panel (b) for $\mathsf{\Omega}=1.25$ and (a) for $\mathsf{\Omega}=1.75$ DMRG simulation results at $L=64$ in PBC.

**Figure 2.**Schematic representation of the spectral function in the Meissner phase. The colored regions have a non-zero spectral weight. The violet region is the spectral weight coming only from the gapless charge modes, the spin modes remaining in their ground state. The green region represents the region where the gapped spin modes contribute to the spectral weight.

**Figure 3.**Spectral function ${A}_{\sigma}(q,\omega )$ as a function of $\omega /{\omega}_{1}^{\sigma}(q,\lambda )$ (on the top panels) for ${u}_{s}^{*}/{u}_{c}=0.5$ and ${K}_{s}^{*}=0.6$. In panel (

**a**) we show the typical situation in the Vortex phase (${K}_{c}=0.8$), while in panel (

**b**) we show the case ${K}_{c}=0.3$. In the

**lower panel**: ${A}_{\sigma}(q,\omega )$ as a function of $\omega $ and q for a fixed applied field $\lambda $ inducing a finite ${q}_{0}\left(\lambda \right)$ for ${u}_{s}^{*}/{u}_{c}=0.5$ with ${K}_{s}^{*}={K}_{c}=0.6$. Finite spectral weights are present only in the colored region. The dashed blue lines correspond to ${\omega}_{1}(q,\lambda )$ and ${\omega}_{1}(q,\lambda )$

**Figure 4.**Spectral function ${A}_{\uparrow}(q,\omega )$ as a function of $\omega $ and q for a fixed applied field $\lambda =\pi /2$, in the Meissner phase (left panel, $\mathsf{\Omega}/t=4$) and in the Vortex phase (right panel $\mathsf{\Omega}/t=1.2$), for mean-field interaction parameter $UN/\left({N}_{s}t\right)=0.6$ and number of sites ${N}_{s}=60$. Spectral lines are broadened by replacing a delta function with a Lorentzian (the width ${10}^{-14}$ in units of J is not visible on the scale of the figure, the broadening is mostly the pixelization of the image.

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**MDPI and ACS Style**

Citro, R.; De Palo, S.; Victorin, N.; Minguzzi, A.; Orignac, E.
Spectral Function of a Boson Ladder in an Artificial Gauge Field. *Condens. Matter* **2020**, *5*, 15.
https://doi.org/10.3390/condmat5010015

**AMA Style**

Citro R, De Palo S, Victorin N, Minguzzi A, Orignac E.
Spectral Function of a Boson Ladder in an Artificial Gauge Field. *Condensed Matter*. 2020; 5(1):15.
https://doi.org/10.3390/condmat5010015

**Chicago/Turabian Style**

Citro, Roberta, Stefania De Palo, Nicolas Victorin, Anna Minguzzi, and Edmond Orignac.
2020. "Spectral Function of a Boson Ladder in an Artificial Gauge Field" *Condensed Matter* 5, no. 1: 15.
https://doi.org/10.3390/condmat5010015