Phase Transitions and Relaxation in Systems with Competing Energy Scales

Carol K. Hall

Haoyu Guo, Debanjan Chowdhury

Metals at the brink of electronic quantum phase transitions display high-temperature superconductivity, competing orders, and unconventional charge transport, revealing strong departures from conventional Fermi liquid behavior. Investigation of these fascinating intertwined phenomena has been at the center of research across a variety of correlated materials over the past many decades. A ubiquitous experimental observation is the emergence of a universal timescale that governs electrical transport and momentum relaxation. In this Letter, we analyze an equally important theoretical question of how the energy contained in the electronic degrees of freedom near a quantum phase transition relaxes to the environment via their coupling to acoustic phonons. Assuming that the bottleneck for energy dissipation is controlled by the coupling between electronic degrees of freedom and acoustic phonons, we present a universal theory of the temperature dependence of the energy relaxation rate in a marginal Fermi liquid. We find that the energy relaxation rate exhibits a complex set of temperature-dependent crossovers controlled by emergent energy scales in the problem. We place these results in the context of recent measurements of the energy relaxation rate via nonlinear optical spectroscopy in the normal state of hole-doped cuprates.

Qi Huang, Ruixiao Yao, Libo Liang +8 more

Quantum critical behavior of many-body phase transitions is one of the most fascinating yet challenging questions in quantum physics. Here, we improved the band-mapping method to investigate the quantum phase transition from superfluid to Mott insulators, and we observed the critical behaviors of quantum phase transitions in both the dynamical steady-state-relaxation region and the phase-oscillation region. Based on various observables, two different values for the same quantum critical parameter are observed. This result is beyond a universal-scaling-law description of quantum phase transitions known as the Kibble-Zurek mechanism, and suggests that multiple quantum critical mechanisms are competing in many-body quantum phase transition experiments in inhomogeneous systems.

Marek Cieplak, Jayanth R. Banavar

A. P. Malozemoff, B. Barbara

We extend earlier critical fractal cluster models of a spin glass phase transition. At the transition temperature in finite field, a negative excluded-volume term dominates a positive saturated-cluster term, giving the negative H2/δ nonlinear susceptibility observed experimentally. The two competing effects in general have different relaxation times and therefore novel implications for dynamic scaling.

David A. Lavis, Roman Frigg