SciPost Submission Page
Lattice Bose polarons at strong coupling and quantum criticality
by Ragheed Alhyder, Victor E. Colussi , Matija Čufar, Joachim Brand, Alessio Recati, Georg M. Bruun
This Submission thread is now published as
Submission summary
| Authors (as registered SciPost users): | Ragheed Alhyder · Joachim Brand · Victor Colussi |
| Submission information | |
|---|---|
| Preprint Link: | scipost_202502_00004v3 (pdf) |
| Date accepted: | June 16, 2025 |
| Date submitted: | June 10, 2025, 12:51 a.m. |
| Submitted by: | Alhyder, Ragheed |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
|
| Approaches: | Theoretical, Computational |
Abstract
The problem of mobile impurities in quantum baths is of fundamental importance in many-body physics. There has recently been significant progress regarding our understanding of this due to cold atom experiments, but so far it has mainly been concerned with cases where the bath has no or only weak interactions, or the impurity interacts weakly with the bath. Here, we address this gap by developing a new theoretical framework for exploring a mobile impurity interacting strongly with a highly correlated bath of bosons in the quantum critical regime of a Mott insulator (MI) to superfluid (SF) quantum phase transition. Our framework is based on a powerful quantum Gutzwiller (QGW) description of the bosonic bath combined with diagrammatic field theory for the impurity-bath interactions. By resuming a selected class of diagrams to infinite order, a rich picture emerges where the impurity is dressed by the fundamental modes of the bath, which change character from gapped particle-hole excitations in the MI to Higgs and gapless Goldstone modes in the SF. This gives rise to the existence of several quasiparticle (polaron) branches with properties reflecting the strongly correlated environment. In particular, one polaron branch exhibits a sharp cusp in its energy, while a new ground-state polaron emerges at the $O(2)$ quantum phase transition point for integer filling, which reflects the nonanalytic behavior at the transition and the appearance of the Goldstone mode in the SF phase. Smooth versions of these features are inherited in the polaron spectrum away from integer filling because of the varying ``Mottness" of the bosonic bath. We furthermore compare our diagrammatic results with quantum Monte Carlo calculations, obtaining excellent agreement. This accuracy is quite remarkable for such a highly non-trivial case of strong interactions between the impurity and bosons in a maximally correlated quantum critical regime, and it establishes the utility of our framework. Finally, our results show how impurities can be used as quantum sensors and highlight fundamental differences between experiments performed at a fixed particle number or a fixed chemical potential.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
In practice, however we agree with the referee that it is more intuitive to show the diagrams in a way that can be employed for the zero-temperature ladder summations used throughout the text. Therefore, we have changed the labeling of the $W$-processes such that $\hat{W}_1$ matches the orientation of $\hat{U}_1$ and likewise for $\hat{W}_2$ and $\hat{U}_2$. This can be seen in the updated Fig. 2a. and Eqs. (10) and (11) and is reflected throughout the text. Furthermore, we have added additional text on lines 126, 174, 181, 441, and 770. In particular, the addition on line 126 clarifies that the coefficients $v_{\lambda, {\bf k}, n}$ and $u_{\lambda, {\bf k}, n}$ can be chosen to be real, which makes evident the properties of the vertices mentioned above. We hope that with this more intuitive diagrammatic representation, it is clarified for the reader how the processes can be linked to construct diagrams describing different zero-temperature observables.
For completeness, we note that in App.~A.5, Fig.~12 the alternative (equivalent) diagrammatic representations of the $\hat{W}_1$ and $\hat{W}_2$ processes are needed to evaluate the general Bethe-Salpeter equation due to the possibility of back-propagating bath excitation lines. We have added additional text in line 855 bringing this to the reader's attention.
List of changes
Summary of changes
Here we detail changes to the manuscript that were made in addition to those discussed already above.
1. Line 738: The word `isotropic' was inserted to describe processes where the momentum orientation is unimportant.
2. Figure 2: The vertex $W_1$ was changed to show the variation which makes it more consistent with the overall formalism.
2. Figure 8: The caption was updated to clarify that the magnitude of the lattice momentum was held fixed in all subplots.
Published as SciPost Phys. 19, 002 (2025)