The opening of the pseudogap in underdoped cuprates breaks up the Fermi surface, which may lead to a breakup of the d-wave order parameter into two subband amplitudes and a low energy Leggett mode due to phase fluctuations between them. This causes a
large increase in the temperature range of superconducting fluctuations with an overdamped Leggett mode. Almost resonant scattering of inter-subband phonons to a state with a pair of Leggett modes causes anomalously strong damping. In the ordered state, the Leggett mode develops a finite energy, suppressing the anomalous phonon damping but leading to an anomaly in the phonon dispersion.
We study the $SU(2)_k$ Wess-Zumino-Novikov-Witten (WZNW) theory perturbed by the trace of the primary field in the adjoint representation, a theory governing the low-energy behaviour of a class of strongly correlated electronic systems. While the mod
el is non-integrable, its dynamics can be investigated using the numerical technique of the truncated conformal spectrum approach combined with numerical and analytical renormalization groups (TCSA+RG). The numerical results so obtained provide support for a semiclassical analysis valid at $kgg 1$. Namely, we find that the low energy behavior is sensitive to the sign of the coupling constant, $lambda$. Moreover for $lambda>0$ this behavior depends on whether $k$ is even or odd. With $k$ even, we find definitive evidence that the model at low energies is equivalent to the massive $O(3)$ sigma model. For $k$ odd, the numerical evidence is more equivocal, but we find indications that the low energy effective theory is critical.
We present new high resolution angle resolved photoemission (ARPES) data for K$_{0.3}$MoO$_3$ (blue bronze) and propose a novel theoretical description of these results. The observed Fermi surface, with two quasi-one-dimensional sheets, is consistent
with a ladder material with a weak inter-ladder coupling. Hence, we base our description on spectral properties of one-dimensional ladders. The marked broadening of the ARPES lineshape, a significant fraction of an eV, is interpreted in terms of spin-charge separation. A high energy feature, which is revealed for the first time in the spectra near the Fermi momentum thanks to improved energy resolution, is seen as a signature of a higher energy bound state of soliton excitations on a ladder.
We analyze the thermalization properties and the validity of the Eigenstate Thermalization Hypothesis in a generic class of quantum Hamiltonians where the quench parameter explicitly breaks a Z_2 symmetry. Natural realizations of such systems are giv
en by random matrices expressed in a block form where the terms responsible for the quench dynamics are the off-diagonal blocks. Our analysis examines both dense and sparse random matrix realizations of the Hamiltonians and the observables. Sparse random matrices may be associated with local quantum Hamiltonians and they show a different spread of the observables on the energy eigenstates with respect to the dense ones. In particular, the numerical data seems to support the existence of rare states, i.e. states where the observables take expectation values which are different compared to the typical ones sampled by the micro-canonical distribution. In the case of sparse random matrices we also extract the finite size behavior of two different time scales associated with the thermalization process.
We study the energy level spacing of perturbed conformal minimal models in finite volume, considering perturbations of such models that are massive but not necessarily integrable. We compute their spectrum using a renormalization group improved trunc
ated conformal spectrum approach. With this method we are able to study systems where more than 40000 states are kept and where we determine the energies of the lowest several thousand eigenstates with high accuracy. We find, as expected, that the level spacing statistics of integrable perturbed minimal models are Poissonian while the statistics of non-integrable perturbations are GOE-like. However by varying the system size (and so controlling the positioning of the theory between its IR and UV limits) one can induce crossovers between the two statistical distributions.
