The enigma of the pseudogap phase of the cuprate superconductors

The last few years have seen significant experimental progress in characterizing the copper-based hole-doped high temperature superconductors in the regime of low hole density, p. Quantum oscillations, NMR, X-ray, and STM experiments have shed much light on the nature of the ordering at low temperatures. We review evidence that the order parameter in the non-Lanthanum-based cuprates is a d-form factor density-wave. This novel order acts as an unexpected window into the electronic structure of the pseudogap phase at higher temperatures in zero field: we argue in favor of a `fractionalized Fermi liquid' (FL*) with 4 pockets of spin S=1/2, charge +e fermions enclosing an area specified by p.Comment: 37 pages, 19 figures, 100+ references. Proceedings of the 50th Karpacz Winter School of Theoretical Physics, 2-9 March 2014, Karpacz, Polan

Higgs criticality in a two-dimensional metal

We analyze a candidate theory for the strange metal near optimal hole-doping in the cuprate superconductors. The theory contains a quantum phase transition between metals with large and small Fermi surfaces of spinless fermions carrying the electromagnetic charge of the electron, but the transition does not directly involve any broken global symmetries. The two metals have emergent SU(2) and U(1) gauge fields respectively, and the transition is driven by the condensation of a real Higgs field, carrying a finite lattice momentum and an adjoint SU(2) gauge charge. This Higgs field measures the local antiferromagnetic correlations in a "rotating reference frame". We propose a global phase diagram around this Higgs transition, and describe its relationship to a variety of recent experiments on the cuprate superconductors.Comment: 30 pages, 7 figures; (v2) added new figur

Onset of many-body chaos in the O(N)O(N) model

The growth of commutators of initially commuting local operators diagnoses the onset of chaos in quantum many-body systems. We compute such commutators of local field operators with $N$ components in the $(2+1)$-dimensional $O(N)$ nonlinear sigma model to leading order in $1/N$. The system is taken to be in thermal equilibrium at a temperature $T$ above the zero temperature quantum critical point separating the symmetry broken and unbroken phases. The commutator grows exponentially in time with a rate denoted $\lambda_L$. At large $N$ the growth of chaos as measured by $\lambda_L$ is slow because the model is weakly interacting, and we find $\lambda_L \approx 3.2 T/N$. The scaling with temperature is dictated by conformal invariance of the underlying quantum critical point. We also show that operators grow ballistically in space with a "butterfly velocity" given by $v_B/c \approx 1$ where $c$ is the Lorentz-invariant speed of particle excitations in the system. We briefly comment on the behavior of $\lambda_L$ and $v_B$ in the neighboring symmetry broken and unbroken phases.Comment: (1+55) pages, 13 figures; (v2) Final published versio

Synchronization of oscillators with long range power law interactions

We present analytical calculations and numerical simulations for the synchronization of oscillators interacting via a long range power law interaction on a one dimensional lattice. We have identified the critical value of the power law exponent $\alpha_c$ across which a transition from a synchronized to an unsynchronized state takes place for a sufficiently strong but finite coupling strength in the large system limit. We find $\alpha_c=3/2$. Frequency entrainment and phase ordering are discussed as a function of $\alpha \geq 1$. The calculations are performed using an expansion about the aligned phase state (spin-wave approximation) and a coarse graining approach. We also generalize the spin-wave results to the {\it d}-dimensional problem.Comment: Final published versio

Quantum oscillations in insulators with neutral Fermi surfaces

We develop a theory of quantum oscillations in insulators with an emergent fermi sea of neutral fermions minimally coupled to an emergent $U(1)$ gauge field. As pointed out by Motrunich (Phys. Rev. B 73, 155115 (2006)), in the presence of a physical magnetic field the emergent magnetic field develops a non-zero value leading to Landau quantization for the neutral fermions. We focus on the magnetic field and temperature dependence of the analogue of the de Haas-van Alphen effect in two- and three-dimensions. At temperatures above the effective cyclotron energy, the magnetization oscillations behave similarly to those of an ordinary metal, albeit in a field of a strength that differs from the physical magnetic field. At low temperatures the oscillations evolve into a series of phase transitions. We provide analytical expressions for the amplitude and period of the oscillations in both of these regimes and simple extrapolations that capture well their crossover. We also describe oscillations in the electrical resistivity of these systems that are expected to be superimposed with the activated temperature behavior characteristic of their insulating nature and discuss suitable experimental conditions for the observation of these effects in mixed-valence insulators and triangular lattice organic materials.Comment: 20 pages, 9 figures, 1 tabl

Mixed-valence insulators with neutral Fermi surfaces

Samarium hexaboride is a classic three-dimensional mixed valence system with a high-temperature metallic phase that evolves into a paramagnetic charge insulator below 40 kelvin. A number of recent experiments have suggested the possibility that the low-temperature insulating bulk hosts electrically neutral gapless fermionic excitations. Here we show that a possible ground state of strongly correlated mixed valence insulators - composite exciton Fermi liquid - hosts a three dimensional Fermi surface of a neutral fermion, that we name the "composite exciton". We describe the mechanism responsible for the formation of such excitons, discuss the phenomenology of the composite exciton Fermi liquids and make comparison to experiments in SmB$_6$.Comment: Final published versio

Effect of magnetization on the tunneling anomaly in compressible quantum Hall states

Tunneling of electrons into a two-dimensional electron system is known to exhibit an anomaly at low bias, in which the tunneling conductance vanishes due to a many-body interaction effect. Recent experiments have measured this anomaly between two copies of the half-filled Landau level as a function of in-plane magnetic field, and they suggest that increasing spin polarization drives a deeper suppression of tunneling. Here we present a theory of the tunneling anomaly between two copies of the partially spin-polarized Halperin-Lee-Read state, and we show that the conventional description of the tunneling anomaly, based on the Coulomb self-energy of the injected charge packet, is inconsistent with the experimental observation. We propose that the experiment is operating in a different regime, not previously considered, in which the charge-spreading action is determined by the compressibility of the composite fermions.Comment: (5+1) pages, 1 figure; (v2) minor changes and added reference to our accompanying paper arXiv:1712.02357; (v3) Final published versio