Quantum critical behaviour in a high-Tc superconductor

Marel, D. van der; Molegraaf, Hajo; Zaanen, Jan; Nussinov, Zohar; Carbone, Fabrizio; Damascelli, A.; Eisaki, H.; Greven, M.; Kes, P.H.; Li, M.

doi:10.1038/nature01978

Cited by 312 publications

(183 citation statements)

References 25 publications

Supporting

Mentioning

160

Contrasting

Unclassified

Order By: Relevance

“…The observation of Planckian dissipation in the quantum critical region of high-T c cuprates [39], as well as the discontinuous Fermi-surface reconstruction [40] and the quasiparticle divergence [41] seen in heavy-fermion intermetallics, clearly shows that at the quantum critical point the metallic system loses its knowledge of the Fermi degeneracy scale. From the above considerations based on the constrained path integral it is therefore clear that the fermion sign structure has to become scale invariant.…”

Section: Sign Structures Of Backflow Fermionsmentioning

confidence: 99%

Entanglement entropies and fermion signs of critical metals

2017

Self Cite

View full text Add to dashboard Cite

The fermion sign problem is often viewed as a sheer inconvenience that plagues numerical studies of strongly interacting electron systems. Only recently has it been suggested that fermion signs are fundamental for the universal behavior of critical metallic systems and crucially enhance their degree of quantum entanglement. In this work we explore potential connections between emergent scale invariance of fermion sign structures and scaling properties of bipartite entanglement entropies. Our analysis is based on a wave-function Ansatz that incorporates collective, long-range backflow correlations into fermionic Slater determinants. Such wave functions mimic the collapse of a Fermi liquid at a quantum critical point. Their nodal surfaces, a representation of the fermion sign structure in many-particle configurations space, show fractal behavior up to a length scale ξ that diverges at a critical backflow strength. We show that the Hausdorff dimension of the fractal nodal surface depends on ξ , the number of fermions and the exponent of the backflow. For the same wave functions we numerically calculate the second Rényi entanglement entropy S 2 . Our results show a crossover from volume scaling, S 2 ∼ θ (θ = 2 in d = 2 dimensions), to the characteristic Fermi-liquid behavior S 2 ∼ ln on scales larger than ξ . We find that volume scaling of the entanglement entropy is a robust feature of critical backflow fermions, independent of the backflow exponent and hence the fractal dimension of the scale invariant sign structure.

show abstract

Section: Sign Structures Of Backflow Fermionsmentioning

confidence: 99%

Entanglement entropies and fermion signs of critical metals

2017

Self Cite

View full text Add to dashboard Cite

show abstract

“…This is observed in various heavy fermion materials [1][2][3][4] and cuprate superconductors 5,6 where a dome of unconventional superconductivity is believed to be nucleated by critical magnetic fluctuations around the quantum phase transition associated with the onset of magnetic order. Theoretical work lends strong support to this idea, arguing for or explicitly showing that non-Fermi liquid physics and an enhanced tendency to Cooper pairing and superconductivity arise near certain quantum critical points [7][8][9][10] .…”

Section: Introductionmentioning

confidence: 99%

Emergent dome of nematic order around a quantum anomalous Hall critical point

2014

View full text Add to dashboard Cite

Motivated by the experimental discovery of the quantum anomalous Hall effect and the interest in quantum phase transitions of correlated electrons, we consider interaction effects at a quantum anomalous Hall critical point. We study a microscopic lattice model of spinful fermions on the triangular lattice which exhibits a C = 2 Chern insulator (CI) phase with a quantized anomalous Hall effect, sandwiched between two normal insulator (NI) phases. The first NI-CI quantum phase transition is driven by simultaneous mass inversion of a pair of Dirac fermions, with short range interactions being perturbatively irrelevant at the transition. The second CI-NI transition is driven by a quadratic band touching point protected by momentum space topology and C6 lattice symmetry. A one-loop renormalization group analysis shows that short range interactions lead to a single marginally relevant perturbation at this transition. We obtain the mean field phase diagram of this model incorporating weak repulsive Hubbard interactions, finding an emergent dome of nematic order around this CI-NI topological critical point. We discuss the crossovers in the Hall conductivity at nonzero temperature, and the Landau theory of the quantum and thermal transitions out of the nematic phase. Our results may be relevant to ferromagnetic double perovskite films with spin-orbit coupling which have been proposed to host such a Chern transition. Our work provides perhaps the simplest example of an emergent phase near a quantum critical point.

show abstract

“…Since the development of marginal Fermi liquid phenomenology [2], quantum criticality has been widely invoked to explain the observed power laws in both the DC [3][4][5][6][7] and AC [8][9][10][11][12][13] transport properties of the copper-oxide superconductors. Because the underlying system is strongly correlated, a microscopic description of the degrees of freedom that are responsible for the quantum critical state is still lacking.…”

Section: Introductionmentioning

confidence: 99%

Unparticles and anomalous dimensions in the cuprates

Karch

Limtragool

Phillips

2016

J. High Energ. Phys.

View full text Add to dashboard Cite

Motivated by the overwhelming evidence some type of quantum criticality underlies the power-law for the optical conductivity and T −linear resistivity in the cuprates, we demonstrate here how a scale-invariant or unparticle sector can lead to a unifying description of the observed scaling forms. We adopt the continuous mass formalism or multi band (flavor) formalism of the unparticle sector by letting various microscopic parameters be mass-dependent. In particular, we show that an effective mass that varies with the flavor index as well as a running band edge and lifetime capture the AC and DC transport phenomenology of the cuprates. A key consequence of the running mass is that the effective dynamical exponent can differ from the underlying bare critical exponent, thereby providing a mechanism for realizing the fractional values of the dynamical exponent required in a previous analysis [1]. We also predict that regardless of the bare dynamical exponent, z, a non-zero anomalous dimension for the current is required. Physically, the anomalous dimension arises because the charge depends on the flavor, mass or energy. The equivalent phenomenon in a d + 1 gravitational construction is the running of the charge along the radial direction. The nature of the superconducting instability in the presence of scale invariant stuff shows that the transition temperature is not necessarily a monotonic function of the pairing interaction.

show abstract

Quantum critical behaviour in a high-Tc superconductor

Cited by 312 publications

References 25 publications

Entanglement entropies and fermion signs of critical metals

Entanglement entropies and fermion signs of critical metals

Emergent dome of nematic order around a quantum anomalous Hall critical point

Unparticles and anomalous dimensions in the cuprates

Contact Info

Product

Resources

About