Coherence scale of coupled Anderson impurities

For two coupled Anderson impurities, two energy scales are present to characterize the evolution from local moment state of the impurities to either of the inter-impurity singlet or the Kondo singlet ground states. The high energy scale is found to deviate from the single-ion Kondo temperature and rather scales as Ruderman-Kittel-Kasuya-Yosida (RKKY) interaction when it becomes dominant. We find that the scaling behavior and the associated physical properties of this scale are consistent with those of a coherence scale defined in heavy fermion systems.Comment: 10 pages, 7 figures, extended versio

Singularity in self-energy and composite fermion excitations of interacting electrons

We propose that a composite fermion operator $f_{i\sigma}(2n_{i{\bar \sigma}}-1)$ could have coherent excitations, where $f_{i\sigma}$ is the fermion operator for interacting electrons and $n_{i{\bar \sigma}}$ is the number operator of the opposite spin. In the two-impurity Anderson model, it is found that the excitation of this composite fermion has a pseudogap in the Kondo regime, and has a finite spectral weight in the regime where the excitation of the regular fermion $f_{i\sigma}$ has a pseudogap. In the latter regime, the self-energy of $f_{i\sigma}$ is found to be singular near Fermi energy. We argue that this composite fermion could develop a Fermi surface with Fermi liquid behaviors but "hidden" from charge excitations in lattice generalizations. We further illustrate that this type of excitations is essential in addressing the pseudogap state and unconventional superconductivity.Comment: 10 pages, 6 figure

Specific Heat and Sound Velocity Distinguish the Relevant Competing Phase in the Pseudogap Region of High Temperature Superconductors

A great step forward towards the understanding of high temperature superconductors are the variety of experimental results which have led to the wide-spread acceptance of the idea that a phase with a broken symmetry competes with superconductivity in the under-doped region, often called the pseudo-gap region. There are a plethora of suggested phases. The idea, that a broken symmetry phase competes with superconductivity makes thermodynamic sense only if the energy gained due to it is comparable to that gained through the superconducting transition in their co-existence region. Extraordinarily, however, no specific heat signature of a phase transition has been identified at the pseudo-gap temperature $T^*$. We use the recent highly accurate sound-velocity measurements and the best available specific heat measurements in YBa$_2$Cu$_3$O$_{6+\delta}$ to show that phase transitions to the universality class of the loop-current ordered state with free-energy reduction similar to the measured superconducting condensation are consistent with the sound velocity and with lack of identifiable observation in the specific heat. We also compare the measured specific heat with some more usual transitions and show that transitions with such symmetry classes can easily be shown by existing specific heat measurements to have energy reduction due to them less than 1/20 the superconducting condensation energy

Crossovers and critical scaling in the one-dimensional transverse-field Ising model

We consider the scaling behavior of thermodynamic quantities in the one-dimensional transverse-field Ising model near its quantum critical point (QCP). Our study has been motivated by the question about the thermodynamical signatures of this paradigmatic quantum critical system and, more generally, by the issue of how quantum criticality accumulates entropy. We find that the crossovers in the phase diagram of temperature and (the non-thermal control parameter) transverse field obey a general scaling ansatz, and so does the critical scaling behavior of the specific heat and magnetic expansion coefficient. Furthermore, the Gr\"{u}neisen ratio diverges in a power-law way when the QCP is accessed as a function of the transverse field at zero temperature, which follows the prediction of quantum critical scaling. However, at the critical field, upon decreasing the temperature, the Gr\"uneisen ratio approaches a constant instead of showing the expected divergence. We are able to understand this unusual result in terms of a peculiar form of the quantum critical scaling function for the free energy; the contribution to the Gr\"uneisen ratio vanishes at the linear order in a suitable Taylor expansion of the scaling function. In spite of this special form of the scaling function, we show that the entropy is still maximized near the QCP, as expected from the general scaling argument. Our results establish the telltale thermodynamic signature of a transverse-field Ising chain, and will thus facilitate the experimental identification of this model quantum-critical system in real materials.Comment: 7 pages, 5 figure