Measuring the imaginary-time dynamics of quantum materials

ABSTRACT

Theoretical analysis typically involves imaginary-time correlation functions. Inferring real-time dynamical response functions from this information is notoriously difficult. However, as we articulate here, it is straightforward to compute imaginary-time correlators from the measured frequency dependence of (real-time) response functions. In addition to facilitating comparison between theory and experiment, the proposed approach can be useful in extracting certain aspects of the (long-time relaxational) dynamics from a complex data set. We illustrate this with an analysis of the nematic response inferred from Raman scattering spectroscopy on the iron-based superconductor $\mathrm{B}\mathrm{a}(\mathrm{F}{\mathrm{e}}_{1-\mathrm{x}}\mathrm{C}{\mathrm{o}}_{\mathrm{x}}{)}_2\mathrm{A}{\mathrm{s}}_2$, which includes a new method for identifying a putative quantum-critical contribution to that response.

KEYWORDS:

• Quantum critical phenomena
• spectroscopy
• strongly correlated electrons

Acknowledgments

We acknowledge helpful discussions with A. Baum, M. Randeria, R. Scalettar and N. Trivedi. D. J. and R. H. gratefully acknowledge the hospitality of the the Stanford Institute for Materials and Energy Sciences (SIMES) at Stanford University and SLAC National Accelerator Laboratory. Financial support for the work came, in part, from the Friedrich-Ebert-Stiftung (D.J.), the Deutsche Forschungsgemeinschaft (DFG) via the Priority Program SPP 1458 (D. J., T. B. and R. H. project no. HA 2071/7-2), the Collaborative Research Center TRR 80 (D. J. and R. H., Project ID 107745057), and the Bavaria California Technology Center BaCaTeC (S. A. K., D. J. and R. H., project no. 21[2016-2]). S. A. K. was supported in part by NSF grant $\mathrm{\#}$ DMR-1608055 at Stanford, S. L. was supported by a Bethe/KIC fellowship at Cornell, and E. B. was supported by the European Research Council under grant HQMAT ($\mathrm{\#}817799$) and by the Minerva foundation.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

We acknowledge helpful discussions with A. Baum, M. Randeria, R. Scalettar and N. Trivedi. D.J. and R.H. gratefully acknowledge the hospitality of the the Stanford Institute for Materials and Energy Sciences (SIMES) at Stanford University and SLAC National Accelerator Laboratory. Financial support for the work came, in part, from the Friedrich-Ebert-Stiftung (D.J.), the Deutsche Forschungsgemeinschaft (DFG) via the Priority Program SPP 1458 (D.J., T.B. and R.H. project no. HA 2071/7-2), the Collaborative Research Center TRR80 (D.J. and R.H., Project ID 107745057) and the Bavaria California Technology Center BaCaTeC (S.A.K., D.J. and R.H., project no. 21[2016-2]). S.A.K. was supported in part by NSF grant $\mathrm{\#}$ DMR-1608055 at Stanford, S.L. was supported by a Bethe/KIC fellowship at Cornell and E.B. was supported by the European Research Council under grant HQMAT ($\mathrm{\#}817799$) and by the Minerva foundation.