Thermodynamics and quantum criticality in cuprate superconductors

We will present elementary scaling arguments focussed on the thermodynamics in the proximity of the quantum critical point in the cuprate superconductors. Extending the analysis centered on the Gr\"uneisen parameter by Rosch, Si and coworkers to the cuprates, we demonstrate that a combination of specific heat- and chemical potential measurements can reveal the nature of the zero temperature singularity. From the known specific heat data it follows that the effective number of time dimensions has to equal the number of space dimensions, while we find a total of six scaling laws governing the temperature and density dependence of the chemical potential, revealing directly the coupling constant scaling dimension.Comment: 4 pages no figure

Stripe fractionalization I: the generation of Ising local symmetry

This is part one in a series of two papers dedicated to the notion that the destruction of the topological order associated with stripe phases is about the simplest theory controlled by local symmetry: Ising gauge theory. This first part is intended to be a tutorial- we will exploit the simple physics of the stripes to vividly display the mathematical beauty of the gauge theory. Stripes, as they occur in the cuprates, are clearly `topological' in the sense that the lines of charges are at the same time domain walls in the antiferromagnet. Imagine that the stripes quantum melt so that all what seems to be around is a singlet superconductor. What if this domain wall-ness is still around in a delocalized form? This turns out to be exactly the kind of `matter' which is described by the Ising gauge theory. The highlight of the theory is the confinement phenomenon, meaning that when the domain wall-ness gives up it will do so in a meat-and-potato phase transition. We suggest that this transition might be the one responsible for the quantum criticality in the cuprates. In part two, we will become more practical, arguing that another phase is possible according to the theory. It might be that this quantum spin-nematic has already been observed in strongly underdoped LSCO

Mottness collapse and statistical quantum criticality

We forward here the case that the anomalous electron states found in cuprate superconductors and related systems are rooted in a deeply non-classical fermion sign structure. The collapse of Mottness as advocated by Phillips and supported by recent DCA results on the Hubbard model is setting the necessary microscopic conditions. The crucial insight is due to Weng who demonstrated that in the presence of Mottness the fundamental workings of quantum statistics changes and we will elaborate on the effects of this Weng statistics with an emphasis on characterizing these further using numerical methods. The pseudogap physics of the underdoped regime appears as a consequence of the altered statistics and the profound question is how to connect this by a continuous quantum phase transition to the overdoped regime ruled by normal Fermi-Dirac statistics. Proof of principle follows from Ceperley's constrained path integral formalism where states can be explicitly constructed showing a merger of Fermi-Dirac sign structure and scale invariance of the quantum dynamics.Comment: 27 pages, 4 figures, submitted to theme issue of Phil. Trans. R. Soc.

Dynamical stripe correlations and the spin fluctuations in cuprate superconductors

It is conjectured that the anomalous spin dynamics observed in the normal state of cuprate superconductors might find its origin in a nearly ordered spin system which is kept in motion by thermally meandering charged domain walls. `Temperature sets the scale' finds a natural explanation, while a crossover to a low temperature quantum domain wall fluid is implied.Comment: 3 pages Revtex. To appear in Physica

The specific heat jump at the superconducting transition and the quantum critical nature of the normal state of Pnictide superconductors

Recently it was discovered that the jump in the specific heat at the superconducting transition in pnictide superconductors is proportional to the superconducting transition temperature to the third power, with the superconducting transition temperature varying from 2 to 25 Kelvin including underdoped and overdoped cases. Relying on standard scaling notions for the thermodynamics of strongly interacting quantum critical states, it is pointed out that this behavior is consistent with a normal state that is a quantum critical metal undergoing a pairing instability.Comment: 4 pages 1 figur

Competition between Hidden Spin and Charge Orderings in Stripe Phase

The correlation between charge and spin orderings in hole-doped antiferromagnets is studied within an effective model of quantum strings fluctuating in an antiferromagnetic background. In particular, we perform the direct estimation of the charge and spin long-range-order parameters by means of the quantum Monte Carlo simulation. A hidden spin long-range order is found to be governed by a competition between the two trends caused by increasing hole mobility: the enhancement of the two-dimensional spin-spin correlation mediated by hole motions and the reformation of a strong stripe order.Comment: 4 pages, 8 figures. Accepted for publication as a Rapid Communication in Physical Review