A recent proposal by Hallam et al. suggested using the chaotic properties of the semiclassical equations of motion, obtained by the time dependent variational principle (TDVP), as a characterization of quantum chaos. In this paper, we calculate the L
yapunov spectrum of the semiclassical theory approximating the quantum dynamics of a strongly interacting Rydberg atom array, which lead to periodic motion. In addition, we calculate the effect of quantum fluctuations around this approximation, and obtain the escape rate from the periodic orbit. We compare this rate to the rate extracted from the exact solution of the quantum theory, and find an order of magnitude discrepancy. We conclude that in this case, chaos in the TDVP equations does not correpond to phsyical properties of the system. Our result complement those of Ho et al. regarding the escape rate from the semiclassical periodic orbit.
We present a new framework for computing low frequency transport properties of strongly correlated, ergodic systems. Our main assumption is that, when a thermalizing diffusive system is driven at frequency $omega$, domains of size $xi simsqrt{D/omega
}$ can be considered as internally thermal, but weakly coupled with each other. We calculate the transport coefficients to lowest order in the coupling, assuming incoherent transport between such domains. Our framework naturally captures the sub-leading non analytic corrections to the transport coefficients, known as hydrodynamic long time tails. In addition, it allows us to obtain a generalized relation between charge and thermal transport coefficients, in the spirit of the Wiedemann-Franz law. We verify our results, which satisfy several non-trivial consistency checks, via exact diagonalization studies on the one-dimensional extended Fermi-Hubbard model.
We construct examples of translationally invariant solvable models of strongly-correlated metals, composed of lattices of Sachdev-Ye-Kitaev dots with identical local interactions. These models display crossovers as a function of temperature into regi
mes with local quantum criticality and marginal-Fermi liquid behavior. In the marginal Fermi liquid regime, the dc resistivity increases linearly with temperature over a broad range of temperatures. By generalizing the form of interactions, we also construct examples of non-Fermi liquids with critical Fermi-surfaces. The self energy has a singular frequency dependence, but lacks momentum dependence, reminiscent of a dynamical mean field theory-like behavior but in dimensions $d<infty$. In the low temperature and strong-coupling limit, a heavy Fermi liquid is formed. The critical Fermi-surface in the non-Fermi liquid regime gives rise to quantum oscillations in the magnetization as a function of an external magnetic field in the absence of quasiparticle excitations. We discuss the implications of these results for local quantum criticality and for fundamental bounds on relaxation rates. Drawing on the lessons from these models, we formulate conjectures on coarse grained descriptions of a class of intermediate scale non-fermi liquid behavior in generic correlated metals.
Quantum spin liquids (QSLs) are intriguing phases of matter possessing fractionalized excitations. Several quasi-two dimensional materials have been proposed as candidate QSLs, but direct evidence for fractionalization in these systems is still lacki
ng. In this paper, we show that the inter-plane thermal conductivity in layered QSLs carries a unique signature of fractionalization. We examine several types of gapless QSL phases - a $Z_2$ QSL with either a Dirac spectrum or a spinon Fermi surface, and a $U(1)$ QSL with a Fermi surface. In all cases, the in-plane and $c-$axis thermal conductivities have a different power law dependence on temperature, due to the different mechanisms of transport in the two directions: in the planes, the thermal current is carried by fractionalized excitations, whereas the inter-plane current is carried by integer (non-fractional) excitations. In layered $Z_2$ and $U(1)$ QSLs with a Fermi surface, the $c-$axis thermal conductivity is parametrically smaller than the in-plane one, but parametrically larger than the phonon contribution at low temperatures.
We calculate the scrambling rate $lambda_L$ and the butterfly velocity $v_B$ associated with the growth of quantum chaos for a solvable large-$N$ electron-phonon system. We study a temperature regime in which the electrical resistivity of this system
exceeds the Mott-Ioffe-Regel limit and increases linearly with temperature - a sign that there are no long-lived charged quasiparticles - although the phonons remain well-defined quasiparticles. The long-lived phonons determine $lambda_L$, rendering it parametrically smaller than the theoretical upper-bound $lambda_L ll lambda_{max}=2pi T/hbar$. Significantly, the chaos properties seem to be intrinsic - $lambda_L$ and $v_B$ are the same for electronic and phononic operators. We consider two models - one in which the phonons are dispersive, and one in which they are dispersionless. In either case, we find that $lambda_L$ is proportional to the inverse phonon lifetime, and $v_B$ is proportional to the effective phonon velocity. The thermal and chaos diffusion constants, $D_E$ and $D_Lequiv v_B^2/lambda_L$, are always comparable, $D_E sim D_L$. In the dispersive phonon case, the charge diffusion constant $D_C$ satisfies $D_Lgg D_C$, while in the dispersionless case $D_L ll D_C$.
The electron dynamics in metals are usually well described by the semiclassical approximation for long-lived quasiparticles. However, in some metals, the scattering rate of the electrons at elevated temperatures becomes comparable to the Fermi energy
; then, this approximation breaks down, and the full quantum-mechanical nature of the electrons must be considered. In this work, we study a solvable, large-$N$ electron-phonon model, which at high temperatures enters the non-quasiparticle regime. In this regime, the model exhibits resistivity saturation to a temperature-independent value of the order of the quantum of resistivity - the first analytically tractable model to do so. The saturation is not due to a fundamental limit on the electron lifetime, but rather to the appearance of a second conductivity channel. This is suggestive of the phenomenological parallel resistor formula, known to describe the resistivity of a variety of saturating metals.
Many metals display resistivity saturation - a substantial decrease in the slope of the resistivity as a function of temperature, that occurs when the electron scattering rate $tau^{-1}$ becomes comparable to the Fermi energy $E_F/hbar$ (the Mott-Iof
fe-Regel limit). At such temperatures, the usual description of a metal in terms of ballistically propagating quasiparticles is no longer valid. We present a tractable model of a large $N$ number of electronic bands coupled to $N^2$ optical phonon modes, which displays a crossover behavior in the resistivity at temperatures where $tau^{-1}sim E_F/hbar$. At low temperatures, the resistivity obeys the familiar linear form, while at high temperatures, the resistivity still increases linearly, but with a modified slope (that can be either lower or higher than the low-temperature slope, depending on the band structure). The high temperature non-Boltzmann regime is interpreted by considering the diffusion constant and the compressibility, both of which scale as the inverse square root of the temperature.
A quasi-exciton condensate is a phase characterized by quasi-long range order of an exciton (electron-hole pair) order parameter. Such a phase can arise naturally in a system of two parallel oppositely doped quantum wires, coupled by repulsive Coulom
b interactions. We show that the quasi-exciton condensate phase can be stabilized in an extended range of parameters, in both spinless and spinful systems. For spinful electrons, the exciton phase is shown to be distinct from the usual quasi-long range ordered Wigner crystal phase characterized by power-law density wave correlations. The two phases can be clearly distinguished through their inter-wire tunneling current-voltage characteristics. In the quasi-exciton condensate phase the tunneling conductivity diverges at low temperatures and voltages, whereas in the Wigner crystal it is strongly suppressed. Both phases are characterized by a divergent Coulomb drag at low temperature. Finally, metallic carbon nanotubes are considered as a special case of such a one dimensional setup, and it is shown that exciton condensation is favorable due to the additional valley degree of freedom.
