Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Interaction-enhanced quantum to classical transport crossover temperature in a Luttinger liquid

Yen-Wen Lu, Michael Mulligan

TL;DR

The paper investigates why strange metals exhibit a persistent $T$-linear transport regime over broad temperatures. Using a bosonized single-channel Luttinger liquid coupled to a 1D acoustic phonon and memory-matrix methods, it derives dc electrical and thermal conductivities in both clean and dirty limits, explicitly incorporating a Debye cutoff. The central result is that the crossover temperature $T_0(K)$ between quantum and classical transport grows with repulsive interactions ($K<1$), sometimes by more than an order of magnitude, effectively broadening the quantum transport window. This interaction-enhanced crossover offers a concrete mechanism for the robust, single-transport-slope behavior observed in strange metals and suggests a general principle that could extend beyond one dimension. The work combines exact bosonization treatment of interactions with a systematic relaxation analysis to connect microscopic couplings to macroscopic transport regimes.

Abstract

Strange metals are highly entangled gapless states of matter that exhibit anomalous transport, such as linear in temperature resistivity, over more than a decade of temperature. Why a single power law should be so robust is an open question. We propose a scenario in which interactions enhance the domain of certain scattering regimes, effectively suppressing other ``would-be regimes." We test this proposal in a one-dimensional Luttinger liquid coupled to a one-dimensional acoustic phonon. We use the memory matrix formalism to calculate the dc electrical and thermal conductivities at low and high temperatures, relative to the Debye cutoff on phonon frequencies, in both the ``clean" (umklapp scattering) and ``dirty" (disorder scattering) limits. We find the crossover temperature separating the low and high temperature regimes to be interaction-dependent, with repulsive interactions substantially increasing it, generally by more than an order of magnitude. This provides a concrete illustration for how interactions can extend a single transport regime over a wider temperature range.

Interaction-enhanced quantum to classical transport crossover temperature in a Luttinger liquid

TL;DR

The paper investigates why strange metals exhibit a persistent -linear transport regime over broad temperatures. Using a bosonized single-channel Luttinger liquid coupled to a 1D acoustic phonon and memory-matrix methods, it derives dc electrical and thermal conductivities in both clean and dirty limits, explicitly incorporating a Debye cutoff. The central result is that the crossover temperature between quantum and classical transport grows with repulsive interactions (), sometimes by more than an order of magnitude, effectively broadening the quantum transport window. This interaction-enhanced crossover offers a concrete mechanism for the robust, single-transport-slope behavior observed in strange metals and suggests a general principle that could extend beyond one dimension. The work combines exact bosonization treatment of interactions with a systematic relaxation analysis to connect microscopic couplings to macroscopic transport regimes.

Abstract

Strange metals are highly entangled gapless states of matter that exhibit anomalous transport, such as linear in temperature resistivity, over more than a decade of temperature. Why a single power law should be so robust is an open question. We propose a scenario in which interactions enhance the domain of certain scattering regimes, effectively suppressing other ``would-be regimes." We test this proposal in a one-dimensional Luttinger liquid coupled to a one-dimensional acoustic phonon. We use the memory matrix formalism to calculate the dc electrical and thermal conductivities at low and high temperatures, relative to the Debye cutoff on phonon frequencies, in both the ``clean" (umklapp scattering) and ``dirty" (disorder scattering) limits. We find the crossover temperature separating the low and high temperature regimes to be interaction-dependent, with repulsive interactions substantially increasing it, generally by more than an order of magnitude. This provides a concrete illustration for how interactions can extend a single transport regime over a wider temperature range.

Paper Structure

This paper contains 13 sections, 65 equations, 2 figures.

Table of Contents

  1. Introduction
  2. Model
  3. Decoupled Fixed Point
  4. Current Relaxation
  5. Transport at low and high temperatures
  6. Memory Matrix
  7. Umklapp scattering
  8. Disorder scattering
  9. Crossover temperature
  10. Conclusion
  11. Static Susceptibilities
  12. Evaluation of $F^{i}_{m, {\cal Q}}$
  13. Disorder Scattering Memory Matrix Details

Figures (2)

  • Figure 1: Low- and high-temperature asymptotics of the memory matrix ${\cal M}$ with intervening crossover temperature $T_0$ in the (a) clean (unklapp-dominated) and (b) dirty (disorder-dominated) limits. Blue (Red) lines are low (high)-temperature asymptotics of the memory matrices, and ${\cal P}, {\cal P'}\in\{J_{T},J_{D}\}$.
  • Figure 2: The crossover temperature of both electrical and thermal conductivites for (a) clean limit(umklapp scattering) and (b) dirty limit(disorder scattering).