Unidirectional (stripe) charge-density-wave order has now been established as a ubiquitous feature in the phase diagram of the cuprate high temperature (HT) superconductors, where it generally competes with superconductivity (SC). None-the-less, on t
heoretical grounds it has been conjectured that stripe order (or other forms of optimal inhomogeneities) may play an essential positive role in the mechanism of HTSC. Here we report density matrix renormalization group studies of the Hubbard model on long 4 and 6 leg cylinders where the hopping matrix elements transverse to the long direction are periodically modulated - mimicing the effect of putative period-2 stripe order. We find even modest amplitude modulations can enhance the long-distance SC correlations by many orders of magnitude, and drive the system into a phase with a substantial spin gap and SC quasi-long-range-order with a Luttinger exponent, $K_{sc} sim 1$.
We have performed density-matrix renormalization group studies of a square lattice $t$-$J$ model with small hole doping, $deltall 1$, on long 4 and 6 leg cylinders. We include frustration in the form of a second-neighbor exchange coupling, $J_2 = J_1
/2$, such that the undoped ($delta=0$) parent state is a quantum spin liquid. In contrast to the relatively short range superconducting (SC) correlations that have been observed in recent studies of the 6-leg cylinder in the absence of frustration, we find power law SC correlations with a Luttinger exponent, $K_{sc} approx 1$, consistent with a strongly diverging SC susceptibility, $chi sim T^{-(2-K_{sc})}$ as the temperature $Tto 0$. The spin-spin correlations - as in the undoped state - fall exponentially suggesting that the SC pairing correlations evolve smoothly from the insulating parent state.
A pair-density-wave (PDW) is a novel superconducting state with an oscillating order parameter. A microscopic mechanism that can give rise to it has been long sought but has not yet been established by any controlled calculation. Here we report a den
sity-matrix renormalization group (DMRG) study of an effective $t$-$J$-$V$ model, which is equivalent to the Holstein-Hubbard model in a strong-coupling limit, on long two-, four- and six-leg triangular cylinders. While a state with long-range PDW order is precluded in one dimension, we find strong quasi-long-range PDW order with a divergent PDW susceptibility as well as spontaneous breaking of time-reversal and inversion symmetries. Despite the strong interactions, the underlying Fermi surfaces and electron pockets around the $K$ and $K^prime$ points in the Brillouin zone can be identified. We conclude that the state is valley-polarized and that the PDW arises from intra-pocket pairing with an incommensurate center of mass momentum. In the two-leg case, the exponential decay of spin correlations and the measured central charge $capprox 1$ are consistent with an unusual realization of a Luther-Emery liquid.
Systems with strong electron-phonon couplings typically exhibit various forms of charge order, while strong electron-electron interactions lead to magnetism. We use determinant quantum Monte Carlo (DQMC) calculations to solve a model on a square latt
ice with a caricature of these interactions. In the limit where electron-electron interactions dominate it has antiferromagnetic (AF) order, while where electron-phonon coupling dominates there is columnar valence-bond solid (VBS) order. We find a novel intervening phase that hosts coexisting nematic and antiferromagnetic orders. We have also found evidence of a Landau-forbidden continuous quantum phase transition with an emergent $O(4)$ symmetry between the VBS and the nematic antiferromagnetic phases.
We present a theoretical framework for understanding the behavior of the normal and superconducting states of overdoped cuprate high temperature superconductors in the vicinity of the doping-tuned quantum superconductor-to-metal transition. The key i
ngredients on which we focus are d-wave pairing, a flat antinodal dispersion, and disorder. Even for homogeneous disorder, these lead to effectively granular superconducting correlations and a superconducting transition temperature determined in large part by the superfluid stiffness rather than the pairing scale.
We analyze the quantum phase diagram of the Holstein-Hubbard model using an asymptotically exact strong-coupling expansion. We find all sorts of interesting phases including a pair-density wave (PDW), a charge 4e (and even a charge 6e) superconductor
, regimes of phase separation, and a variety of distinct charge-density-wave (CDW), spin-density-wave (SDW) and superconducting regimes. We chart the crossovers that occur as a function of the degree of retardation, i.e. the ratio of characteristic phonon frequency to the strength of interactions.
We propose a lattice scale two-band generalized Hubbard model as a caricature of the electronic structure of twisted bilayer graphene. Various possible broken symmetry phases can arise, including a nematic phase (which is a form of orbital ferromagne
t) and an orbital-triplet spin-singlet superconducting phase. Concerning the mechanism of superconductivity -- we propose an analogy with superconductivity in alkali-doped C$_{60}$ in which a violation of Hunds first rule plays a central role.
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.
We develop a hydrodynamic description of the resistivity and magnetoresistance of an electron liquid in a smooth disorder potential. This approach is valid when the electron-electron scattering length is sufficiently short. In a broad range of temper
atures, the dissipation is dominated by heat fluxes in the electron fluid, and the resistivity is inversely proportional to the thermal conductivity, $kappa$. This is in striking contrast with the Stokes flow, in which the resistance is independent of $kappa$ and proportional to the fluid viscosity. We also identify a new hydrodynamic mechanism of spin magnetoresistance.
