Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study
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2024
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| author | Jha, Rishabh Kehrein, Stefan Louw, Jan C. |
| author_facet | Jha, Rishabh Kehrein, Stefan Louw, Jan C. |
| contents | We present a functional-based approach to compute thermal expectation values for actions expressed in the $G-Σ$ formalism, applicable to any time sequence ordering. Utilizing this framework, we analyze the linear response to an electric field in various Sachdev-Ye-Kitaev (SYK) chains. We consider the SYK chain where each dot is a complex $q/2$-body interacting SYK model, and we allow for $r/2$-body nearest-neighbor hopping where $r=κq$. We find exact analytical expressions in the large-$q$ limit for conductivities across all temperatures at leading order in $1/q$ for three cases, namely $κ= \{ 1/2, 1, 2\}$. When $κ= \{1/2, 1\}$, we observe linear-in-temperature $T$ resistivities at low temperatures, indicative of strange metal behavior. Conversely, when $κ= 2$, the resistivity diverges as a power law at low temperatures, namely as $1/T^2$, resembling insulating behavior. As $T$ increases, there is a crossover to Fermi liquid behavior ($\sim T^2$) at the minimum resistivity. Beyond this, another crossover occurs to strange metal behavior ($\sim T$). In comparison to previous linear-in-$T$ results in the literature, we also show that the resistivity behavior exists even below the MIR bound, indicating a true strange metal instead of a bad metal. In particular, we find for the $κ= 2$ case a smooth crossover from an insulating phase to a Fermi liquid behavior to a true strange metal and eventually becoming a bad metal as temperature increases. We extend and generalize previously known results on resistivities to all temperatures, do a comparative analysis across the three models where we highlight the universal features and invoke scaling arguments to create a physical picture out of our analyses. Remarkably, we find a universal maximum DC conductivity across all three models when the hopping coupling strength becomes large. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2407_20733 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study Jha, Rishabh Kehrein, Stefan Louw, Jan C. Strongly Correlated Electrons Quantum Physics We present a functional-based approach to compute thermal expectation values for actions expressed in the $G-Σ$ formalism, applicable to any time sequence ordering. Utilizing this framework, we analyze the linear response to an electric field in various Sachdev-Ye-Kitaev (SYK) chains. We consider the SYK chain where each dot is a complex $q/2$-body interacting SYK model, and we allow for $r/2$-body nearest-neighbor hopping where $r=κq$. We find exact analytical expressions in the large-$q$ limit for conductivities across all temperatures at leading order in $1/q$ for three cases, namely $κ= \{ 1/2, 1, 2\}$. When $κ= \{1/2, 1\}$, we observe linear-in-temperature $T$ resistivities at low temperatures, indicative of strange metal behavior. Conversely, when $κ= 2$, the resistivity diverges as a power law at low temperatures, namely as $1/T^2$, resembling insulating behavior. As $T$ increases, there is a crossover to Fermi liquid behavior ($\sim T^2$) at the minimum resistivity. Beyond this, another crossover occurs to strange metal behavior ($\sim T$). In comparison to previous linear-in-$T$ results in the literature, we also show that the resistivity behavior exists even below the MIR bound, indicating a true strange metal instead of a bad metal. In particular, we find for the $κ= 2$ case a smooth crossover from an insulating phase to a Fermi liquid behavior to a true strange metal and eventually becoming a bad metal as temperature increases. We extend and generalize previously known results on resistivities to all temperatures, do a comparative analysis across the three models where we highlight the universal features and invoke scaling arguments to create a physical picture out of our analyses. Remarkably, we find a universal maximum DC conductivity across all three models when the hopping coupling strength becomes large. |
| title | Current Correlations and Conductivity in SYK-Like Systems: An Analytical Study |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2407.20733 |